Nicolas Rashevsky
Encyclopedia
Nicolas Rashevsky was a Ukrainian
-American
theoretical biologist
who pioneered mathematical biology
, and is also considered the father of mathematical biophysics
and theoretical biology.
at the University of Kiev in Russia
before 1917, and immigrated first to Turkey
, Poland
, France
, and then to the US in 1924 because of the October revolution
. In USA he worked at first for the Westinghouse
Research Labs in Pittsburgh where he focused on the theoretical physics modeling of the cell division and the mathematics of cell fission, a subject that was anecdotally said to have attracted fission-related defense interests. He was awarded a Rockefeller Fellowship in 1934 and went to the University of Chicago to take up the appointment of assistant professor in the Department of Physiology. In 1938 he made his first major contribution by publishing the first book on Mathematical Biophysics, and then in 1939 he also founded the first mathematical biology
international journal entitled The Bulletin of Mathematical Biophysics (BMB); these two essential contributions founded the field of mathematical biology
, with the BMB journal serving as the focus of contributing mathematical biologists over the last 70 years.
and propositional logic formulation of the hierarchical organization of organisms and human societies. He also introduced the concept of "organismic sets", that was later developed by other authors through applications of category theory
to relational biology
, organismic supercategories
and Complex Systems Biology
.
In 1938 he published the first book on mathematical biology and mathematical biophysics entitled: "Mathematical Biophysics: Physico-Mathematical Foundations of Biology." This fundamental book was then followed in 1940 by "Advances and applications of mathematical biology.", and in
1947 by "Mathematical theory of human relations", an approach to a mathematical model of society. In the same year he establishes the World' s first PhD program in Mathematical Biology
at the University of Chicago
. Only J. H. Woodger seems to have preceded in 1937 Rashevsky's efforts in mathematical biology with his genetic axiom system. However, Woodger's `genetical axiom system' has had only very limited impact on the subsequent development of genetics because it is restricted to Mendelian genetics; one could similarly comment on Rosen's later papers on quantum genetics
that—unlike his other work on complexity and life, categories of metabolic-replication systems, complex dynamics, etc.— did not make any apparent impact on either molecular biology
or molecular genetics
, DNA dynamics, DNA
, and so on.
, Herbert Daniel Landahl, Robert Rosen and Anatol Rapoport
. In 1948, Anatol Rapoport took over Rashevsky's course in mathematical biology, so that Rashevsky could teach mathematical sociology instead.
although current developments in complex systems biology
clearly follow in his footsteps. In 1954 the budget for his Committee of Mathematical Biology was drastically cut; however, this was at least in part politically imposed, rather than scientifically, motivated. Thus, the subsequent
University of Chicago
administration—notably represented by the genetics Nobel laureate George Wells Beadle— who reversed in the 1960s the previous position and quadrupled the financial support for Rashevsky's Committee for Mathematical Biology research activities ("Reminiscences of Nicolas Rashevsky." by Robert Rosen, written in late 1972). There was later however a fall out between the retiring Nicolas Rashevsky and the
University of Chicago president over the successor to the Chair of the Committee of Mathematical Biology; Nicolas Rashevsky strongly supported Dr. Herbert Landahl-his first PhD student to graduate in Mathematical Biophysics, whereas the president wished to appoint a certain US biostatistician. The result was Rashevsky's move to Ann Arbor, Michigan, and his taking ownership of the well-funded "Bulletin of Mathematical Biophysics".
, with the purpose of "dissemination of information regarding Mathematical Biology". In his later years, after 1968, he became again very active in relational biology
and held, as well as Chaired, in 1970 the first international "Symposium of Mathematical Biology" at Toledo, Ohio, in USA with the help of his former PhD student, Dr. Anthony Bartholomay, who has become the Chairman of the first Department of Mathematical Medicine at Ohio University
. The meeting was sponsored by Mathematical Biology, Inc.
, and also by J. H. Woodger `axiomatic (Mendelian) genetics', to launch his own search and quest for biological principles, and also to formulate mathematically precise principles and axioms of biology. He then developed his own highly original approach to address the fundamental question of What is Life?
that another theoretical physicist, Erwin Schrödinger
, has asked before him and Robert Rosen from the narrower viewpoint of quantum theory
in biology. He wished to reach this `holy grail' of (theoretical/ mathematical) biology, but his heavy work during the late 1960s— in spite of his related health problems— took its toll, and finally prevented him in 1972 to reach his ultimate goal.
. From Prague, he moved in the 1930s to Paris, France, and then to New York, Pittsburgh and Chicago, USA. His life has been dedicated to the science that he founded, Mathematical Biology, and his wife Emily was very supportive and appreciative of his scientific efforts, accompanying him at the scientific meetings that he either initiated or attended. He cut a tall, impressive figure with a slight Russian accent, but a clear voice and thought to the very day when in 1972 he died from a heart attack caused by coronary heart disease. His generosity was very well known and is often recognized in print by former associates or visitors. As the Chief Editor of BMB he had a declared policy of helping the authors to optimize their presentation of submitted papers, as well as proving many valuable suggestions to the submitting authors. His suggested detailed changes, additions and further developments were like a real `gold mine' for the submitting authors. He managed to stay aloof of all science `politics' most of the time, even in very adverse circumstances such as those during the MacCarthy
era when completely unfounded political accusations were made about one or two members of his close research group. Not unlike another American theoretical physicist Robert Oppenheimer, he then had much to lose for his loyal support of the wrongly accused researcher in his group.
Ukrainians
Ukrainians are an East Slavic ethnic group native to Ukraine, which is the sixth-largest nation in Europe. The Constitution of Ukraine applies the term 'Ukrainians' to all its citizens...
-American
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
theoretical biologist
Biologist
A biologist is a scientist devoted to and producing results in biology through the study of life. Typically biologists study organisms and their relationship to their environment. Biologists involved in basic research attempt to discover underlying mechanisms that govern how organisms work...
who pioneered mathematical biology
Mathematical biology
Mathematical and theoretical biology is an interdisciplinary scientific research field with a range of applications in biology, medicine and biotechnology...
, and is also considered the father of mathematical biophysics
Biophysics
Biophysics is an interdisciplinary science that uses the methods of physical science to study biological systems. Studies included under the branches of biophysics span all levels of biological organization, from the molecular scale to whole organisms and ecosystems...
and theoretical biology.
Academic career
He studied theoretical physicsTheoretical physics
Theoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena...
at the University of Kiev in Russia
Russia
Russia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...
before 1917, and immigrated first to Turkey
Turkey
Turkey , known officially as the Republic of Turkey , is a Eurasian country located in Western Asia and in East Thrace in Southeastern Europe...
, Poland
Poland
Poland , officially the Republic of Poland , is a country in Central Europe bordered by Germany to the west; the Czech Republic and Slovakia to the south; Ukraine, Belarus and Lithuania to the east; and the Baltic Sea and Kaliningrad Oblast, a Russian exclave, to the north...
, France
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
, and then to the US in 1924 because of the October revolution
October Revolution
The October Revolution , also known as the Great October Socialist Revolution , Red October, the October Uprising or the Bolshevik Revolution, was a political revolution and a part of the Russian Revolution of 1917...
. In USA he worked at first for the Westinghouse
Westinghouse Electric (1886)
Westinghouse Electric was an American manufacturing company. It was founded in 1886 as Westinghouse Electric Company and later renamed Westinghouse Electric Corporation by George Westinghouse. The company purchased CBS in 1995 and became CBS Corporation in 1997...
Research Labs in Pittsburgh where he focused on the theoretical physics modeling of the cell division and the mathematics of cell fission, a subject that was anecdotally said to have attracted fission-related defense interests. He was awarded a Rockefeller Fellowship in 1934 and went to the University of Chicago to take up the appointment of assistant professor in the Department of Physiology. In 1938 he made his first major contribution by publishing the first book on Mathematical Biophysics, and then in 1939 he also founded the first mathematical biology
Mathematical biology
Mathematical and theoretical biology is an interdisciplinary scientific research field with a range of applications in biology, medicine and biotechnology...
international journal entitled The Bulletin of Mathematical Biophysics (BMB); these two essential contributions founded the field of mathematical biology
Mathematical biology
Mathematical and theoretical biology is an interdisciplinary scientific research field with a range of applications in biology, medicine and biotechnology...
, with the BMB journal serving as the focus of contributing mathematical biologists over the last 70 years.
Major scientific contributions
His later efforts focused on the topology of biological systems, the formulation of fundamental principles in biology, relational biology, set theorySet theory
Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...
and propositional logic formulation of the hierarchical organization of organisms and human societies. He also introduced the concept of "organismic sets", that was later developed by other authors through applications of category theory
Category theory
Category theory is an area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows , where these collections satisfy certain basic conditions...
to relational biology
, organismic supercategories
Higher-dimensional algebra
Supercategories were first introduced in 1970, and were subsequently developed for applications in theoretical physics and mathematical biology or mathematical biophysics....
and Complex Systems Biology
Systems biology
Systems biology is a term used to describe a number of trends in bioscience research, and a movement which draws on those trends. Proponents describe systems biology as a biology-based inter-disciplinary study field that focuses on complex interactions in biological systems, claiming that it uses...
.
In 1938 he published the first book on mathematical biology and mathematical biophysics entitled: "Mathematical Biophysics: Physico-Mathematical Foundations of Biology." This fundamental book was then followed in 1940 by "Advances and applications of mathematical biology.", and in
1947 by "Mathematical theory of human relations", an approach to a mathematical model of society. In the same year he establishes the World' s first PhD program in Mathematical Biology
Mathematical biology
Mathematical and theoretical biology is an interdisciplinary scientific research field with a range of applications in biology, medicine and biotechnology...
at the University of Chicago
University of Chicago
The University of Chicago is a private research university in Chicago, Illinois, USA. It was founded by the American Baptist Education Society with a donation from oil magnate and philanthropist John D. Rockefeller and incorporated in 1890...
. Only J. H. Woodger seems to have preceded in 1937 Rashevsky's efforts in mathematical biology with his genetic axiom system. However, Woodger's `genetical axiom system' has had only very limited impact on the subsequent development of genetics because it is restricted to Mendelian genetics; one could similarly comment on Rosen's later papers on quantum genetics
Molecular genetics
Molecular genetics is the field of biology and genetics that studies the structure and function of genes at a molecular level. The field studies how the genes are transferred from generation to generation. Molecular genetics employs the methods of genetics and molecular biology...
that—unlike his other work on complexity and life, categories of metabolic-replication systems, complex dynamics, etc.— did not make any apparent impact on either molecular biology
Molecular biology
Molecular biology is the branch of biology that deals with the molecular basis of biological activity. This field overlaps with other areas of biology and chemistry, particularly genetics and biochemistry...
or molecular genetics
Molecular genetics
Molecular genetics is the field of biology and genetics that studies the structure and function of genes at a molecular level. The field studies how the genes are transferred from generation to generation. Molecular genetics employs the methods of genetics and molecular biology...
, DNA dynamics, DNA
DNA
Deoxyribonucleic acid is a nucleic acid that contains the genetic instructions used in the development and functioning of all known living organisms . The DNA segments that carry this genetic information are called genes, but other DNA sequences have structural purposes, or are involved in...
, and so on.
Rashevsky's most notable students
Some of Rashevsky's most outstanding PhD students who earned their doctorate under his supervision were: George KarremanGeorge Karreman
George Karreman was a Dutch-born US physicist, mathematical biophysicist and mathematical/theoretical biologist. He was the first President of the Society for Mathematical Biology .- Biography :Karreman's father was Chief Engineer for the Dutch Merchant Marine...
, Herbert Daniel Landahl, Robert Rosen and Anatol Rapoport
Anatol Rapoport
Anatol Rapoport was a Russian-born American Jewish mathematical psychologist. He contributed to general systems theory, mathematical biology and to the mathematical modeling of social interaction and stochastic models of contagion.-Biography:...
. In 1948, Anatol Rapoport took over Rashevsky's course in mathematical biology, so that Rashevsky could teach mathematical sociology instead.
Administrative and political obstacles
However, his more advanced ideas and abstract relational biology concepts found little support in the beginning amongst practicing experimental or molecular biologists,although current developments in complex systems biology
Systems biology
Systems biology is a term used to describe a number of trends in bioscience research, and a movement which draws on those trends. Proponents describe systems biology as a biology-based inter-disciplinary study field that focuses on complex interactions in biological systems, claiming that it uses...
clearly follow in his footsteps. In 1954 the budget for his Committee of Mathematical Biology was drastically cut; however, this was at least in part politically imposed, rather than scientifically, motivated. Thus, the subsequent
University of Chicago
University of Chicago
The University of Chicago is a private research university in Chicago, Illinois, USA. It was founded by the American Baptist Education Society with a donation from oil magnate and philanthropist John D. Rockefeller and incorporated in 1890...
administration—notably represented by the genetics Nobel laureate George Wells Beadle— who reversed in the 1960s the previous position and quadrupled the financial support for Rashevsky's Committee for Mathematical Biology research activities ("Reminiscences of Nicolas Rashevsky." by Robert Rosen, written in late 1972). There was later however a fall out between the retiring Nicolas Rashevsky and the
University of Chicago president over the successor to the Chair of the Committee of Mathematical Biology; Nicolas Rashevsky strongly supported Dr. Herbert Landahl-his first PhD student to graduate in Mathematical Biophysics, whereas the president wished to appoint a certain US biostatistician. The result was Rashevsky's move to Ann Arbor, Michigan, and his taking ownership of the well-funded "Bulletin of Mathematical Biophysics".
Formation of Mathematical Biology, Inc.
He also formed in 1969 a non-profit organization , "Mathematical Biology, Incorporated", which was to be the precursor of "The Society for Mathematical Biology"Society for Mathematical Biology
The Society for Mathematical Biology is an international association co-founded in 1972 in USA by Drs.George Karreman, Herbert Daniel Landahl and by Anthony Bartholomay for the furtherance of joint scientific activities between Mathematics and Biology research communities,...
, with the purpose of "dissemination of information regarding Mathematical Biology". In his later years, after 1968, he became again very active in relational biology
Mathematical biology
Mathematical and theoretical biology is an interdisciplinary scientific research field with a range of applications in biology, medicine and biotechnology...
and held, as well as Chaired, in 1970 the first international "Symposium of Mathematical Biology" at Toledo, Ohio, in USA with the help of his former PhD student, Dr. Anthony Bartholomay, who has become the Chairman of the first Department of Mathematical Medicine at Ohio University
Ohio University
Ohio University is a public university located in the Midwestern United States in Athens, Ohio, situated on an campus...
. The meeting was sponsored by Mathematical Biology, Inc.
Final quest for principles of biology
Rashevsky was greatly influenced and inspired both by Herbert Spencer's book on the Principles of Biology (1898)Herbert Spencer
Herbert Spencer was an English philosopher, biologist, sociologist, and prominent classical liberal political theorist of the Victorian era....
, and also by J. H. Woodger `axiomatic (Mendelian) genetics', to launch his own search and quest for biological principles, and also to formulate mathematically precise principles and axioms of biology. He then developed his own highly original approach to address the fundamental question of What is Life?
What is life?
What is Life and similar may refer to:* "What is Life", a song by George Harrison* What Is Life?, a book by Nobel laureate Erwin Schrödinger, in which he tries to answer the question in physical/chemical terms...
that another theoretical physicist, Erwin Schrödinger
Erwin Schrödinger
Erwin Rudolf Josef Alexander Schrödinger was an Austrian physicist and theoretical biologist who was one of the fathers of quantum mechanics, and is famed for a number of important contributions to physics, especially the Schrödinger equation, for which he received the Nobel Prize in Physics in 1933...
, has asked before him and Robert Rosen from the narrower viewpoint of quantum theory
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
in biology. He wished to reach this `holy grail' of (theoretical/ mathematical) biology, but his heavy work during the late 1960s— in spite of his related health problems— took its toll, and finally prevented him in 1972 to reach his ultimate goal.
Biography
In 1917, Nicolas Rashevsky joins the White Russian Navy and in 1920 he and his wife, Countess Emily had to flee for their lives to Constantinople where he taught at the American College. In 1921 they moved to Prague where he taught both special and general relativityGeneral relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
. From Prague, he moved in the 1930s to Paris, France, and then to New York, Pittsburgh and Chicago, USA. His life has been dedicated to the science that he founded, Mathematical Biology, and his wife Emily was very supportive and appreciative of his scientific efforts, accompanying him at the scientific meetings that he either initiated or attended. He cut a tall, impressive figure with a slight Russian accent, but a clear voice and thought to the very day when in 1972 he died from a heart attack caused by coronary heart disease. His generosity was very well known and is often recognized in print by former associates or visitors. As the Chief Editor of BMB he had a declared policy of helping the authors to optimize their presentation of submitted papers, as well as proving many valuable suggestions to the submitting authors. His suggested detailed changes, additions and further developments were like a real `gold mine' for the submitting authors. He managed to stay aloof of all science `politics' most of the time, even in very adverse circumstances such as those during the MacCarthy
Joseph McCarthy
Joseph Raymond "Joe" McCarthy was an American politician who served as a Republican U.S. Senator from the state of Wisconsin from 1947 until his death in 1957...
era when completely unfounded political accusations were made about one or two members of his close research group. Not unlike another American theoretical physicist Robert Oppenheimer, he then had much to lose for his loyal support of the wrongly accused researcher in his group.
Works
- Physico-mathematical aspects of Excitation and Conduction in Nerves., Cold Springs Harbor Symposia on Quantitative Biology.IV: Excitation Phenomena., 1936, p.90.
- Mathematical Biophysics:Physico-Mathematical Foundations of Biology. Univ. of Chicago Press. : Chicago Press, 1938/1948 (2nd ed.).
- Mathematical Theory of Human Relations: An Approach to Mathematical Biology of Social Phenomena. Bloomington, ID: Principia Press, 1947/1949 (2nd ed.)
- Topology and life: In search of general mathematical principles in biology and sociology. Bulletin of Mathematical Biophysics 16 (1954): 317–348.
- Proceedings of the International School of Physics "Enrico Fermi", Course 16, Physico-Mathematical Aspects of Biology. : Academic Press, 1964
- Some Medical Aspects of Mathematical Biology. Springfield, IL: Charles C. Thomas, 1964
- The Representation of Organisms in Terms of Predicates, Bulletin of Mathematical Biophysics 27 (1965): 477-491.
- Outline of a Unified Approach to Physics, Biology and Sociology., Bulletin of Mathematical Biophysics 31 (1969): 159-198.
- Looking at History through Mathematics, 1972
- Organismic Sets., William Clowes & Sons., London, Beccles and Cochester, 1972.
Further reading
- Bartholomay, A. F., G. Karreman and H. D. Landahl (1972). "Obituary of Nicolas Rashevsky.", Bull. Math. Biophys. 34.
- Rosen, Robert. 1972. Tribute to Nicolas Rashevsky 1899-1972. Progress in Theoretical Biology 2.
- Tara H. Abraham. 2004. Journal of the History of Biology, 37: 333-385.Nicholas Rashevsky's Mathematical Biophysics
- Rosen Robert. 1972. "Reminiscences of Nicolas Rashevsky", unpublished paper.
- Rosen, Robert. 1958. The representation of biological systems from the standpoint of the theory of categories. Bulletin of Mathematical Biophysics 20: 317–341.
- Natural Transformations of Organismic Structures., Bulletin of Mathematical Biology, 42: 431-446, Baianu, I.C.: 1980.
- Elsasser, M.W.: 1981, A Form of Logic Suited for Biology., In: Robert, Rosen, ed., Progress in Theoretical Biology, Volume 6, Academic Press, New York and London, pp 23–62.
- Rosen, Robert. 1985. The physics of complexity. Systems Research 2: 171–175.
- Rosen, Robert. 1985. Organisms as causal systems which are not mechanisms. In R. Rosen, Theoretical Biology and Complexity, 165–203.
- Rosen, Robert. 1979. Biology and system theory: An overview. In Klir, Proceedings of the System Theory Conference - Applied General Systems Research,
- Rosen, Robert. 1977. Complexity as a system property. International Journal of General Systems 3: 227–232.
- Rosen, Robert. 1977. Complexity and system description. In Hartnett, Systems, 169–175.
- Rosen, R. 1973. A unified approach to physics, biology, and sociology. In Rosen, Foundations of Mathematical Biology, 177–190.
- Rosen, R. 1972.Quantum genetics. In R. Rosen, Foundations of Mathematical Biology, 215–252.
- Rosen, R. 1972. Morphogenesis. In Rosen, Foundations of Mathematical Biology, 1–77.
- Rosen, R. 1972. Mechanics of epigenetic control. In R. Rosen, Foundations of Mathematical Biology, 79–140.
External links
- Books by Rashevsky
- The Bulletin of Mathematical Biophysics
- Rashevsky's theory of two-factor systems for neural networks
See also
- Mathematical biologyMathematical biologyMathematical and theoretical biology is an interdisciplinary scientific research field with a range of applications in biology, medicine and biotechnology...
- Principles of BiologyHerbert SpencerHerbert Spencer was an English philosopher, biologist, sociologist, and prominent classical liberal political theorist of the Victorian era....
- Relational BiologyMathematical biologyMathematical and theoretical biology is an interdisciplinary scientific research field with a range of applications in biology, medicine and biotechnology...
- BiocyberneticsBiocyberneticsBiocybernetics is the application of cybernetics to biological science, composed of biological disciplines that benefit from the application of cybernetics: neurology, multicellular systems and others...
- Mathematical sociologyMathematical sociologyMathematical sociology is the usage of mathematics to construct social theories. Mathematical sociology aims to take sociological theory, which is strong in intuitive content but weak from a formal point of view, and to express it in formal terms...
- Bulletin of Mathematical BiophysicsSociety for Mathematical BiologyThe Society for Mathematical Biology is an international association co-founded in 1972 in USA by Drs.George Karreman, Herbert Daniel Landahl and by Anthony Bartholomay for the furtherance of joint scientific activities between Mathematics and Biology research communities,...
- Complex Systems biologySystems biologySystems biology is a term used to describe a number of trends in bioscience research, and a movement which draws on those trends. Proponents describe systems biology as a biology-based inter-disciplinary study field that focuses on complex interactions in biological systems, claiming that it uses...
- Theoretical biology
- Mathematical BiophysicsBiophysicsBiophysics is an interdisciplinary science that uses the methods of physical science to study biological systems. Studies included under the branches of biophysics span all levels of biological organization, from the molecular scale to whole organisms and ecosystems...
- BioinformaticsBioinformaticsBioinformatics is the application of computer science and information technology to the field of biology and medicine. Bioinformatics deals with algorithms, databases and information systems, web technologies, artificial intelligence and soft computing, information and computation theory, software...
- Society for Mathematical BiologySociety for Mathematical BiologyThe Society for Mathematical Biology is an international association co-founded in 1972 in USA by Drs.George Karreman, Herbert Daniel Landahl and by Anthony Bartholomay for the furtherance of joint scientific activities between Mathematics and Biology research communities,...
- The Society for Mathematical Biology
- Organismic set theorySet theorySet theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...
- OrganismOrganismIn biology, an organism is any contiguous living system . In at least some form, all organisms are capable of response to stimuli, reproduction, growth and development, and maintenance of homoeostasis as a stable whole.An organism may either be unicellular or, as in the case of humans, comprise...
- Organismic sets of zeroth orderGene regulatory networkA gene regulatory network or genetic regulatory network is a collection of DNA segments in a cell whichinteract with each other indirectly and with other substances in the cell, thereby governing the rates at which genes in the network are transcribed into mRNA.In general, each mRNA molecule goes...
- Organismic developmentMorphogenesisMorphogenesis , is the biological process that causes an organism to develop its shape...
- OrganizationOrganizationAn organization is a social group which distributes tasks for a collective goal. The word itself is derived from the Greek word organon, itself derived from the better-known word ergon - as we know `organ` - and it means a compartment for a particular job.There are a variety of legal types of...
- Two-factor theory of nerve impulseAction potentialIn physiology, an action potential is a short-lasting event in which the electrical membrane potential of a cell rapidly rises and falls, following a consistent trajectory. Action potentials occur in several types of animal cells, called excitable cells, which include neurons, muscle cells, and...
- Mathematical logicMathematical logicMathematical logic is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic. The field includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics...
- TopologyTopologyTopology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
- Epigenetic landscapeEpigenetic landscapeEpigenetic landscape is a metaphor for biological development. Its originator, Conrad Hal Waddington, said that cell fates were established in development much like a marble rolls down to the point of lowest local elevation...
- Network theoryNetwork theoryNetwork theory is an area of computer science and network science and part of graph theory. It has application in many disciplines including statistical physics, particle physics, computer science, biology, economics, operations research, and sociology...
- Graph theoryGraph theoryIn mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...
- Algebraic topologyAlgebraic topologyAlgebraic topology is a branch of mathematics which uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence.Although algebraic topology...
- Category theoryCategory theoryCategory theory is an area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows , where these collections satisfy certain basic conditions...
- Symbolic logic
- Relation algebraRelation algebraIn mathematics and abstract algebra, a relation algebra is a residuated Boolean algebra expanded with an involution called converse, a unary operation...
- NeuronNeuronA neuron is an electrically excitable cell that processes and transmits information by electrical and chemical signaling. Chemical signaling occurs via synapses, specialized connections with other cells. Neurons connect to each other to form networks. Neurons are the core components of the nervous...
- NeurophysiologyNeurophysiologyNeurophysiology is a part of physiology. Neurophysiology is the study of nervous system function...
- Neural networkNeural networkThe term neural network was traditionally used to refer to a network or circuit of biological neurons. The modern usage of the term often refers to artificial neural networks, which are composed of artificial neurons or nodes...
s - George KarremanGeorge KarremanGeorge Karreman was a Dutch-born US physicist, mathematical biophysicist and mathematical/theoretical biologist. He was the first President of the Society for Mathematical Biology .- Biography :Karreman's father was Chief Engineer for the Dutch Merchant Marine...
- Robert Rosen
- Conrad Hal WaddingtonConrad Hal WaddingtonConrad Hal Waddington CBE FRS FRSE was a developmental biologist, paleontologist, geneticist, embryologist and philosopher who laid the foundations for systems biology...
- Brian GoodwinBrian GoodwinBrian Carey Goodwin was a Canadian mathematician and biologist, a Professor Emeritus at the Open University and a key founder of the field of theoretical biology.He made key contributions to the foundations of biomathematics, complex systems and generative models in developmental biology...
- Herbert SpencerHerbert SpencerHerbert Spencer was an English philosopher, biologist, sociologist, and prominent classical liberal political theorist of the Victorian era....
- Brownian motionBrownian motionBrownian motion or pedesis is the presumably random drifting of particles suspended in a fluid or the mathematical model used to describe such random movements, which is often called a particle theory.The mathematical model of Brownian motion has several real-world applications...
-theory - Theoretical physicsTheoretical physicsTheoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena...
- October revolutionOctober RevolutionThe October Revolution , also known as the Great October Socialist Revolution , Red October, the October Uprising or the Bolshevik Revolution, was a political revolution and a part of the Russian Revolution of 1917...
- University of Kiev
- Cell divisionCell divisionCell division is the process by which a parent cell divides into two or more daughter cells . Cell division is usually a small segment of a larger cell cycle. This type of cell division in eukaryotes is known as mitosis, and leaves the daughter cell capable of dividing again. The corresponding sort...