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Telegraph Process
In probability theory, the telegraph process is a memoryless continuous-time stochastic process that shows two distinct values. It models burst noise (also called popcorn noise or random telegraph signal). If the two possible values that a random variable can take are ''c_1'' and ''c_2'', then the process can be described by the following master equations: :\partial_t P(c_1, t, x, t_0)=-\lambda_1 P(c_1, t, x, t_0)+\lambda_2 P(c_2, t, x, t_0) and :\partial_t P(c_2, t, x, t_0)=\lambda_1 P(c_1, t, x, t_0)-\lambda_2 P(c_2, t, x, t_0). where \lambda_1 is the transition rate for going from state c_1 to state c_2 and \lambda_2 is the transition rate for going from going from state c_2 to state c_1. The process is also known under the names Kac process (after mathematician Mark Kac), and dichotomous random process. Solution The master equation is compactly written in a matrix form by introducing a vector \mathbf= x, t_0),P(c_2, t, x, t_0)/math>, :\frac=W\mathbf P where :W=\begin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Theory
Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of the sample space is called an event. Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes (which provide mathematical abstractions of non-deterministic or uncertain processes or measured quantities that may either be single occurrences or evolve over time in a random fashion). Although it is not possible to perfectly predict random events, much can be said about their behavior. Two major results in probability ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluorescence Intermittency
Fluorescence intermittency, or blinking, is the phenomenon of random switching between ON (bright) and OFF (dark) states of the emitter under its continuous excitation. It is a common property of the nanoscale emitters (molecular fluorophores, colloidal quantum dots) related to the competition between the radiative and non-radiative relaxation pathways. The peculiar feature of such blinking in most cases is the power-law (in contrast to exponential) statistics of the ON and OFF time distributions, meaning that the measurements of the time-averaged intensity of a single emitter is not reproducible in different experiments and implying a complex dynamics of the involved process. In other words, in one experiment the emitter can blink frequently, while in another it may stay ON (or OFF) for almost entire length of the experiment (even for extremely long measurement times). For CdSe-ZnS core-shell nanocrystals, "charge trapping" is the dominant theory explaining observed power-law blink ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Stochastic Processes Topics
In the mathematics of probability, a stochastic process is a random function. In practical applications, the domain over which the function is defined is a time interval (''time series'') or a region of space (''random field''). Familiar examples of time series include stock market and exchange rate fluctuations, signals such as speech, audio and video; medical data such as a patient's EKG, EEG, blood pressure or temperature; and random movement such as Brownian motion or random walks. Examples of random fields include static images, random topographies (landscapes), or composition variations of an inhomogeneous material. Stochastic processes topics :''This list is currently incomplete.'' See also :Stochastic processes * Basic affine jump diffusion * Bernoulli process: discrete-time processes with two possible states. ** Bernoulli schemes: discrete-time processes with ''N'' possible states; every stationary process in ''N'' outcomes is a Bernoulli scheme, and vice versa. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Markov Chain
A Markov chain or Markov process is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happens next depends only on the state of affairs ''now''." A countably infinite sequence, in which the chain moves state at discrete time steps, gives a discrete-time Markov chain (DTMC). A continuous-time process is called a continuous-time Markov chain (CTMC). It is named after the Russian mathematician Andrey Markov. Markov chains have many applications as statistical models of real-world processes, such as studying cruise control systems in motor vehicles, queues or lines of customers arriving at an airport, currency exchange rates and animal population dynamics. Markov processes are the basis for general stochastic simulation methods known as Markov chain Monte Carlo, which are used for simulating sampling from complex probability dist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transcription Factor
In molecular biology, a transcription factor (TF) (or sequence-specific DNA-binding factor) is a protein that controls the rate of transcription of genetic information from DNA to messenger RNA, by binding to a specific DNA sequence. The function of TFs is to regulate—turn on and off—genes in order to make sure that they are expressed in the desired cells at the right time and in the right amount throughout the life of the cell and the organism. Groups of TFs function in a coordinated fashion to direct cell division, cell growth, and cell death throughout life; cell migration and organization (body plan) during embryonic development; and intermittently in response to signals from outside the cell, such as a hormone. There are up to 1600 TFs in the human genome. Transcription factors are members of the proteome as well as regulome. TFs work alone or with other proteins in a complex, by promoting (as an activator), or blocking (as a repressor) the recruitment of RNA ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Biology
Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary information encoded in genes, which can be transmitted to future generations. Another major theme is evolution, which explains the unity and diversity of life. Energy processing is also important to life as it allows organisms to move, grow, and reproduce. Finally, all organisms are able to regulate their own internal environments. Biologists are able to study life at multiple levels of organization, from the molecular biology of a cell to the anatomy and physiology of plants and animals, and evolution of populations.Based on definition from: Hence, there are multiple subdisciplines within biology, each defined by the nature of their research questions and the tools that they use. Like other scientists, biologists use the sc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stock
In finance, stock (also capital stock) consists of all the shares by which ownership of a corporation or company is divided.Longman Business English Dictionary: "stock - ''especially AmE'' one of the shares into which ownership of a company is divided, or these shares considered together" "When a company issues shares or stocks ''especially AmE'', it makes them available for people to buy for the first time." (Especially in American English, the word "stocks" is also used to refer to shares.) A single share of the stock means fractional ownership of the corporation in proportion to the total number of shares. This typically entitles the shareholder (stockholder) to that fraction of the company's earnings, proceeds from liquidation of assets (after discharge of all senior claims such as secured and unsecured debt), or voting power, often dividing these up in proportion to the amount of money each stockholder has invested. Not all stock is necessarily equal, as certain classe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finance
Finance is the study and discipline of money, currency and capital assets. It is related to, but not synonymous with economics, the study of production, distribution, and consumption of money, assets, goods and services (the discipline of financial economics bridges the two). Finance activities take place in financial systems at various scopes, thus the field can be roughly divided into personal, corporate, and public finance. In a financial system, assets are bought, sold, or traded as financial instruments, such as currencies, loans, bonds, shares, stocks, options, futures, etc. Assets can also be banked, invested, and insured to maximize value and minimize loss. In practice, risks are always present in any financial action and entities. A broad range of subfields within finance exist due to its wide scope. Asset, money, risk and investment management aim to maximize value and minimize volatility. Financial analysis is viability, stability, and profitability asse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponential Distribution
In probability theory and statistics, the exponential distribution is the probability distribution of the time between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate. It is a particular case of the gamma distribution. It is the continuous analogue of the geometric distribution, and it has the key property of being memoryless. In addition to being used for the analysis of Poisson point processes it is found in various other contexts. The exponential distribution is not the same as the class of exponential families of distributions. This is a large class of probability distributions that includes the exponential distribution as one of its members, but also includes many other distributions, like the normal, binomial, gamma, and Poisson distributions. Definitions Probability density function The probability density function (pdf) of an exponential distribution is : f(x;\lambda) = \begin \lambda ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Tail
Algebraic may refer to any subject related to algebra in mathematics and related branches like algebraic number theory and algebraic topology. The word algebra itself has several meanings. Algebraic may also refer to: * Algebraic data type, a datatype in computer programming each of whose values is data from other datatypes wrapped in one of the constructors of the datatype * Algebraic numbers, a complex number that is a root of a non-zero polynomial in one variable with integer coefficients * Algebraic functions, functions satisfying certain polynomials * Algebraic element, an element of a field extension which is a root of some polynomial over the base field * Algebraic extension, a field extension such that every element is an algebraic element over the base field * Algebraic definition, a definition in mathematical logic which is given using only equalities between terms * Algebraic structure, a set with one or more finitary operations defined on it * Algebraic, the order of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Distribution
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of would take the value 0.5 (1 in 2 or 1/2) for , and 0.5 for (assuming that the coin is fair). Examples of random phenomena include the weather conditions at some future date, the height of a randomly selected person, the fraction of male students in a school, the results of a survey to be conducted, etc. Introduction A probability distribution is a mathematical description of the probabilities of events, subsets of the sample space. The sample space, often denoted by \Omega, is the set of all possible outcomes of a random phe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Single Molecule Experiment
A single-molecule experiment is an experiment that investigates the properties of individual molecules. Single-molecule studies may be contrasted with measurements on an ensemble or bulk collection of molecules, where the individual behavior of molecules cannot be distinguished, and only average characteristics can be measured. Since many measurement techniques in biology, chemistry, and physics are not sensitive enough to observe single molecules, single-molecule fluorescence techniques (that have emerged since the 1990s for probing various processes on the level of individual molecules) caused a lot of excitement, since these supplied many new details on the measured processes that were not accessible in the past. Indeed, since the 1990s, many techniques for probing individual molecules have been developed. The first single-molecule experiments were patch clamp experiments performed in the 1970s, but these were limited to studying ion channels. Today, systems investigated using ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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