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Stochastic Matrix
In mathematics, a stochastic matrix is a square matrix used to describe the transitions of a Markov chain. Each of its entries is a nonnegative real number representing a probability. It is also called a probability matrix, transition matrix, substitution matrix, or Markov matrix. The stochastic matrix was first developed by Andrey Markov at the beginning of the 20th century, and has found use throughout a wide variety of scientific fields, including probability theory, statistics, mathematical finance and linear algebra, as well as computer science and population genetics. There are several different definitions and types of stochastic matrices: :A right stochastic matrix is a real square matrix, with each row summing to 1. :A left stochastic matrix is a real square matrix, with each column summing to 1. :A doubly stochastic matrix is a square matrix of nonnegative real numbers with each row and column summing to 1. In the same vein, one may define a stochastic vector (al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Square Matrix
In mathematics, a square matrix is a matrix with the same number of rows and columns. An ''n''-by-''n'' matrix is known as a square matrix of order Any two square matrices of the same order can be added and multiplied. Square matrices are often used to represent simple linear transformations, such as shearing or rotation. For example, if R is a square matrix representing a rotation (rotation matrix) and \mathbf is a column vector describing the position of a point in space, the product R\mathbf yields another column vector describing the position of that point after that rotation. If \mathbf is a row vector, the same transformation can be obtained using where R^ is the transpose of Main diagonal The entries a_ (''i'' = 1, …, ''n'') form the main diagonal of a square matrix. They lie on the imaginary line which runs from the top left corner to the bottom right corner of the matrix. For instance, the main diagonal of the 4×4 matrix above contains the elements , , , . ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Andrej Markov
Andrey, Andrej or Andrei (in Cyrillic script: Андрей, Андреј or Андрэй) is a form of Andreas/ Ἀνδρέας in Slavic languages and Romanian. People with the name include: *Andrei of Polotsk ( – 1399), Lithuanian nobleman *Andrei Alexandrescu, Romanian computer programmer *Andrey Amador, Costa Rican cyclist *Andrei Arlovski, Belarusian mixed martial artist *Andrey Arshavin, Russian football player *Andrej Babiš, Czech prime minister *Andrey Belousov (born 1959), Russian politician *Andrey Bolotov, Russian agriculturalist and memoirist *Andrey Borodin, Russian financial expert and businessman *Andrei Chikatilo, prolific and cannibalistic Russian serial killer and rapist *Andrei Denisov (weightlifter) (born 1963), Israeli Olympic weightlifter *Andrey Ershov, Russian computer scientist *Andrey Esionov, Russian painter *Andrei Glavina, Istro-Romanian writer and politician *Andrei Gromyko (1909–1989), Belarusian Soviet politician and diplomat * Andrey Ivanov, s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Set
In mathematics, particularly set theory, a finite set is a set that has a finite number of elements. Informally, a finite set is a set which one could in principle count and finish counting. For example, :\ is a finite set with five elements. The number of elements of a finite set is a natural number (possibly zero) and is called the ''cardinality (or the cardinal number)'' of the set. A set that is not a finite set is called an '' infinite set''. For example, the set of all positive integers is infinite: :\. Finite sets are particularly important in combinatorics, the mathematical study of counting. Many arguments involving finite sets rely on the pigeonhole principle, which states that there cannot exist an injective function from a larger finite set to a smaller finite set. Definition and terminology Formally, a set is called finite if there exists a bijection :f\colon S\to\ for some natural number . The number is the set's cardinality, denoted as . The empty set o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Land Change Modeling
Land change models (LCMs) describe, project, and explain changes in and the dynamics of land use and land-cover. LCMs are a means of understanding ways that humans change the Earth's surface in the past, present, and future. Land change models are valuable in development policy, helping guide more appropriate decisions for resource management and the natural environment at a variety of scales ranging from a small piece of land to the entire spatial extent. Moreover, developments within land-cover, environmental and socio-economic data (as well as within technological infrastructures) have increased opportunities for land change modeling to help support and influence decisions that affect human-environment systems, as national and international attention increasingly focuses on issues of global climate change and sustainability. Importance Changes in land systems have consequences for climate and environmental change on every scale. Therefore, decisions and policies in rela ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Human Resource Management
Humans (''Homo sapiens'') are the most abundant and widespread species of primate, characterized by bipedalism and exceptional cognitive skills due to a large and complex brain. This has enabled the development of advanced tools, culture, and language. Humans are highly social and tend to live in complex social structures composed of many cooperating and competing groups, from families and kinship networks to political states. Social interactions between humans have established a wide variety of values, social norms, and rituals, which bolster human society. Its intelligence and its desire to understand and influence the environment and to explain and manipulate phenomena have motivated humanity's development of science, philosophy, mythology, religion, and other fields of study. Although some scientists equate the term ''humans'' with all members of the genus ''Homo'', in common usage, it generally refers to ''Homo sapiens'', the only extant member. Anatomica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Medical Diagnosis
Medical diagnosis (abbreviated Dx, Dx, or Ds) is the process of determining which disease or condition explains a person's symptoms and signs. It is most often referred to as diagnosis with the medical context being implicit. The information required for diagnosis is typically collected from a history and physical examination of the person seeking medical care. Often, one or more diagnostic procedures, such as medical tests, are also done during the process. Sometimes posthumous diagnosis is considered a kind of medical diagnosis. Diagnosis is often challenging because many signs and symptoms are nonspecific. For example, redness of the skin ( erythema), by itself, is a sign of many disorders and thus does not tell the healthcare professional what is wrong. Thus differential diagnosis, in which several possible explanations are compared and contrasted, must be performed. This involves the correlation of various pieces of information followed by the recognition and different ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Structural Engineering
Structural engineering is a sub-discipline of civil engineering in which structural engineers are trained to design the 'bones and muscles' that create the form and shape of man-made structures. Structural engineers also must understand and calculate the stability, strength, rigidity and earthquake-susceptibility of built structures for buildings and nonbuilding structures. The structural designs are integrated with those of other designers such as architects and building services engineer and often supervise the construction of projects by contractors on site. They can also be involved in the design of machinery, medical equipment, and vehicles where structural integrity affects functioning and safety. See glossary of structural engineering. Structural engineering theory is based upon applied physical laws and empirical knowledge of the structural performance of different materials and geometries. Structural engineering design uses a number of relatively simple structur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Residential Area
A residential area is a land used in which housing predominates, as opposed to industrial and commercial areas. Housing may vary significantly between, and through, residential areas. These include single-family housing, multi-family residential, or mobile homes. Zoning for residential use may permit some services or work opportunities or may totally exclude business and industry. It may permit high density land use or only permit low density uses. Residential zoning usually includes a smaller FAR (floor area ratio) than business, commercial or industrial/manufacturing zoning. The area may be large or small. Overview In certain residential areas, especially rural, large tracts of land may have no services whatever, such that residents seeking services must use a motor vehicle or other transportation, so the need for transportation has resulted in land development following existing or planned transport infrastructure such as rail and road. Development patterns may b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Behavioural Sciences
Behavioral sciences explore the cognitive processes within organisms and the behavioral interactions between organisms in the natural world. It involves the systematic analysis and investigation of human and animal behavior through naturalistic observation, controlled scientific experimentation and mathematical modeling. It attempts to accomplish legitimate, objective conclusions through rigorous formulations and observation.Klemke, E. D., Hollinger, R., and Kline, A. D., (1980), Introduction to the book in 'Introductory Readings in the Philosophy of Science': Buffalo, New York, Prometheus Books p 11-12 Examples of behavioral sciences include psychology, psychobiology, anthropology, economics, and cognitive science. Generally, behavioral science primarily has shown how human action often seeks to generalize about human behavior as it relates to society and its impact on society as a whole. Categories Behavioral sciences include two broad categories: neural ''Information s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Network Analysis (electrical Circuits)
A network, in the context of electrical engineering and electronics, is a collection of interconnected components. Network analysis is the process of finding the voltages across, and the currents through, all network components. There are many techniques for calculating these values. However, for the most part, the techniques assume linear components. Except where stated, the methods described in this article are applicable only to ''linear'' network analysis. Definitions Equivalent circuits A useful procedure in network analysis is to simplify the network by reducing the number of components. This can be done by replacing physical components with other notional components that have the same effect. A particular technique might directly reduce the number of components, for instance by combining impedances in series. On the other hand, it might merely change the form into one in which the components can be reduced in a later operation. For instance, one might transform a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Econometrics
Econometrics is the application of statistical methods to economic data in order to give empirical content to economic relationships. M. Hashem Pesaran (1987). "Econometrics," '' The New Palgrave: A Dictionary of Economics'', v. 2, p. 8 p. 8–22 Reprinted in J. Eatwell ''et al.'', eds. (1990). ''Econometrics: The New Palgrave''p. 1 p. 1–34Abstract (2008 revision by J. Geweke, J. Horowitz, and H. P. Pesaran). More precisely, it is "the quantitative analysis of actual economic phenomena based on the concurrent development of theory and observation, related by appropriate methods of inference". An introductory economics textbook describes econometrics as allowing economists "to sift through mountains of data to extract simple relationships". Jan Tinbergen is one of the two founding fathers of econometrics. The other, Ragnar Frisch, also coined the term in the sense in which it is used today. A basic tool for econometrics is the multiple linear regression model. ''Economet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Andrey Kolmogorov
Andrey Nikolaevich Kolmogorov ( rus, Андре́й Никола́евич Колмого́ров, p=ɐnˈdrʲej nʲɪkɐˈlajɪvʲɪtɕ kəlmɐˈɡorəf, a=Ru-Andrey Nikolaevich Kolmogorov.ogg, 25 April 1903 – 20 October 1987) was a Soviet mathematician who contributed to the mathematics of probability theory, topology, intuitionistic logic, turbulence, classical mechanics, algorithmic information theory and computational complexity. Biography Early life Andrey Kolmogorov was born in Tambov, about 500 kilometers south-southeast of Moscow, in 1903. His unmarried mother, Maria Y. Kolmogorova, died giving birth to him. Andrey was raised by two of his aunts in Tunoshna (near Yaroslavl) at the estate of his grandfather, a well-to-do nobleman. Little is known about Andrey's father. He was supposedly named Nikolai Matveevich Kataev and had been an agronomist. Kataev had been exiled from St. Petersburg to the Yaroslavl province after his participation in the revolu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
