1.
Fields in biology
–
Biology is a natural science concerned with the study of life and living organisms, including their structure, function, growth, evolution, distribution, identification and taxonomy. Modern biology is a vast and eclectic field, composed of branches and subdisciplines. However, despite the broad scope of biology, there are certain unifying concepts within it that consolidate it into single, coherent field. In general, biology recognizes the cell as the unit of life, genes as the basic unit of heredity. It is also understood today that all organisms survive by consuming and transforming energy and by regulating their internal environment to maintain a stable, the term biology is derived from the Greek word βίος, bios, life and the suffix -λογία, -logia, study of. The Latin-language form of the term first appeared in 1736 when Swedish scientist Carl Linnaeus used biologi in his Bibliotheca botanica, the first German use, Biologie, was in a 1771 translation of Linnaeus work. In 1797, Theodor Georg August Roose used the term in the preface of a book, karl Friedrich Burdach used the term in 1800 in a more restricted sense of the study of human beings from a morphological, physiological and psychological perspective. The science that concerns itself with these objects we will indicate by the biology or the doctrine of life. Although modern biology is a recent development, sciences related to. Natural philosophy was studied as early as the ancient civilizations of Mesopotamia, Egypt, the Indian subcontinent, however, the origins of modern biology and its approach to the study of nature are most often traced back to ancient Greece. While the formal study of medicine back to Hippocrates, it was Aristotle who contributed most extensively to the development of biology. Especially important are his History of Animals and other works where he showed naturalist leanings, and later more empirical works that focused on biological causation and the diversity of life. Aristotles successor at the Lyceum, Theophrastus, wrote a series of books on botany that survived as the most important contribution of antiquity to the plant sciences, even into the Middle Ages. Scholars of the medieval Islamic world who wrote on biology included al-Jahiz, Al-Dīnawarī, who wrote on botany, biology began to quickly develop and grow with Anton van Leeuwenhoeks dramatic improvement of the microscope. It was then that scholars discovered spermatozoa, bacteria, infusoria, investigations by Jan Swammerdam led to new interest in entomology and helped to develop the basic techniques of microscopic dissection and staining. Advances in microscopy also had a impact on biological thinking. In the early 19th century, a number of biologists pointed to the importance of the cell. Thanks to the work of Robert Remak and Rudolf Virchow, however, meanwhile, taxonomy and classification became the focus of natural historians

Fields in biology

Fields in biology

Fields in biology

Fields in biology

2.
Character (biology)
–
For example, eye color is a character of an organism, while blue, brown and hazel are traits. A phenotypic trait is an obvious, observable, and measurable trait, it is the expression of genes in an observable way. An example of a trait is hair color, underlying genes, which make up the genotype, control the hair color, but the actual hair color. The inheritable unit that may influence a trait is called a gene, a gene is a portion of a chromosome, which is a very long and compacted string of DNA and proteins. An important reference point along a chromosome is the centromere, the distance from a gene to the centromere is referred to as the locus or map location. The nucleus of a cell contains two of each chromosome, with homologous pairs of chromosomes having the same genes at the same loci. Different phenotypic traits are caused by different forms of genes, or alleles, a gene is only a DNA code sequence, the slightly different variations of that sequence are called alleles. Alleles can be different and produce different product RNAs. Combinations of different alleles thus go on to different traits through the information flow charted above. For example, if the alleles on homologous chromosomes exhibit a simple dominance relationship and his most famous analyses were based on clear-cut traits with simple dominance. He determined that the units, what we now call genes. His tool was statistics The biochemistry of the intermediate proteins determines how they interact in the cell, therefore, biochemistry predicts how different combinations of alleles will produce varying traits. Extended expression patterns seen in diploid organisms include facets of incomplete dominance, codominance, incomplete dominance is the condition in which neither allele dominates the other in one heterozygote. Instead the phenotype is intermediate in heterozygotes, thus you can tell that each allele is present in the heterozygote. Codominance refers to the relationship that occurs when two alleles are both expressed in the heterozygote, and both phenotypes are seen simultaneously. Multiple alleles refers to the situation there are more than 2 common alleles of a particular gene. Blood groups in humans is a classic example, the ABO blood group proteins are important in determining blood type in humans, and this is determined by different alleles of the one locus. Schizotypy is an example of a phenotypic trait found in schizophrenia-spectrum disorders

Character (biology)
–
Blue

human eye.

3.
Formal expression
–
In mathematics, computer science, and linguistics, a formal language is a set of strings of symbols together with a set of rules that are specific to it. The alphabet of a language is the set of symbols, letters. The strings formed from this alphabet are called words, and the words belong to a particular formal language are sometimes called well-formed words or well-formed formulas. A formal language is defined by means of a formal grammar such as a regular grammar or context-free grammar. The field of language theory studies primarily the purely syntactical aspects of such languages—that is. Formal language theory sprang out of linguistics, as a way of understanding the syntactic regularities of natural languages. The first formal language is thought to be the one used by Gottlob Frege in his Begriffsschrift, literally meaning concept writing, axel Thues early semi-Thue system, which can be used for rewriting strings, was influential on formal grammars. The elements of an alphabet are called its letters, alphabets may be infinite, however, most definitions in formal language theory specify finite alphabets, and most results only apply to them. A word over an alphabet can be any sequence of letters. The set of all words over an alphabet Σ is usually denoted by Σ*, the length of a word is the number of letters it is composed of. For any alphabet there is one word of length 0, the empty word. By concatenation one can combine two words to form a new word, whose length is the sum of the lengths of the original words, the result of concatenating a word with the empty word is the original word. A formal language L over an alphabet Σ is a subset of Σ*, that is, sometimes the sets of words are grouped into expressions, whereas rules and constraints may be formulated for the creation of well-formed expressions. In computer science and mathematics, which do not usually deal with natural languages, in practice, there are many languages that can be described by rules, such as regular languages or context-free languages. The notion of a formal grammar may be closer to the concept of a language. By an abuse of the definition, a formal language is often thought of as being equipped with a formal grammar that describes it. The following rules describe a formal language L over the alphabet Σ =, Every nonempty string that does not contain + or =, a string containing = is in L if and only if there is exactly one =, and it separates two valid strings of L. A string containing + but not = is in L if, no string is in L other than those implied by the previous rules

Formal expression
–
Structure of a syntactically well-formed, although nonsensical English sentence (

historical example from Chomsky 1957).

4.
Markov state model
–
A hidden Markov model is a statistical Markov model in which the system being modeled is assumed to be a Markov process with unobserved states. An HMM can be presented as the simplest dynamic Bayesian network, the mathematics behind the HMM were developed by L. E. Baum and coworkers. It is closely related to a work on the optimal nonlinear filtering problem by Ruslan L. Stratonovich. In simpler Markov models, the state is visible to the observer. In a hidden Markov model, the state is not directly visible, each state has a probability distribution over the possible output tokens. Therefore, the sequence of tokens generated by an HMM gives some information about the sequence of states, in its discrete form, a hidden Markov process can be visualized as a generalization of the Urn problem with replacement. Consider this example, in a room that is not visible to an observer there is a genie, the room contains urns X1, X2, X3, … each of which contains a known mix of balls, each ball labeled y1, y2, y3, …. The genie chooses an urn in that room and randomly draws a ball from that urn and it then puts the ball onto a conveyor belt, where the observer can observe the sequence of the balls but not the sequence of urns from which they were drawn. The genie has some procedure to choose urns, the choice of the urn for the n-th ball depends only upon a random number, the choice of urn does not directly depend on the urns chosen before this single previous urn, therefore, this is called a Markov process. It can be described by the part of Figure 1. The Markov process itself cannot be observed, only the sequence of labeled balls and this is illustrated by the lower part of the diagram shown in Figure 1, where one can see that balls y1, y2, y3, y4 can be drawn at each state. However, the observer can work out other information, such as the likelihood that the ball came from each of the urns. The diagram below shows the architecture of an instantiated HMM. Each oval shape represents a variable that can adopt any of a number of values. The random variable x is the state at time t. The random variable y is the observation at time t, the arrows in the diagram denote conditional dependencies. This is called the Markov property, similarly, the value of the observed variable y only depends on the value of the hidden variable x. In the standard type of hidden Markov model considered here, the space of the hidden variables is discrete

Markov state model
–

Machine learning and

data mining
5.
Elementary geometry
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Geometry is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer, Geometry arose independently in a number of early cultures as a practical way for dealing with lengths, areas, and volumes. Geometry began to see elements of mathematical science emerging in the West as early as the 6th century BC. By the 3rd century BC, geometry was put into a form by Euclid, whose treatment, Euclids Elements. Geometry arose independently in India, with texts providing rules for geometric constructions appearing as early as the 3rd century BC, islamic scientists preserved Greek ideas and expanded on them during the Middle Ages. By the early 17th century, geometry had been put on a solid footing by mathematicians such as René Descartes. Since then, and into modern times, geometry has expanded into non-Euclidean geometry and manifolds, while geometry has evolved significantly throughout the years, there are some general concepts that are more or less fundamental to geometry. These include the concepts of points, lines, planes, surfaces, angles, contemporary geometry has many subfields, Euclidean geometry is geometry in its classical sense. The mandatory educational curriculum of the majority of nations includes the study of points, lines, planes, angles, triangles, congruence, similarity, solid figures, circles, Euclidean geometry also has applications in computer science, crystallography, and various branches of modern mathematics. Differential geometry uses techniques of calculus and linear algebra to problems in geometry. It has applications in physics, including in general relativity, topology is the field concerned with the properties of geometric objects that are unchanged by continuous mappings. In practice, this often means dealing with large-scale properties of spaces, convex geometry investigates convex shapes in the Euclidean space and its more abstract analogues, often using techniques of real analysis. It has close connections to convex analysis, optimization and functional analysis, algebraic geometry studies geometry through the use of multivariate polynomials and other algebraic techniques. It has applications in areas, including cryptography and string theory. Discrete geometry is concerned mainly with questions of relative position of simple objects, such as points. It shares many methods and principles with combinatorics, Geometry has applications to many fields, including art, architecture, physics, as well as to other branches of mathematics. The earliest recorded beginnings of geometry can be traced to ancient Mesopotamia, the earliest known texts on geometry are the Egyptian Rhind Papyrus and Moscow Papyrus, the Babylonian clay tablets such as Plimpton 322. For example, the Moscow Papyrus gives a formula for calculating the volume of a truncated pyramid, later clay tablets demonstrate that Babylonian astronomers implemented trapezoid procedures for computing Jupiters position and motion within time-velocity space

Elementary geometry
–
Visual checking of the

Pythagorean theorem for the (3, 4, 5)

triangle as in the

Chou Pei Suan Ching 500–200 BC.

Elementary geometry
–
An illustration of

Desargues' theorem, an important result in

Euclidean and

projective geometry
Elementary geometry
–
Geometry lessons in the 20th century

Elementary geometry
–
A

European and an

Arab practicing geometry in the 15th century.

6.
Financial Models
–
In economics, a model is a theoretical construct representing economic processes by a set of variables and a set of logical and/or quantitative relationships between them. The economic model is a framework designed to illustrate complex processes, often. Frequently, economic models posit structural parameters, structural parameters are underlying parameters in a model or class of models. A model may have various exogenous variables, and those variables may change to various responses by economic variables. Methodological uses of models include investigation, theorizing, and fitting theories to the world, simplification is particularly important for economics given the enormous complexity of economic processes. Selection is important because the nature of a model will often determine what facts will be looked at. Planning and allocation, in the case of centrally planned economies, since the 1990s many long-term risk management models have incorporated economic relationships between simulated variables in an attempt to detect high-exposure future scenarios. A model establishes a framework for applying logic and mathematics that can be independently discussed and tested. Policies and arguments that rely on economic models have a basis for soundness. Therefore, conclusions drawn from models will be representations of economic facts. However, properly constructed models can remove extraneous information and isolate useful approximations of key relationships, in this way more can be understood about the relationships in question than by trying to understand the entire economic process. The details of construction vary with type of model and its application. Generally any modelling process has two steps, generating a model, then checking the model for accuracy, the diagnostic step is important because a model is only useful to the extent that it accurately mirrors the relationships that it purports to describe. Creating and diagnosing a model is frequently an iterative process in which the model is modified with each iteration of diagnosis, once a satisfactory model is found, it should be double checked by applying it to a different data set. Stochastic models are formulated using stochastic processes and they model economically observable values over time. Most of econometrics is based on statistics to formulate and test hypotheses about these processes or estimate parameters for them, examples of these are autoregressive moving average models and related ones such as autoregressive conditional heteroskedasticity and GARCH models for the modelling of heteroskedasticity. Non-stochastic models may be qualitative or quantitative. For such models, economists often use two-dimensional graphs instead of functions, qualitative models – although almost all economic models involve some form of mathematical or quantitative analysis, qualitative models are occasionally used

Financial Models
–
A diagram of the

IS/LM model
7.
Semantic model
–
A conceptual model is a representation of a system, made of the composition of concepts which are used to help people know, understand, or simulate a subject the model represents. Some models are physical objects, for example, a toy model which may be assembled, the term conceptual model may be used to refer to models which are formed after a conceptualization or generalization process. Conceptual models are often abstractions of things in the world whether physical or social. Semantics studies are relevant to various stages of formation and use as Semantics is basically about concepts. The term conceptual model is normal and it could mean a model of concept or it could mean a model that is conceptual. A distinction can be made between what models are and what models are models of, with the exception of iconic models, such as a scale model of Winchester Cathedral, most models are concepts. But they are, mostly, intended to be models of world states of affairs. The value of a model is directly proportional to how well it corresponds to a past, present, future. A model of a concept is different because in order to be a good model it need not have this real world correspondence. Conceptual models also range in terms of the scope of the matter that they are taken to represent. A model may, for instance, represent a single thing, whole classes of things, the variety and scope of conceptual models is due to then variety of purposes had by the people using them. Conceptual modeling is the activity of formally describing some aspects of the physical and social world around us for the purposes of understanding, a conceptual models primary objective is to convey the fundamental principles and basic functionality of the system which it represents. Also, a model must be developed in such a way as to provide an easily understood system interpretation for the models users. A conceptual model, when implemented properly, should satisfy four fundamental objectives, figure 1 below, depicts the role of the conceptual model in a typical system development scheme. It is clear if the conceptual model is not fully developed. These failures do occur in the industry and have linked to, lack of user input, incomplete or unclear requirements. Those weak links in the design and development process can be traced to improper execution of the fundamental objectives of conceptual modeling. The importance of conceptual modeling is evident when such systemic failures are mitigated by thorough system development, as systems have become increasingly complex, the role of conceptual modeling has dramatically expanded

Semantic model
–
For other uses, see

Model (disambiguation) and

Conceptual model (computer science).

8.
Model (science)
–
Modelling is an essential and inseparable part of many scientific disciplines have their own ideas about specific types of modelling. There is also an increasing attention to modelling in fields such as science education, philosophy of science, systems theory. There is growing collection of methods, techniques and meta-theory about all kinds of specialized scientific modelling, a scientific model seeks to represent empirical objects, phenomena, and physical processes in a logical and objective way. All models are in simulacra, that is, simplified reflections of reality that, despite being approximations, building and disputing models is fundamental to the scientific enterprise. Attempts to formalize the principles of the sciences use an interpretation to model reality. The aim of these attempts is to construct a system that will not produce theoretical consequences that are contrary to what is found in reality. Predictions or other statements drawn from such a formal system mirror or map the world only insofar as these scientific models are true. For the scientist, a model is also a way in which the thought processes can be amplified. Such computer models are in silico, other types of scientific models are in vivo and in vitro. Models are typically used when it is impossible or impractical to create experimental conditions in which scientists can directly measure outcomes. Direct measurement of outcomes under controlled conditions will always be more reliable than modelled estimates of outcomes, within modelling and simulation, a model is a task-driven, purposeful simplification and abstraction of a perception of reality, shaped by physical, legal, and cognitive constraints. It is task-driven, because a model is captured with a question or task in mind. Simplifications leave all the known and observed entities and their relation out that are not important for the task, abstraction aggregates information that is important, but not needed in the same detail as the object of interest. Both activities, simplification and abstraction, are done purposefully, however, they are done based on a perception of reality. This perception is already a model in itself, as it comes with a physical constraint, there are also constraints on what we are able to legally observe with our current tools and methods, and cognitive constraints which limit what we are able to explain with our current theories. This model comprises the propertied concepts, their behavior, and their relations in formal form and is referred to as a Conceptual model. In order to execute the model, it needs to be implemented as a Computer simulation and this requires more choices, such as numerical approximations or the use of heuristics. Despite all these epistemological and computational constraints, simulation has been recognized as the pillar of scientific methods, theory building, simulation

Model (science)
–
Example of the integrated use of Modelling and Simulation in Defence life cycle management. The modelling and simulation in this image is represented in the center of the image with the three containers.

Model (science)
–
Example of scientific modelling. A schematic of chemical and transport processes related to atmospheric composition.

9.
Pyhsics
–
Physics is the natural science that involves the study of matter and its motion and behavior through space and time, along with related concepts such as energy and force. One of the most fundamental disciplines, the main goal of physics is to understand how the universe behaves. Physics is one of the oldest academic disciplines, perhaps the oldest through its inclusion of astronomy, Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the mechanisms of other sciences while opening new avenues of research in areas such as mathematics. Physics also makes significant contributions through advances in new technologies that arise from theoretical breakthroughs, the United Nations named 2005 the World Year of Physics. Astronomy is the oldest of the natural sciences, the stars and planets were often a target of worship, believed to represent their gods. While the explanations for these phenomena were often unscientific and lacking in evidence, according to Asger Aaboe, the origins of Western astronomy can be found in Mesopotamia, and all Western efforts in the exact sciences are descended from late Babylonian astronomy. The most notable innovations were in the field of optics and vision, which came from the works of many scientists like Ibn Sahl, Al-Kindi, Ibn al-Haytham, Al-Farisi and Avicenna. The most notable work was The Book of Optics, written by Ibn Al-Haitham, in which he was not only the first to disprove the ancient Greek idea about vision, but also came up with a new theory. In the book, he was also the first to study the phenomenon of the pinhole camera, many later European scholars and fellow polymaths, from Robert Grosseteste and Leonardo da Vinci to René Descartes, Johannes Kepler and Isaac Newton, were in his debt. Indeed, the influence of Ibn al-Haythams Optics ranks alongside that of Newtons work of the same title, the translation of The Book of Optics had a huge impact on Europe. From it, later European scholars were able to build the devices as what Ibn al-Haytham did. From this, such important things as eyeglasses, magnifying glasses, telescopes, Physics became a separate science when early modern Europeans used experimental and quantitative methods to discover what are now considered to be the laws of physics. Newton also developed calculus, the study of change, which provided new mathematical methods for solving physical problems. The discovery of new laws in thermodynamics, chemistry, and electromagnetics resulted from greater research efforts during the Industrial Revolution as energy needs increased, however, inaccuracies in classical mechanics for very small objects and very high velocities led to the development of modern physics in the 20th century. Modern physics began in the early 20th century with the work of Max Planck in quantum theory, both of these theories came about due to inaccuracies in classical mechanics in certain situations. Quantum mechanics would come to be pioneered by Werner Heisenberg, Erwin Schrödinger, from this early work, and work in related fields, the Standard Model of particle physics was derived. Areas of mathematics in general are important to this field, such as the study of probabilities, in many ways, physics stems from ancient Greek philosophy

Pyhsics
–
Further information:

Outline of physics
Pyhsics
–
Ancient

Egyptian astronomy is evident in monuments like the

ceiling of Senemut's tomb from the

Eighteenth Dynasty of Egypt.

Pyhsics
–

Sir Isaac Newton (1643–1727), whose

laws of motion and

universal gravitation were major milestones in classical physics

Pyhsics
–

Albert Einstein (1879–1955), whose work on the

photoelectric effect and the

theory of relativity led to a revolution in 20th century physics