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Normalized
Normalization or normalisation refers to a process that makes something more normal or regular. Science * Normalization process theory, a sociological theory of the implementation of new technologies or innovations * Normalization model, used in visual neuroscience * Normalization in quantum mechanics, see and normalized solution * Normalization (sociology) or social normalization, the process through which ideas and behaviors that may fall outside of social norms come to be regarded as "normal" Mathematics and statistics * Normalization of an algebraic variety, the operation consisting in taking locally the integral closure of the ring of regular functions * Normalization (statistics), adjustments of values or distributions in statistics ** Quantile normalization, statistical technique for making two distributions identical in statistical properties * Normalizing (abstract rewriting), an abstract rewriting system in which every object has at least one normal form ** Normaliz ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normalized Solution (mathematics)
In mathematics, a normalized solution to an ordinary or partial differential equation is a solution with prescribed norm, that is, a solution which satisfies a condition like \int_ , u(x), ^2 \, dx = 1. In this article, the normalized solution is introduced by using the nonlinear Schrödinger equation. The nonlinear Schrödinger equation (NLSE) is a fundamental equation in quantum mechanics and other various fields of physics, describing the evolution of complex wave functions. In Quantum Physics, normalization means that the total probability of finding a quantum particle anywhere in the universe is unity. Definition and variational framework In order to illustrate this concept, consider the following nonlinear Schrödinger equation with prescribed norm: : -\Delta u + \lambda u = f(u), \quad \int_ , u, ^2 \, dx = 1, where \Delta is a Laplacian operator, N\ge1, \lambda\in \mathbb is a Lagrange multiplier and f is a nonlinearity. If we want to find a normalized solution to th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Database Normalization
Database normalization is the process of structuring a relational database in accordance with a series of so-called '' normal forms'' in order to reduce data redundancy and improve data integrity. It was first proposed by British computer scientist Edgar F. Codd as part of his relational model. Normalization entails organizing the columns (attributes) and tables (relations) of a database to ensure that their dependencies are properly enforced by database integrity constraints. It is accomplished by applying some formal rules either by a process of ''synthesis'' (creating a new database design) or ''decomposition'' (improving an existing database design). Objectives A basic objective of the first normal form defined by Codd in 1970 was to permit data to be queried and manipulated using a "universal data sub-language" grounded in first-order logic. An example of such a language is SQL, though it is one that Codd regarded as seriously flawed. The objectives of normalization ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normalized Frequency (digital Signal Processing)
In digital signal processing (DSP), a normalized frequency is a ratio of a variable frequency (f) and a constant frequency associated with a system (such as a '' sampling rate'', f_s). Some software applications require normalized inputs and produce normalized outputs, which can be re-scaled to physical units when necessary. Mathematical derivations are usually done in normalized units, relevant to a wide range of applications. Examples of normalization A typical choice of characteristic frequency is the '' sampling rate'' (f_s) that is used to create the digital signal from a continuous one. The normalized quantity, f' = \tfrac, has the unit ''cycle per sample'' regardless of whether the original signal is a function of time or distance. For example, when f is expressed in Hz (''cycles per second''), f_s is expressed in ''samples per second''. Some programs (such as MATLAB toolboxes) that design filters with real-valued coefficients prefer the Nyquist frequency (f_s/2) as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scientific Notation
Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form, since to do so would require writing out an inconveniently long string of digits. It may be referred to as scientific form or standard index form, or standard form in the United Kingdom. This base ten notation is commonly used by scientists, mathematicians, and engineers, in part because it can simplify certain arithmetic operations. On scientific calculators, it is usually known as "SCI" display mode. In scientific notation, nonzero numbers are written in the form or ''m'' times ten raised to the power of ''n'', where ''n'' is an integer, and the coefficient ''m'' is a nonzero real number (usually between 1 and 10 in absolute value, and nearly always written as a terminating decimal). The integer ''n'' is called the exponent and the real number ''m'' is called the '' significand'' or ''mantissa''. The term "mantissa" can be ambiguous where loga ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normalized Number
In applied mathematics, a number is normalized when it is written in scientific notation with one non-zero decimal digit before the decimal point.. Thus, a real number, when written out in normalized scientific notation, is as follows: :\pm d_0 . d_1 d_2 d_3 \dots \times 10^n where ''n'' is an integer, d_0, d_1, d_2, d_3, \ldots, are the digits of the number in base 10, and d_0 is not zero. That is, its leading digit (i.e., leftmost) is not zero and is followed by the decimal point. Simply speaking, a number is ''normalized'' when it is written in the form of ''a'' × 10''n'' where 1 ≤ , ''a'', < 10 without leading zeros in ''a''. This is the ''standard form'' of . An alternative style is to have the first non-zero digit ''after'' the decimal point. Examples As examples, the number 918.082 in normalized f ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dimensional Normalization
Dimensional modeling (DM) is part of the '' Business Dimensional Lifecycle'' methodology developed by Ralph Kimball which includes a set of methods, techniques and concepts for use in data warehouse design. The approach focuses on identifying the key business processes within a business and modelling and implementing these first before adding additional business processes, as a bottom-up approach. An alternative approach from Inmon advocates a top down design of the model of all the enterprise data using tools such as entity-relationship modeling (ER). Description Dimensional modeling always uses the concepts of facts (measures), and dimensions (context). Facts are typically (but not always) numeric values that can be aggregated, and dimensions are groups of hierarchies and descriptors that define the facts. For example, sales amount is a fact; timestamp, product, register#, store#, etc. are elements of dimensions. Dimensional models are built by business process area, e.g. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Text Normalization
Text normalization is the process of transforming text into a single canonical form that it might not have had before. Normalizing text before storing or processing it allows for separation of concerns, since input is guaranteed to be consistent before operations are performed on it. Text normalization requires being aware of what type of text is to be normalized and how it is to be processed afterwards; there is no all-purpose normalization procedure. Applications Text normalization is frequently used when converting text to speech. Numbers, dates, acronyms, and abbreviations are non-standard "words" that need to be pronounced differently depending on context.Sproat, R.; Black, A.; Chen, S.; Kumar, S.; Ostendorf, M.; Richards, C. (2001). "Normalization of non-standard words." ''Computer Speech and Language'' 15; 287–333. doibr>10.1006/csla.2001.0169 For example: * "$200" would be pronounced as "two hundred dollars" in English, but as "lua selau tālā" in Samoan. * "vi" ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
URL Normalization
URI normalization is the process by which Uniform Resource Identifier, URIs are modified and standardized in a consistent manner. The goal of the normalization process is to transform a URI into a normalized URI so it is possible to determine if two syntactically different URIs may be equivalent. Search engines employ URI normalization in order to correctly rank pages that may be found with multiple URIs, and to reduce indexing of duplicate pages. Web crawlers perform URI normalization in order to avoid crawling the same resource more than once. Web browsers may perform normalization to determine if a link has been visited or to determine if a Web cache, page has been cached. Web servers may also perform normalization for many reasons (i.e. to be able to more easily intercept security risks coming from client requests, to use only one absolute file name for each resource stored in their caches, named in log files, etc.). Normalization process There are several types of normaliz ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NFD Normalization
Unicode equivalence is the specification by the Unicode character encoding standard that some sequences of code points represent essentially the same character. This feature was introduced in the standard to allow compatibility with pre-existing standard character sets, which often included similar or identical characters. Unicode provides two such notions, canonical equivalence and compatibility. Code point sequences that are defined as canonically equivalent are assumed to have the same appearance and meaning when printed or displayed. For example, the code point followed by is defined by Unicode to be canonically equivalent to the single code point of the Spanish alphabet). Therefore, those sequences should be displayed in the same manner, should be treated in the same way by applications such as alphabetizing names or searching, and may be substituted for each other. Similarly, each Hangul syllable block that is encoded as a single character may be equivalently encode ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normalizing Constant
In probability theory, a normalizing constant or normalizing factor is used to reduce any probability function to a probability density function with total probability of one. For example, a Gaussian function can be normalized into a probability density function, which gives the standard normal distribution. In Bayes' theorem, a normalizing constant is used to ensure that the sum of all possible hypotheses equals 1. Other uses of normalizing constants include making the value of a Legendre polynomial at 1 and in the orthogonality of orthonormal functions. A similar concept has been used in areas other than probability, such as for polynomials. Definition In probability theory, a normalizing constant is a constant by which an everywhere non-negative function must be multiplied so the area under its graph is 1, e.g., to make it a probability density function or a probability mass function. Examples If we start from the simple Gaussian function p(x) = e^, \quad x\in(-\infty,\ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normalization (machine Learning)
In machine learning, normalization is a statistical technique with various applications. There are two main forms of normalization, namely ''data normalization'' and ''activation normalization''. Data normalization (or feature scaling) includes methods that rescale input data so that the features have the same range, mean, variance, or other statistical properties. For instance, a popular choice of feature scaling method is min-max normalization, where each feature is transformed to have the same range (typically ,1/math> or 1,1/math>). This solves the problem of different features having vastly different scales, for example if one feature is measured in kilometers and another in nanometers. Activation normalization, on the other hand, is specific to deep learning, and includes methods that rescale the activation of hidden neurons inside neural networks. Normalization is often used to: * increase the speed of training convergence, * reduce sensitivity to variations and feat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normalization (statistics)
In statistics and applications of statistics, normalization can have a range of meanings. In the simplest cases, normalization of ratings means adjusting values measured on different scales to a notionally common scale, often prior to averaging. In more complicated cases, normalization may refer to more sophisticated adjustments where the intention is to bring the entire probability distributions of adjusted values into alignment. In the case of normalization of scores in educational assessment, there may be an intention to align distributions to a normal distribution. A different approach to normalization of probability distributions is quantile normalization, where the quantiles of the different measures are brought into alignment. In another usage in statistics, normalization refers to the creation of shifted and scaled versions of statistics, where the intention is that these normalized values allow the comparison of corresponding normalized values for different datasets in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
