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Deterministic System (mathematics)
In mathematics, computer science and physics, a deterministic system is a system in which no randomness is involved in the development of future states of the system. A deterministic model will thus always produce the same output from a given starting condition or initial state. In physics Physical laws that are described by differential equations represent deterministic systems, even though the state of the system at a given point in time may be difficult to describe explicitly. In quantum mechanics, the Schrödinger equation, which describes the continuous time evolution of a system's wave function, is deterministic. However, the relationship between a system's wave function and the observable properties of the system appears to be non-deterministic. In mathematics The systems studied in chaos theory are deterministic. If the initial state were known exactly, then the future state of such a system could theoretically be predicted. However, in practice, knowledge about the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Model Of Computation
In computer science, and more specifically in computability theory and computational complexity theory, a model of computation is a model which describes how an output of a mathematical function is computed given an input. A model describes how units of computations, memories, and communications are organized. The computational complexity of an algorithm can be measured given a model of computation. Using a model allows studying the performance of algorithms independently of the variations that are specific to particular implementations and specific technology. Categories Models of computation can be classified into three categories: sequential models, functional models, and concurrent models. Sequential models Sequential models include: * Finite-state machines * Post machines ( Post–Turing machines and tag machines). * Pushdown automata * Register machines ** Random-access machines * Turing machines * Decision tree model * External memory model Functional models Functio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic Process
In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables in a probability space, where the index of the family often has the interpretation of time. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. Examples include the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule. Stochastic processes have applications in many disciplines such as biology, chemistry, ecology Ecology () is the natural science of the relationships among living organisms and their Natural environment, environment. Ecology considers organisms at the individual, population, community (ecology), community, ecosystem, and biosphere lev ..., neuroscience, physics, image processing, signal processing, stochastic control, control theory, information theory, computer scien ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Model
A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of Sample (statistics), sample data (and similar data from a larger Statistical population, population). A statistical model represents, often in considerably idealized form, the Data generating process, data-generating process. When referring specifically to probability, probabilities, the corresponding term is probabilistic model. All Statistical hypothesis testing, statistical hypothesis tests and all Estimator, statistical estimators are derived via statistical models. More generally, statistical models are part of the foundation of statistical inference. A statistical model is usually specified as a mathematical relationship between one or more random variables and other non-random variables. As such, a statistical model is "a formal representation of a theory" (Herman J. Adèr, Herman Adèr quoting Kenneth A. Bollen, Kenneth Bollen). Introduction Informally, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scientific Modelling
Scientific modelling is an activity that produces models representing empirical objects, phenomena, and physical processes, to make a particular part or feature of the world easier to understand, define, quantify, visualize, or simulate. It requires selecting and identifying relevant aspects of a situation in the real world and then developing a model to replicate a system with those features. Different types of models may be used for different purposes, such as conceptual models to better understand, operational models to operationalize, mathematical models to quantify, computational models to simulate, and graphical models to visualize the subject. Modelling is an essential and inseparable part of many scientific disciplines, each of which has its own ideas about specific types of modelling. The following was said by John von Neumann. There is also an increasing attention to scientific modelling in fields such as science education, philosophy of science, systems theor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamical System
In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock pendulum, fluid dynamics, the flow of water in a pipe, the Brownian motion, random motion of particles in the air, and population dynamics, the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured. Time can be measured by integers, by real number, real or complex numbers or can be a more general algebraic object, losing the memory of its physical origin, and the space may be a manifold or simply a Set (mathematics), set, without the need of a Differentiability, smooth space-time structure defined on it. At any given time, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deterministic System (philosophy)
A deterministic system is a conceptual model of the philosophical doctrine of determinism applied to a system for understanding everything that has and will occur in the system, based on the physical outcomes of causality. In a deterministic system, every action, or cause, produces a reaction, or effect, and every reaction, in turn, becomes the cause of subsequent reactions. The totality of these cascading events can theoretically show exactly how the system will exist at any moment in time. To understand this concept, start with a fairly small system. Visualize a set of three dominoes lined up in a row with each domino less than a domino's length away from its neighbors. Once the first domino has toppled, the third domino will topple because the second will topple upon being contacted by the first domino. Small deterministic systems are easy to visualize, but are necessarily linked to the rest of reality by an initial cause and/or final effect. To go back to the dominoes, some ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differences Between Stochastic And Deterministic Spiking Neural Network Models-4LGzDtgMUkk
Difference commonly refers to: * Difference (philosophy), the set of properties by which items are distinguished * Difference (mathematics), the result of a subtraction Difference, The Difference, Differences or Differently may also refer to: Music * ''Difference'' (album), by Dreamtale, 2005 * ''The Difference'' (album), Pendleton, 2008 * "The Difference" (The Wallflowers song), 1997 * "Differences" (song), by Ginuwine, 2001 * ''Differently'' (album), by Cassie Davis, 2009 ** "Differently" (song), by Cassie Davis, 2009 * "Difference", a song by Benjamin Clementine from the 2022 album ''And I Have Been'' * "The Difference", a song by Matchbox Twenty from the 2002 album ''More Than You Think You Are'' * "The Difference", a song by Westlife from the 2009 album ''Where We Are'' * "The Difference", a song by Nick Jonas from the 2016 album '' Last Year Was Complicated'' * "The Difference", a song by Meek Mill featuring Quavo, from the 2016 mixtape '' DC4'' * "The Difference", a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Real Business-cycle Theory
Real business-cycle theory (RBC theory) is a class of new classical macroeconomics macroeconomic model, models in which business-cycle fluctuations are accounted for by Real vs. nominal in economics, real, in contrast to nominal, Shock (economics), shocks. RBC theory sees business cycle fluctuations as the economic efficiency, efficient response to exogenous variable, exogenous changes in the real economic environment. That is, the level of national output necessarily maximizes expected utility, ''expected'' utility. In RBC models, business cycles are described as "real" because they reflect optimal adjustments by economic agents rather than failures of Market clearing, markets to clear. As a result, RBC theory suggests that governments should concentrate on long-term structural change rather than intervention through discretionary fiscal policy, fiscal or monetary policy. These ideas are strongly associated with freshwater economics within the neoclassical economics tradition, pa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ramsey–Cass–Koopmans Model
The Ramsey–Cass–Koopmans model (also known as the Ramsey growth model or the neoclassical growth model) is a foundational model in neoclassical economics that describes the dynamics of economic growth over time. It builds upon the pioneering work of Frank P. Ramsey (1928), with later extensions by David Cass and Tjalling Koopmans in the 1960s. The model extends the Solow–Swan model by Exogenous and endogenous variables, endogenizing the Saving, savings rate through explicit microfoundations of Consumption (economics), consumption behavior: rather than assuming a constant saving rate, the model derives it from the intertemporal optimization of a representative agent who chooses Consumption (economics), consumption to maximize utility over an infinite horizon. This approach leads to a richer dynamic structure in the transition to the long-run Steady state (macroeconomics), steady state, and yields a Pareto efficiency, Pareto efficient outcome.This efficiency result depends not o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hardware Random Number Generator
In computing, a hardware random number generator (HRNG), true random number generator (TRNG), non-deterministic random bit generator (NRBG), or physical random number generator is a device that generates random numbers from a physical process capable of producing entropy, unlike a pseudorandom number generator (PRNG) that utilizes a deterministic algorithm and non-physical nondeterministic random bit generators that do not include hardware dedicated to generation of entropy. Many natural phenomena generate low-level, statistically random "noise" signals, including thermal and shot noise, jitter and metastability of electronic circuits, Brownian motion, and atmospheric noise. Researchers also used the photoelectric effect, involving a beam splitter, other quantum phenomena, and even the nuclear decay (due to practical considerations the latter, as well as the atmospheric noise, is not viable except for fairly restricted applications or online distribution services). Wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pseudorandom Number Generator
A pseudorandom number generator (PRNG), also known as a deterministic random bit generator (DRBG), is an algorithm for generating a sequence of numbers whose properties approximate the properties of sequences of random number generation, random numbers. The PRNG-generated sequence is not truly random, because it is completely determined by an initial value, called the PRNG's ''random seed, seed'' (which may include truly random values). Although sequences that are closer to truly random can be generated using hardware random number generators, ''pseudorandom number generators'' are important in practice for their speed in number generation and their reproducibility. PRNGs are central in applications such as simulations (e.g. for the Monte Carlo method), electronic games (e.g. for procedural generation), and cryptography. Cryptographic applications require the output not to be predictable from earlier outputs, and more cryptographically-secure pseudorandom number generator, elabora ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
