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Time Series
In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Examples of time series are heights of ocean tides, counts of sunspots, and the daily closing value of the Dow Jones Industrial Average. A time series is very frequently plotted via a run chart (which is a temporal line chart). Time series are used in statistics, signal processing, pattern recognition, econometrics, mathematical finance, weather forecasting, earthquake prediction, electroencephalography, control engineering, astronomy, communications engineering, and largely in any domain of applied science and engineering which involves temporal measurements. Time series ''analysis'' comprises methods for analyzing time series data in order to extract meaningful statistics and other characteristics of the data. Time series ''f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electroencephalography
Electroencephalography (EEG) is a method to record an electrogram of the spontaneous electrical activity of the brain. The biosignal, bio signals detected by EEG have been shown to represent the postsynaptic potentials of pyramidal neurons in the neocortex and allocortex. It is typically non-invasive, with the EEG electrodes placed along the scalp (commonly called "scalp EEG") using the 10–20 system (EEG), International 10–20 system, or variations of it. Electrocorticography, involving surgical placement of electrodes, is sometimes called Electrocorticography, "intracranial EEG". Clinical interpretation of EEG recordings is most often performed by visual inspection of the tracing or quantitative EEG, quantitative EEG analysis. Voltage fluctuations measured by the EEG bioamplifier, bio amplifier and electrodes allow the evaluation of normal Brain activity and meditation, brain activity. As the electrical activity monitored by EEG originates in neurons in the underlying Huma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time Reversibility
In mathematics and physics, time-reversibility is the property (mathematics), property of a process whose governing rules remain unchanged when the direction of its sequence of actions is reversed. A deterministic process is time-reversible if the time-reversed process satisfies the same dynamic equation (other), dynamic equations as the original process; in other words, the equations are invariant (mathematics), invariant or symmetrical under a change in the Sign (mathematics), sign of time. A stochastic process is reversible if the statistical properties of the process are the same as the statistical properties for time-reversed data from the same process. Mathematics In mathematics, a dynamical system is time-reversible if the forward evolution is one-to-one function, one-to-one, so that for every state there exists a transformation (an Involution (mathematics), involution) π which gives a one-to-one mapping between the time-reversed evolution of any one state and t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic
Stochastic (; ) is the property of being well-described by a random probability distribution. ''Stochasticity'' and ''randomness'' are technically distinct concepts: the former refers to a modeling approach, while the latter describes phenomena; in everyday conversation, however, these terms are often used interchangeably. In probability theory, the formal concept of a '' stochastic process'' is also referred to as a ''random process''. Stochasticity is used in many different fields, including image processing, signal processing, computer science, information theory, telecommunications, chemistry, ecology, neuroscience, physics, and cryptography. It is also used in finance (e.g., stochastic oscillator), due to seemingly random changes in the different markets within the financial sector and in medicine, linguistics, music, media, colour theory, botany, manufacturing and geomorphology. Etymology The word ''stochastic'' in English was originally used as an adjective with the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spatial Data Analysis
Spatial analysis is any of the formal techniques which study entities using their topological, geometric, or geographic properties, primarily used in Urban Design. Spatial analysis includes a variety of techniques using different analytic approaches, especially '' spatial statistics''. It may be applied in fields as diverse as astronomy, with its studies of the placement of galaxies in the cosmos, or to chip fabrication engineering, with its use of "place and route" algorithms to build complex wiring structures. In a more restricted sense, spatial analysis is geospatial analysis, the technique applied to structures at the human scale, most notably in the analysis of geographic data. It may also applied to genomics, as in transcriptomics data, but is primarily for spatial data. Complex issues arise in spatial analysis, many of which are neither clearly defined nor completely resolved, but form the basis for current research. The most fundamental of these is the problem of de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cross-sectional Study
In statistics and econometrics, cross-sectional data is a type of data collected by observing many subjects (such as individuals, firms, countries, or regions) at a single point or period of time. Analysis of cross-sectional data usually consists of comparing the differences among selected subjects, typically with no regard to differences in time. For example, if we want to measure current obesity levels in a population, we could draw a sample of 1,000 people randomly from that population (also known as a cross section of that population), measure their weight and height, and calculate what percentage of that sample is categorized as obese. This cross-sectional sample provides us with a snapshot of that population, at that one point in time. Note that we do not know based on one cross-sectional sample if obesity is increasing or decreasing; we can only describe the current proportion. Cross-sectional data differs from ''time series'' data, in which the same small-scale or aggreg ... [...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] |
Model (abstract)
The term conceptual model refers to any model that is formed after a wikt:concept#Noun, conceptualization or generalization process. Conceptual models are often abstractions of things in the real world, whether physical or social. Semantics, Semantic studies are relevant to various stages of process of concept formation, concept formation. Semantics is fundamentally a study of concepts, the meaning that thinking beings give to various elements of their experience. Overview Concept models and conceptual models The value of a conceptual model is usually directly proportional to how well it corresponds to a past, present, future, actual or potential state of affairs. A concept model (a model of a concept) is quite different because in order to be a good model it need not have this real world correspondence. In artificial intelligence, conceptual models and conceptual graphs are used for building expert systems and knowledge-based systems; here the analysts are concerned to repres ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time
Time is the continuous progression of existence that occurs in an apparently irreversible process, irreversible succession from the past, through the present, and into the future. It is a component quantity of various measurements used to sequence events, to compare the duration of events (or the intervals between them), and to quantify rates of change of quantities in material reality or in the qualia, conscious experience. Time is often referred to as a fourth dimension, along with Three-dimensional space, three spatial dimensions. Time is one of the seven fundamental physical quantities in both the International System of Units (SI) and International System of Quantities. The SI base unit of time is the second, which is defined by measuring the electronic transition frequency of caesium atoms. General relativity is the primary framework for understanding how spacetime works. Through advances in both theoretical and experimental investigations of spacetime, it has been shown ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Engineering
Engineering is the practice of using natural science, mathematics, and the engineering design process to Problem solving#Engineering, solve problems within technology, increase efficiency and productivity, and improve Systems engineering, systems. Modern engineering comprises many subfields which include designing and improving infrastructure, machinery, vehicles, electronics, Materials engineering, materials, and energy systems. The Academic discipline, discipline of engineering encompasses a broad range of more Academic specialization, specialized fields of engineering, each with a more specific emphasis for applications of applied mathematics, mathematics and applied science, science. See glossary of engineering. The word '':wikt:engineering, engineering'' is derived from the Latin . Definition The American Engineers' Council for Professional Development (the predecessor of the Accreditation Board for Engineering and Technology aka ABET) has defined "engineering" as: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Applied Science
Applied science is the application of the scientific method and scientific knowledge to attain practical goals. It includes a broad range of disciplines, such as engineering and medicine. Applied science is often contrasted with basic science, which is focused on advancing scientific theories and laws that explain and predict natural or other phenomena. There are applied natural sciences, as well as applied formal and social sciences. Applied science examples include genetic epidemiology which applies statistics and probability theory, and applied psychology, including criminology. Applied research Applied research is the use of empirical methods to collect data for practical purposes. It accesses and uses accumulated theories, knowledge, methods, and techniques for a specific State (polity), state, Commerce, business, or customer, client-driven purpose. In contrast to engineering, applied research does not include analyses or optimization of business, economics, and costs. App ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
