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Reduced Dimensions Form
In biophysics and related fields, reduced dimension forms (RDFs) are unique on-off mechanisms for random walks that generate two-state trajectories (see Fig. 1 for an example of a RDF and Fig. 2 for an example of a two-state trajectory). It has been shown that RDFs solve two-state trajectories, since only one RDF can be constructed from the data, where this property does not hold for on-off kinetic schemes, where many kinetic schemes can be constructed from a particular two-state trajectory (even from an ideal on-off trajectory). Two-state time trajectories are very common in measurements in chemistry, physics, and the biophysics of individual molecules (e.g. measurements of protein dynamics and DNA and RNA dynamics, [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Biophysics
Biophysics is an interdisciplinary science that applies approaches and methods traditionally used in physics to study biological phenomena. Biophysics covers all scales of biological organization, from molecular to organismic and populations. Biophysical research shares significant overlap with biochemistry, molecular biology, physical chemistry, physiology, nanotechnology, bioengineering, computational biology, biomechanics, developmental biology and systems biology. The term ''biophysics'' was originally introduced by Karl Pearson in 1892.Roland Glaser. Biophysics: An Introduction'. Springer; 23 April 2012. . The term ''biophysics'' is also regularly used in academia to indicate the study of the physical quantities (e.g. electric current, temperature, stress, entropy) in biological systems. Other biological sciences also perform research on the biophysical properties of living organisms including molecular biology, cell biology, chemical biology, and biochemistry. Overview ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Two State Trajectory
A two-state trajectory (also termed two-state time trajectory or a trajectory with two states) is a dynamical signal that fluctuates between two distinct values: ON and OFF, open and closed, +/-, etc. Mathematically, the signal X(t) has, for every t, either the value X(t)=c_\mathrm or X(t)=c_\mathrm. In most applications, the signal is stochastic; nevertheless, it can have deterministic ON-OFF components. A completely deterministic two-state trajectory is a square wave. There are many ways one can create a two-state signal, e.g. flipping a coin repeatedly. A stochastic two-state trajectory is among the simplest stochastic processes. Extensions include: three-state trajectories, higher discrete state trajectories, and continuous trajectories in any dimension. Two state trajectories in biophysics, and related fields Two state trajectories are very common. Here, we focus on relevant trajectories in scientific experiments: these are seen in measurements in chemistry, physics, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
WHAT RDF DOES
What or WHAT may refer to: * What, an interrogative pronoun and adverb * "What?", one of the Five Ws used in journalism Film and television * ''What!'' (film) or ''The Whip and the Body'', a 1963 Italian film directed by Mario Bava * '' What?'' (film), a 1972 film directed by Roman Polanski * "What", the name of the second baseman in Abbott and Costello's comedy routine "Who's on First?" * "What?", the catchphrase of professional wrestler Stone Cold Steve Austin Music * ''what.'', a comedy/music album by Bo Burnham, 2013 * What Records, a UK record label * What? Records, a US record label Songs * "What" (song), by Melinda Marx, 1965 * "What?" (Rob Zombie song), 2009 * "What?" (SB19 song), 2021 * "What?", by 666 from ''The Soft Boys'' * "What", by Bassnectar from ''Vava Voom'' * "What?", by Corrosion of Conformity from ''Eye for an Eye'' * "What?", by the Move from ''Looking On'' * "What?", by A Tribe Called Quest from ''The Low-End Theory'' Science and technology * Web H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kinetic Scheme
In physics, chemistry and related fields, a kinetic scheme is a network of states and connections between them representing the scheme of a dynamical process. Usually a kinetic scheme represents a Markovian process, while for non-Markovian processes generalized kinetic schemes are used. Figure 1 shows an illustration of a kinetic scheme. A Markovian kinetic scheme Mathematical description A kinetic scheme is a network (a directed graph) of distinct states (although repetition of states may occur and this depends on the system), where each pair of states ''i'' and ''j'' are associated with directional rates, A_ (and A_). It is described with a master equation: a first-order differential equation for the probability \vec of a system to occupy each one its states at time ''t'' (element ''i'' represents state ''i''). Written in a matrix form, this states: \frac=\mathbf\vec, where \mathbf is the matrix of connections (rates) A_. In a Markovian kinetic scheme the connections are cons ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Microscopic Reversibility
The principle of microscopic reversibility in physics and chemistry is twofold: * First, it states that the microscopic detailed dynamics of particles and fields is time-reversible because the microscopic equations of motion are symmetric with respect to inversion in time (T-symmetry); * Second, it relates to the statistical description of the kinetics of macroscopic or mesoscopic systems as an ensemble of elementary processes: collisions, elementary transitions or reactions. For these processes, the consequence of the microscopic T-symmetry is: ''Corresponding to every individual process there is a reverse process, and in a state of equilibrium the average rate of every process is equal to the average rate of its reverse process.'' History of microscopic reversibility The idea of microscopic reversibility was born together with physical kinetics. In 1872, Ludwig Boltzmann represented kinetics of gases as statistical ensemble of elementary collisions.Boltzmann, L. (1964), Lectures on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rejection Sampling
In numerical analysis and computational statistics, rejection sampling is a basic technique used to generate observations from a distribution. It is also commonly called the acceptance-rejection method or "accept-reject algorithm" and is a type of exact simulation method. The method works for any distribution in \mathbb^m with a density. Rejection sampling is based on the observation that to sample a random variable in one dimension, one can perform a uniformly random sampling of the two-dimensional Cartesian graph, and keep the samples in the region under the graph of its density function. Note that this property can be extended to ''N''-dimension functions. Description To visualize the motivation behind rejection sampling, imagine graphing the density function of a random variable onto a large rectangular board and throwing darts at it. Assume that the darts are uniformly distributed around the board. Now remove all of the darts that are outside the area under the curve. The rem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gillespie Algorithm
In probability theory, the Gillespie algorithm (or the Doob-Gillespie algorithm or ''Stochastic Simulation Algorithm'', the SSA) generates a statistically correct trajectory (possible solution) of a stochastic equation system for which the reaction rates are known. It was created by Joseph L. Doob and others (circa 1945), presented by Dan Gillespie in 1976, and popularized in 1977 in a paper where he uses it to simulate chemical or biochemical systems of reactions efficiently and accurately using limited computational power (see stochastic simulation). As computers have become faster, the algorithm has been used to simulate increasingly complex systems. The algorithm is particularly useful for simulating reactions within cells, where the number of reagents is low and keeping track of the position and behaviour of individual molecules is computationally feasible. Mathematically, it is a variant of a dynamic Monte Carlo method and similar to the kinetic Monte Carlo methods. It is used h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Walk
In mathematics, a random walk is a random process that describes a path that consists of a succession of random steps on some mathematical space. An elementary example of a random walk is the random walk on the integer number line \mathbb Z which starts at 0, and at each step moves +1 or −1 with equal probability. Other examples include the path traced by a molecule as it travels in a liquid or a gas (see Brownian motion), the search path of a foraging animal, or the price of a fluctuating stock and the financial status of a gambler. Random walks have applications to engineering and many scientific fields including ecology, psychology, computer science, physics, chemistry, biology, economics, and sociology. The term ''random walk'' was first introduced by Karl Pearson in 1905. Lattice random walk A popular random walk model is that of a random walk on a regular lattice, where at each step the location jumps to another site according to some probability distribution. In a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Dot
Quantum dots (QDs) are semiconductor particles a few nanometres in size, having light, optical and electronics, electronic properties that differ from those of larger particles as a result of quantum mechanics. They are a central topic in nanotechnology. When the quantum dots are illuminated by UV light, an electron in the quantum dot can be excited to a state of higher energy. In the case of a semiconductor, semiconducting quantum dot, this process corresponds to the transition of an electron from the valence band to the conductance band. The excited electron can drop back into the valence band releasing its energy as light. This light emission (photoluminescence) is illustrated in the figure on the right. The color of that light depends on the energy difference between the conductance band and the valence band, or the transition between discrete energy states when band structure is no longer a good definition in QDs. In the language of materials science, nanoscale semiconductor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Enzyme
Enzymes () are proteins that act as biological catalysts by accelerating chemical reactions. The molecules upon which enzymes may act are called substrates, and the enzyme converts the substrates into different molecules known as products. Almost all metabolic processes in the cell need enzyme catalysis in order to occur at rates fast enough to sustain life. Metabolic pathways depend upon enzymes to catalyze individual steps. The study of enzymes is called ''enzymology'' and the field of pseudoenzyme analysis recognizes that during evolution, some enzymes have lost the ability to carry out biological catalysis, which is often reflected in their amino acid sequences and unusual 'pseudocatalytic' properties. Enzymes are known to catalyze more than 5,000 biochemical reaction types. Other biocatalysts are catalytic RNA molecules, called ribozymes. Enzymes' specificity comes from their unique three-dimensional structures. Like all catalysts, enzymes increase the reaction ra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
