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ice cube than far away from it. If energies of the molecules located near a given point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for a certain temperature. If the energies of the molecules located near another point are observed, they will be distributed according to the Maxwell–Boltzmann distribution for another temperature. Local thermodynamic equilibrium does not require either local or global stationarity. In other words, each small locality need not have a constant temperature. However, it does require that each small locality change slowly enough to practically sustain its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by exchanges between the system and the outside. For example, a globally-stable stationary state could be maintained inside the glass of water by continuously adding finely powdered ice into it to compensate for the melting, and continuously draining off the meltwater. Natural transport phenomena may lead a system from local to global thermodynamic equilibrium. Going back to our example, the diffusion of heat will lead our glass of water toward global thermodynamic equilibrium, a state in which the temperature of the glass is completely homogeneous. == Reservations == Careful and well informed writers about thermodynamics, in their accounts of thermodynamic equilibrium, often enough make provisos or reservations to their statements. Some writers leave such reservations merely implied or more or less unstated. For example, one widely cited writer, H. B. Callen writes in this context: "In actuality, few systems are in absolute and true equilibrium." He refers to radioactive processes and remarks that they may take "cosmic times to complete, [and] generally can be ignored". He adds "In practice, the criterion for equilibrium is circular. Operationally, a system is in an equilibrium state if its properties are
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consistently described by thermodynamic theory!" J.A. Beattie and I. Oppenheim write: "Insistence on a strict interpretation of the definition of equilibrium would rule out the application of thermodynamics to practically all states of real systems." Another author, cited by Callen as giving a "scholarly and rigorous treatment", and cited by Adkins as having written a "classic text", A.B. Pippard writes in that text: "Given long enough a supercooled vapour will eventually condense, ... . The time involved may be so enormous, however, perhaps 10100 years or more, ... . For most purposes, provided the rapid change is not artificially stimulated, the systems may be regarded as being in equilibrium." Another author, A. Münster, writes in this context. He observes that thermonuclear processes often occur so slowly that they can be ignored in thermodynamics. He comments: "The concept 'absolute equilibrium' or 'equilibrium with respect to all imaginable processes', has therefore, no physical significance." He therefore states that: "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." According to L. Tisza: "... in the discussion of phenomena near absolute zero. The absolute predictions of the classical theory become particularly vague because the occurrence of frozen-in nonequilibrium states is very common." == Definitions == The most general kind of thermodynamic equilibrium of a system is through contact with the surroundings that allows simultaneous passages of all chemical substances and all kinds of energy. A system in thermodynamic equilibrium may move with uniform acceleration through space but must not change its shape or size while doing so; thus it is defined by a rigid volume in space. It may lie within external fields of force, determined by external factors of far greater extent than the system itself, so that events within the system cannot in an appreciable
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amount affect the external fields of force. The system can be in thermodynamic equilibrium only if the external force fields are uniform, and are determining its uniform acceleration, or if it lies in a non-uniform force field but is held stationary there by local forces, such as mechanical pressures, on its surface. Thermodynamic equilibrium is a primitive notion of the theory of thermodynamics. According to P.M. Morse: "It should be emphasized that the fact that there are thermodynamic states, ..., and the fact that there are thermodynamic variables which are uniquely specified by the equilibrium state ... are not conclusions deduced logically from some philosophical first principles. They are conclusions ineluctably drawn from more than two centuries of experiments." This means that thermodynamic equilibrium is not to be defined solely in terms of other theoretical concepts of thermodynamics. M. Bailyn proposes a fundamental law of thermodynamics that defines and postulates the existence of states of thermodynamic equilibrium. Textbook definitions of thermodynamic equilibrium are often stated carefully, with some reservation or other. For example, A. Münster writes: "An isolated system is in thermodynamic equilibrium when, in the system, no changes of state are occurring at a measurable rate." There are two reservations stated here; the system is isolated; any changes of state are immeasurably slow. He discusses the second proviso by giving an account of a mixture oxygen and hydrogen at room temperature in the absence of a catalyst. Münster points out that a thermodynamic equilibrium state is described by fewer macroscopic variables than is any other state of a given system. This is partly, but not entirely, because all flows within and through the system are zero. R. Haase's presentation of thermodynamics does not start with a restriction to thermodynamic equilibrium because he intends to allow for non-equilibrium thermodynamics. He
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considers an arbitrary system with time invariant properties. He tests it for thermodynamic equilibrium by cutting it off from all external influences, except external force fields. If after insulation, nothing changes, he says that the system was in equilibrium. In a section headed "Thermodynamic equilibrium", H.B. Callen defines equilibrium states in a paragraph. He points out that they "are determined by intrinsic factors" within the system. They are "terminal states", towards which the systems evolve, over time, which may occur with "glacial slowness". This statement does not explicitly say that for thermodynamic equilibrium, the system must be isolated; Callen does not spell out what he means by the words "intrinsic factors". Another textbook writer, C.J. Adkins, explicitly allows thermodynamic equilibrium to occur in a system which is not isolated. His system is, however, closed with respect to transfer of matter. He writes: "In general, the approach to thermodynamic equilibrium will involve both thermal and work-like interactions with the surroundings." He distinguishes such thermodynamic equilibrium from thermal equilibrium, in which only thermal contact is mediating transfer of energy. Another textbook author, J.R. Partington, writes: "(i) An equilibrium state is one which is independent of time." But, referring to systems "which are only apparently in equilibrium", he adds : "Such systems are in states of ″false equilibrium.″" Partington's statement does not explicitly state that the equilibrium refers to an isolated system. Like Münster, Partington also refers to the mixture of oxygen and hydrogen. He adds a proviso that "In a true equilibrium state, the smallest change of any external condition which influences the state will produce a small change of state ..." This proviso means that thermodynamic equilibrium must be stable against small perturbations; this requirement is essential for the strict meaning of thermodynamic equilibrium. A student textbook by F.H. Crawford has
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a section headed "Thermodynamic Equilibrium". It distinguishes several drivers of flows, and then says: "These are examples of the apparently universal tendency of isolated systems toward a state of complete mechanical, thermal, chemical, and electrical—or, in a single word, thermodynamic—equilibrium." A monograph on classical thermodynamics by H.A. Buchdahl considers the "equilibrium of a thermodynamic system", without actually writing the phrase "thermodynamic equilibrium". Referring to systems closed to exchange of matter, Buchdahl writes: "If a system is in a terminal condition which is properly static, it will be said to be in equilibrium." Buchdahl's monograph also discusses amorphous glass, for the purposes of thermodynamic description. It states: "More precisely, the glass may be regarded as being in equilibrium so long as experimental tests show that 'slow' transitions are in effect reversible." It is not customary to make this proviso part of the definition of thermodynamic equilibrium, but the converse is usually assumed: that if a body in thermodynamic equilibrium is subject to a sufficiently slow process, that process may be considered to be sufficiently nearly reversible, and the body remains sufficiently nearly in thermodynamic equilibrium during the process. A. Münster carefully extends his definition of thermodynamic equilibrium for isolated systems by introducing a concept of contact equilibrium. This specifies particular processes that are allowed when considering thermodynamic equilibrium for non-isolated systems, with special concern for open systems, which may gain or lose matter from or to their surroundings. A contact equilibrium is between the system of interest and a system in the surroundings, brought into contact with the system of interest, the contact being through a special kind of wall; for the rest, the whole joint system is isolated. Walls of this special kind were also considered by C. Carathéodory, and are mentioned by other writers also. They are selectively permeable.
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They may be permeable only to mechanical work, or only to heat, or only to some particular chemical substance. Each contact equilibrium defines an intensive parameter; for example, a wall permeable only to heat defines an empirical temperature. A contact equilibrium can exist for each chemical constituent of the system of interest. In a contact equilibrium, despite the possible exchange through the selectively permeable wall, the system of interest is changeless, as if it were in isolated thermodynamic equilibrium. This scheme follows the general rule that "... we can consider an equilibrium only with respect to specified processes and defined experimental conditions." Thermodynamic equilibrium for an open system means that, with respect to every relevant kind of selectively permeable wall, contact equilibrium exists when the respective intensive parameters of the system and surroundings are equal. This definition does not consider the most general kind of thermodynamic equilibrium, which is through unselective contacts. This definition does not simply state that no current of matter or energy exists in the interior or at the boundaries; but it is compatible with the following definition, which does so state. M. Zemansky also distinguishes mechanical, chemical, and thermal equilibrium. He then writes: "When the conditions for all three types of equilibrium are satisfied, the system is said to be in a state of thermodynamic equilibrium". P.M. Morse writes that thermodynamics is concerned with "states of thermodynamic equilibrium". He also uses the phrase "thermal equilibrium" while discussing transfer of energy as heat between a body and a heat reservoir in its surroundings, though not explicitly defining a special term 'thermal equilibrium'. J.R. Waldram writes of "a definite thermodynamic state". He defines the term "thermal equilibrium" for a system "when its observables have ceased to change over time". But shortly below that definition he writes of a
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piece of glass that has not yet reached its "full thermodynamic equilibrium state". Considering equilibrium states, M. Bailyn writes: "Each intensive variable has its own type of equilibrium." He then defines thermal equilibrium, mechanical equilibrium, and material equilibrium. Accordingly, he writes: "If all the intensive variables become uniform, thermodynamic equilibrium is said to exist." He is not here considering the presence of an external force field. J.G. Kirkwood and I. Oppenheim define thermodynamic equilibrium as follows: "A system is in a state of thermodynamic equilibrium if, during the time period allotted for experimentation, (a) its intensive properties are independent of time and (b) no current of matter or energy exists in its interior or at its boundaries with the surroundings." It is evident that they are not restricting the definition to isolated or to closed systems. They do not discuss the possibility of changes that occur with "glacial slowness", and proceed beyond the time period allotted for experimentation. They note that for two systems in contact, there exists a small subclass of intensive properties such that if all those of that small subclass are respectively equal, then all respective intensive properties are equal. States of thermodynamic equilibrium may be defined by this subclass, provided some other conditions are satisfied. == Characteristics of a state of internal thermodynamic equilibrium == === Homogeneity in the absence of external forces === A thermodynamic system consisting of a single phase in the absence of external forces, in its own internal thermodynamic equilibrium, is homogeneous. This means that the material in any small volume element of the system can be interchanged with the material of any other geometrically congruent volume element of the system, and the effect is to leave the system thermodynamically unchanged. In general, a strong external force field makes a system of
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a single phase in its own internal thermodynamic equilibrium inhomogeneous with respect to some intensive variables. For example, a relatively dense component of a mixture can be concentrated by centrifugation. === Uniform temperature === Such equilibrium inhomogeneity, induced by external forces, does not occur for the intensive variable temperature. According to E.A. Guggenheim, "The most important conception of thermodynamics is temperature." Planck introduces his treatise with a brief account of heat and temperature and thermal equilibrium, and then announces: "In the following we shall deal chiefly with homogeneous, isotropic bodies of any form, possessing throughout their substance the same temperature and density, and subject to a uniform pressure acting everywhere perpendicular to the surface." As did Carathéodory, Planck was setting aside surface effects and external fields and anisotropic crystals. Though referring to temperature, Planck did not there explicitly refer to the concept of thermodynamic equilibrium. In contrast, Carathéodory's scheme of presentation of classical thermodynamics for closed systems postulates the concept of an "equilibrium state" following Gibbs (Gibbs speaks routinely of a "thermodynamic state"), though not explicitly using the phrase 'thermodynamic equilibrium', nor explicitly postulating the existence of a temperature to define it. Although thermodynamic laws are immutable, systems can be created that delay the time to reach thermodynamic equilibrium. In a thought experiment, Reed A. Howald conceived of a system called "The Fizz Keeper"consisting of a cap with a nozzle that can re-pressurize any standard bottle of carbonated beverage. Nitrogen and oxygen, which air are mostly made out of, would keep getting pumped in, which would slow down the rate at which the carbon dioxide fizzles out of the system. This is possible because the thermodynamic equilibrium between the unconverted and converted carbon dioxide inside the bottle would stay the same. To come to this conclusion, he also appeals to
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Henry's Law, which states that gases dissolve in direct proportion to their partial pressures. By influencing the partial pressure on the top of a closed system, this would help slow down the rate of fizzing out of carbonated beverages which is governed by thermodynamic equilibrium. The equilibria of carbon dioxide and other gases would not change, however the partial pressure on top would slow down the rate of dissolution extending the time a gas stays in a particular state. due to the nature of thermal equilibrium of the remainder of the beverage. The equilibrium constant of carbon dioxide would be completely independent of the nitrogen and oxygen pumped into the system, which would slow down the diffusion of gas, and yet not have an impact on the thermodynamics of the entire system. The temperature within a system in thermodynamic equilibrium is uniform in space as well as in time. In a system in its own state of internal thermodynamic equilibrium, there are no net internal macroscopic flows. In particular, this means that all local parts of the system are in mutual radiative exchange equilibrium. This means that the temperature of the system is spatially uniform. This is so in all cases, including those of non-uniform external force fields. For an externally imposed gravitational field, this may be proved in macroscopic thermodynamic terms, by the calculus of variations, using the method of Langrangian multipliers. Considerations of kinetic theory or statistical mechanics also support this statement. In order that a system may be in its own internal state of thermodynamic equilibrium, it is of course necessary, but not sufficient, that it be in its own internal state of thermal equilibrium; it is possible for a system to reach internal mechanical equilibrium before it reaches internal thermal equilibrium. === Number of real variables
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needed for specification === In his exposition of his scheme of closed system equilibrium thermodynamics, C. Carathéodory initially postulates that experiment reveals that a definite number of real variables define the states that are the points of the manifold of equilibria. In the words of Prigogine and Defay (1945): "It is a matter of experience that when we have specified a certain number of macroscopic properties of a system, then all the other properties are fixed." As noted above, according to A. Münster, the number of variables needed to define a thermodynamic equilibrium is the least for any state of a given isolated system. As noted above, J.G. Kirkwood and I. Oppenheim point out that a state of thermodynamic equilibrium may be defined by a special subclass of intensive variables, with a definite number of members in that subclass. If the thermodynamic equilibrium lies in an external force field, it is only the temperature that can in general be expected to be spatially uniform. Intensive variables other than temperature will in general be non-uniform if the external force field is non-zero. In such a case, in general, additional variables are needed to describe the spatial non-uniformity. === Stability against small perturbations === As noted above, J.R. Partington points out that a state of thermodynamic equilibrium is stable against small transient perturbations. Without this condition, in general, experiments intended to study systems in thermodynamic equilibrium are in severe difficulties. === Approach to thermodynamic equilibrium within an isolated system === When a body of material starts from a non-equilibrium state of inhomogeneity or chemical non-equilibrium, and is then isolated, it spontaneously evolves towards its own internal state of thermodynamic equilibrium. It is not necessary that all aspects of internal thermodynamic equilibrium be reached simultaneously; some can be established before others. For example,
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in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium. Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium. === Fluctuations within an isolated system in its own internal thermodynamic equilibrium === In an isolated system, thermodynamic equilibrium by definition persists over an indefinitely long time. In classical physics it is often convenient to ignore the effects of measurement and this is assumed in the present account. To consider the notion of fluctuations in an isolated thermodynamic system, a convenient example is a system specified by its extensive state variables, internal energy, volume, and mass composition. By definition they are time-invariant. By definition, they combine with time-invariant nominal values of their conjugate intensive functions of state, inverse temperature, pressure divided by temperature, and the chemical potentials divided by temperature, so as to exactly obey the laws of thermodynamics. But the laws of thermodynamics, combined with the values of the specifying extensive variables of state, are not sufficient to provide knowledge of those nominal values. Further information is needed, namely, of the constitutive properties of the system. It may be admitted that on repeated measurement of those conjugate intensive functions of state, they are found to have slightly different values from time to time. Such variability is regarded as due to internal fluctuations. The different measured values average to their nominal values. If the system is truly macroscopic as postulated by classical thermodynamics, then the fluctuations are too small to detect macroscopically. This is called the thermodynamic limit. In effect, the molecular nature of matter and the quantal nature of momentum transfer have vanished from sight, too small to see. According to Buchdahl: "... there is no
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place within the strictly phenomenological theory for the idea of fluctuations about equilibrium (see, however, Section 76)." If the system is repeatedly subdivided, eventually a system is produced that is small enough to exhibit obvious fluctuations. This is a mesoscopic level of investigation. The fluctuations are then directly dependent on the natures of the various walls of the system. The precise choice of independent state variables is then important. At this stage, statistical features of the laws of thermodynamics become apparent. If the mesoscopic system is further repeatedly divided, eventually a microscopic system is produced. Then the molecular character of matter and the quantal nature of momentum transfer become important in the processes of fluctuation. One has left the realm of classical or macroscopic thermodynamics, and one needs quantum statistical mechanics. The fluctuations can become relatively dominant, and questions of measurement become important. The statement that 'the system is its own internal thermodynamic equilibrium' may be taken to mean that 'indefinitely many such measurements have been taken from time to time, with no trend in time in the various measured values'. Thus the statement, that 'a system is in its own internal thermodynamic equilibrium, with stated nominal values of its functions of state conjugate to its specifying state variables', is far far more informative than a statement that 'a set of single simultaneous measurements of those functions of state have those same values'. This is because the single measurements might have been made during a slight fluctuation, away from another set of nominal values of those conjugate intensive functions of state, that is due to unknown and different constitutive properties. A single measurement cannot tell whether that might be so, unless there is also knowledge of the nominal values that belong to the equilibrium state. === Thermal equilibrium === An
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explicit distinction between 'thermal equilibrium' and 'thermodynamic equilibrium' is made by B. C. Eu. He considers two systems in thermal contact, one a thermometer, the other a system in which there are several occurring irreversible processes, entailing non-zero fluxes; the two systems are separated by a wall permeable only to heat. He considers the case in which, over the time scale of interest, it happens that both the thermometer reading and the irreversible processes are steady. Then there is thermal equilibrium without thermodynamic equilibrium. Eu proposes consequently that the zeroth law of thermodynamics can be considered to apply even when thermodynamic equilibrium is not present; also he proposes that if changes are occurring so fast that a steady temperature cannot be defined, then "it is no longer possible to describe the process by means of a thermodynamic formalism. In other words, thermodynamics has no meaning for such a process." This illustrates the importance for thermodynamics of the concept of temperature. Thermal equilibrium is achieved when two systems in thermal contact with each other cease to have a net exchange of energy. It follows that if two systems are in thermal equilibrium, then their temperatures are the same. Thermal equilibrium occurs when a system's macroscopic thermal observables have ceased to change with time. For example, an ideal gas whose distribution function has stabilised to a specific Maxwell–Boltzmann distribution would be in thermal equilibrium. This outcome allows a single temperature and pressure to be attributed to the whole system. For an isolated body, it is quite possible for mechanical equilibrium to be reached before thermal equilibrium is reached, but eventually, all aspects of equilibrium, including thermal equilibrium, are necessary for thermodynamic equilibrium. == Non-equilibrium == A system's internal state of thermodynamic equilibrium should be distinguished from a "stationary state" in which thermodynamic
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parameters are unchanging in time but the system is not isolated, so that there are, into and out of the system, non-zero macroscopic fluxes which are constant in time. Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Most systems found in nature are not in thermodynamic equilibrium because they are changing or can be triggered to change over time, and are continuously and discontinuously subject to flux of matter and energy to and from other systems. The thermodynamic study of non-equilibrium systems requires more general concepts than are dealt with by equilibrium thermodynamics. Many natural systems still today remain beyond the scope of currently known macroscopic thermodynamic methods. Laws governing systems which are far from equilibrium are also debatable. One of the guiding principles for these systems is the maximum entropy production principle. It states that a non-equilibrium system evolves such as to maximize its entropy production. == See also == Thermodynamic models Non-random two-liquid model (NRTL model) - Phase equilibrium calculations UNIQUAC model - Phase equilibrium calculations Time crystal Topics in control theory Other related topics == General references == C. Michael Hogan, Leda C. Patmore and Harry Seidman (1973) Statistical Prediction of Dynamic Thermal Equilibrium Temperatures using Standard Meteorological Data Bases, Second Edition (EPA-660/2-73-003 2006) United States Environmental Protection Agency Office of Research and Development, Washington, D.C. [1] Cesare Barbieri (2007) Fundamentals of Astronomy. First Edition (QB43.3.B37 2006) CRC Press ISBN 0-7503-0886-9, ISBN 978-0-7503-0886-1 F. Mandl (1988) Statistical Physics, Second Edition, John Wiley & Sons Hans R. Griem (2005) Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics), Cambridge University Press, New York ISBN 0-521-61941-6 == References == == Cited bibliography == Adkins, C.J. (1968/1983). Equilibrium Thermodynamics, third edition, McGraw-Hill, London, ISBN 0-521-25445-0. Bailyn, M. (1994). A Survey of
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{
"page_id": 265823,
"source": null,
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Thermodynamics, American Institute of Physics Press, New York, ISBN 0-88318-797-3. Beattie, J.A., Oppenheim, I. (1979). Principles of Thermodynamics, Elsevier Scientific Publishing, Amsterdam, ISBN 0-444-41806-7. Boltzmann, L. (1896/1964). Lectures on Gas Theory, translated by S.G. Brush, University of California Press, Berkeley. Buchdahl, H.A. (1966). The Concepts of Classical Thermodynamics, Cambridge University Press, Cambridge UK. Callen, H.B. (1960/1985). Thermodynamics and an Introduction to Thermostatistics, (1st edition 1960) 2nd edition 1985, Wiley, New York, ISBN 0-471-86256-8. Carathéodory, C. (1909). Untersuchungen über die Grundlagen der Thermodynamik, Mathematische Annalen, 67: 355–386. A translation may be found here. Also a mostly reliable translation is to be found at Kestin, J. (1976). The Second Law of Thermodynamics, Dowden, Hutchinson & Ross, Stroudsburg PA. Chapman, S., Cowling, T.G. (1939/1970). The Mathematical Theory of Non-uniform gases. An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases, third edition 1970, Cambridge University Press, London. Crawford, F.H. (1963). Heat, Thermodynamics, and Statistical Physics, Rupert Hart-Davis, London, Harcourt, Brace & World, Inc. de Groot, S.R., Mazur, P. (1962). Non-equilibrium Thermodynamics, North-Holland, Amsterdam. Reprinted (1984), Dover Publications Inc., New York, ISBN 0486647412. Denbigh, K.G. (1951). Thermodynamics of the Steady State, Methuen, London. Eu, B.C. (2002). Generalized Thermodynamics. The Thermodynamics of Irreversible Processes and Generalized Hydrodynamics, Kluwer Academic Publishers, Dordrecht, ISBN 1-4020-0788-4. Fitts, D.D. (1962). Nonequilibrium thermodynamics. A Phenomenological Theory of Irreversible Processes in Fluid Systems, McGraw-Hill, New York. Gibbs, J.W. (1876/1878). On the equilibrium of heterogeneous substances, Trans. Conn. Acad., 3: 108–248, 343–524, reprinted in The Collected Works of J. Willard Gibbs, PhD, LL. D., edited by W.R. Longley, R.G. Van Name, Longmans, Green & Co., New York, 1928, volume 1, pp. 55–353. Griem, H.R. (2005). Principles of Plasma Spectroscopy (Cambridge Monographs on Plasma Physics), Cambridge University Press, New York ISBN 0-521-61941-6. Guggenheim, E.A. (1949/1967). Thermodynamics. An Advanced Treatment
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{
"page_id": 265823,
"source": null,
"title": "Thermodynamic equilibrium"
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for Chemists and Physicists, fifth revised edition, North-Holland, Amsterdam. Haase, R. (1971). Survey of Fundamental Laws, chapter 1 of Thermodynamics, pages 1–97 of volume 1, ed. W. Jost, of Physical Chemistry. An Advanced Treatise, ed. H. Eyring, D. Henderson, W. Jost, Academic Press, New York, lcn 73–117081. Kirkwood, J.G., Oppenheim, I. (1961). Chemical Thermodynamics, McGraw-Hill Book Company, New York. Landsberg, P.T. (1961). Thermodynamics with Quantum Statistical Illustrations, Interscience, New York. Levine, I.N. (1983), Physical Chemistry, second edition, McGraw-Hill, New York, ISBN 978-0072538625. Lieb, E. H.; Yngvason, J. (1999). "The Physics and Mathematics of the Second Law of Thermodynamics". Phys. Rep. 310 (1): 1–96. arXiv:cond-mat/9708200. Bibcode:1999PhR...310....1L. doi:10.1016/S0370-1573(98)00082-9. S2CID 119620408. Maxwell, J.C. (1867). "On the dynamical theory of gases". Phil. Trans. R. Soc. Lond. 157: 49–88. Morse, P.M. (1969). Thermal Physics, second edition, W.A. Benjamin, Inc, New York. Münster, A. (1970). Classical Thermodynamics, translated by E.S. Halberstadt, Wiley–Interscience, London. Partington, J.R. (1949). An Advanced Treatise on Physical Chemistry, volume 1, Fundamental Principles. The Properties of Gases, Longmans, Green and Co., London. Pippard, A.B. (1957/1966). The Elements of Classical Thermodynamics, reprinted with corrections 1966, Cambridge University Press, London. Planck. M. (1914). The Theory of Heat Radiation, a translation by Masius, M. of the second German edition, P. Blakiston's Son & Co., Philadelphia. Prigogine, I. (1947). Étude Thermodynamique des Phénomènes irréversibles, Dunod, Paris, and Desoers, Liège. Prigogine, I., Defay, R. (1950/1954). Chemical Thermodynamics, Longmans, Green & Co, London. Silbey, R.J., Alberty, R.A., Bawendi, M.G. (1955/2005). Physical Chemistry, fourth edition, Wiley, Hoboken NJ. ter Haar, D., Wergeland, H. (1966). Elements of Thermodynamics, Addison-Wesley Publishing, Reading MA. Thomson, W. (March 1851). "On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam". Transactions of the Royal Society of Edinburgh. XX (part II): 261–268,
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289–298. Also published in Thomson, W. (December 1852). "On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam". Phil. Mag. 4. IV (22): 8–21. Retrieved 25 June 2012. Tisza, L. (1966). Generalized Thermodynamics, M.I.T Press, Cambridge MA. Uhlenbeck, G.E., Ford, G.W. (1963). Lectures in Statistical Mechanics, American Mathematical Society, Providence RI. Waldram, J.R. (1985). The Theory of Thermodynamics, Cambridge University Press, Cambridge UK, ISBN 0-521-24575-3. Zemansky, M. (1937/1968). Heat and Thermodynamics. An Intermediate Textbook, fifth edition 1967, McGraw–Hill Book Company, New York. == External links == Breakdown of Local Thermodynamic Equilibrium George W. Collins, The Fundamentals of Stellar Astrophysics, Chapter 15 Local Thermodynamic Equilibrium Non-Local Thermodynamic Equilibrium in Cloudy Planetary Atmospheres Paper by R. E. Samueison quantifying the effects due to non-LTE in an atmosphere Thermodynamic Equilibrium, Local and otherwise lecture by Michael Richmond
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A generative adversarial network (GAN) is a class of machine learning frameworks and a prominent framework for approaching generative artificial intelligence. The concept was initially developed by Ian Goodfellow and his colleagues in June 2014. In a GAN, two neural networks compete with each other in the form of a zero-sum game, where one agent's gain is another agent's loss. Given a training set, this technique learns to generate new data with the same statistics as the training set. For example, a GAN trained on photographs can generate new photographs that look at least superficially authentic to human observers, having many realistic characteristics. Though originally proposed as a form of generative model for unsupervised learning, GANs have also proved useful for semi-supervised learning, fully supervised learning, and reinforcement learning. The core idea of a GAN is based on the "indirect" training through the discriminator, another neural network that can tell how "realistic" the input seems, which itself is also being updated dynamically. This means that the generator is not trained to minimize the distance to a specific image, but rather to fool the discriminator. This enables the model to learn in an unsupervised manner. GANs are similar to mimicry in evolutionary biology, with an evolutionary arms race between both networks. == Definition == === Mathematical === The original GAN is defined as the following game: Each probability space ( Ω , μ ref ) {\displaystyle (\Omega ,\mu _{\text{ref}})} defines a GAN game. There are 2 players: generator and discriminator. The generator's strategy set is P ( Ω ) {\displaystyle {\mathcal {P}}(\Omega )} , the set of all probability measures μ G {\displaystyle \mu _{G}} on Ω {\displaystyle \Omega } . The discriminator's strategy set is the set of Markov kernels μ D : Ω → P [ 0 , 1
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] {\displaystyle \mu _{D}:\Omega \to {\mathcal {P}}[0,1]} , where P [ 0 , 1 ] {\displaystyle {\mathcal {P}}[0,1]} is the set of probability measures on [ 0 , 1 ] {\displaystyle [0,1]} . The GAN game is a zero-sum game, with objective function L ( μ G , μ D ) := E x ∼ μ ref , y ∼ μ D ( x ) [ ln y ] + E x ∼ μ G , y ∼ μ D ( x ) [ ln ( 1 − y ) ] . {\displaystyle L(\mu _{G},\mu _{D}):=\operatorname {E} _{x\sim \mu _{\text{ref}},y\sim \mu _{D}(x)}[\ln y]+\operatorname {E} _{x\sim \mu _{G},y\sim \mu _{D}(x)}[\ln(1-y)].} The generator aims to minimize the objective, and the discriminator aims to maximize the objective. The generator's task is to approach μ G ≈ μ ref {\displaystyle \mu _{G}\approx \mu _{\text{ref}}} , that is, to match its own output distribution as closely as possible to the reference distribution. The discriminator's task is to output a value close to 1 when the input appears to be from the reference distribution, and to output a value close to 0 when the input looks like it came from the generator distribution. === In practice === The generative network generates candidates while the discriminative network evaluates them. The contest operates in terms of data distributions. Typically, the generative network learns to map from a latent space to a data distribution of interest, while the discriminative network distinguishes candidates produced by the generator from the true data distribution. The generative network's training objective is to increase the error rate of the discriminative network (i.e., "fool" the discriminator network by producing novel candidates that the discriminator thinks are not synthesized (are part of the true data distribution)). A known dataset serves as the
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initial training data for the discriminator. Training involves presenting it with samples from the training dataset until it achieves acceptable accuracy. The generator is trained based on whether it succeeds in fooling the discriminator. Typically, the generator is seeded with randomized input that is sampled from a predefined latent space (e.g. a multivariate normal distribution). Thereafter, candidates synthesized by the generator are evaluated by the discriminator. Independent backpropagation procedures are applied to both networks so that the generator produces better samples, while the discriminator becomes more skilled at flagging synthetic samples. When used for image generation, the generator is typically a deconvolutional neural network, and the discriminator is a convolutional neural network. === Relation to other statistical machine learning methods === GANs are implicit generative models, which means that they do not explicitly model the likelihood function nor provide a means for finding the latent variable corresponding to a given sample, unlike alternatives such as flow-based generative model. Compared to fully visible belief networks such as WaveNet and PixelRNN and autoregressive models in general, GANs can generate one complete sample in one pass, rather than multiple passes through the network. Compared to Boltzmann machines and linear ICA, there is no restriction on the type of function used by the network. Since neural networks are universal approximators, GANs are asymptotically consistent. Variational autoencoders might be universal approximators, but it is not proven as of 2017. == Mathematical properties == === Measure-theoretic considerations === This section provides some of the mathematical theory behind these methods. In modern probability theory based on measure theory, a probability space also needs to be equipped with a σ-algebra. As a result, a more rigorous definition of the GAN game would make the following changes:Each probability space ( Ω , B , μ ref ) {\displaystyle (\Omega
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,{\mathcal {B}},\mu _{\text{ref}})} defines a GAN game. The generator's strategy set is P ( Ω , B ) {\displaystyle {\mathcal {P}}(\Omega ,{\mathcal {B}})} , the set of all probability measures μ G {\displaystyle \mu _{G}} on the measure-space ( Ω , B ) {\displaystyle (\Omega ,{\mathcal {B}})} . The discriminator's strategy set is the set of Markov kernels μ D : ( Ω , B ) → P ( [ 0 , 1 ] , B ( [ 0 , 1 ] ) ) {\displaystyle \mu _{D}:(\Omega ,{\mathcal {B}})\to {\mathcal {P}}([0,1],{\mathcal {B}}([0,1]))} , where B ( [ 0 , 1 ] ) {\displaystyle {\mathcal {B}}([0,1])} is the Borel σ-algebra on [ 0 , 1 ] {\displaystyle [0,1]} .Since issues of measurability never arise in practice, these will not concern us further. === Choice of the strategy set === In the most generic version of the GAN game described above, the strategy set for the discriminator contains all Markov kernels μ D : Ω → P [ 0 , 1 ] {\displaystyle \mu _{D}:\Omega \to {\mathcal {P}}[0,1]} , and the strategy set for the generator contains arbitrary probability distributions μ G {\displaystyle \mu _{G}} on Ω {\displaystyle \Omega } . However, as shown below, the optimal discriminator strategy against any μ G {\displaystyle \mu _{G}} is deterministic, so there is no loss of generality in restricting the discriminator's strategies to deterministic functions D : Ω → [ 0 , 1 ] {\displaystyle D:\Omega \to [0,1]} . In most applications, D {\displaystyle D} is a deep neural network function. As for the generator, while μ G {\displaystyle \mu _{G}} could theoretically be any computable probability distribution, in practice, it is usually implemented as a pushforward: μ G = μ Z ∘ G − 1 {\displaystyle \mu _{G}=\mu _{Z}\circ G^{-1}} . That is,
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start with a random variable z ∼ μ Z {\displaystyle z\sim \mu _{Z}} , where μ Z {\displaystyle \mu _{Z}} is a probability distribution that is easy to compute (such as the uniform distribution, or the Gaussian distribution), then define a function G : Ω Z → Ω {\displaystyle G:\Omega _{Z}\to \Omega } . Then the distribution μ G {\displaystyle \mu _{G}} is the distribution of G ( z ) {\displaystyle G(z)} . Consequently, the generator's strategy is usually defined as just G {\displaystyle G} , leaving z ∼ μ Z {\displaystyle z\sim \mu _{Z}} implicit. In this formalism, the GAN game objective is L ( G , D ) := E x ∼ μ ref [ ln D ( x ) ] + E z ∼ μ Z [ ln ( 1 − D ( G ( z ) ) ) ] . {\displaystyle L(G,D):=\operatorname {E} _{x\sim \mu _{\text{ref}}}[\ln D(x)]+\operatorname {E} _{z\sim \mu _{Z}}[\ln(1-D(G(z)))].} === Generative reparametrization === The GAN architecture has two main components. One is casting optimization into a game, of form min G max D L ( G , D ) {\displaystyle \min _{G}\max _{D}L(G,D)} , which is different from the usual kind of optimization, of form min θ L ( θ ) {\displaystyle \min _{\theta }L(\theta )} . The other is the decomposition of μ G {\displaystyle \mu _{G}} into μ Z ∘ G − 1 {\displaystyle \mu _{Z}\circ G^{-1}} , which can be understood as a reparametrization trick. To see its significance, one must compare GAN with previous methods for learning generative models, which were plagued with "intractable probabilistic computations that arise in maximum likelihood estimation and related strategies". At the same time, Kingma and Welling and Rezende et al. developed the same idea of reparametrization into a general stochastic
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backpropagation method. Among its first applications was the variational autoencoder. === Move order and strategic equilibria === In the original paper, as well as most subsequent papers, it is usually assumed that the generator moves first, and the discriminator moves second, thus giving the following minimax game: min μ G max μ D L ( μ G , μ D ) := E x ∼ μ ref , y ∼ μ D ( x ) [ ln y ] + E x ∼ μ G , y ∼ μ D ( x ) [ ln ( 1 − y ) ] . {\displaystyle \min _{\mu _{G}}\max _{\mu _{D}}L(\mu _{G},\mu _{D}):=\operatorname {E} _{x\sim \mu _{\text{ref}},y\sim \mu _{D}(x)}[\ln y]+\operatorname {E} _{x\sim \mu _{G},y\sim \mu _{D}(x)}[\ln(1-y)].} If both the generator's and the discriminator's strategy sets are spanned by a finite number of strategies, then by the minimax theorem, min μ G max μ D L ( μ G , μ D ) = max μ D min μ G L ( μ G , μ D ) {\displaystyle \min _{\mu _{G}}\max _{\mu _{D}}L(\mu _{G},\mu _{D})=\max _{\mu _{D}}\min _{\mu _{G}}L(\mu _{G},\mu _{D})} that is, the move order does not matter. However, since the strategy sets are both not finitely spanned, the minimax theorem does not apply, and the idea of an "equilibrium" becomes delicate. To wit, there are the following different concepts of equilibrium: Equilibrium when generator moves first, and discriminator moves second: μ ^ G ∈ arg min μ G max μ D L ( μ G , μ D ) , μ ^ D ∈ arg max μ D L ( μ ^ G , μ D ) , {\displaystyle {\hat {\mu }}_{G}\in \arg \min _{\mu _{G}}\max _{\mu _{D}}L(\mu _{G},\mu _{D}),\quad {\hat {\mu }}_{D}\in \arg \max
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_{\mu _{D}}L({\hat {\mu }}_{G},\mu _{D}),\quad } Equilibrium when discriminator moves first, and generator moves second: μ ^ D ∈ arg max μ D min μ G L ( μ G , μ D ) , μ ^ G ∈ arg min μ G L ( μ G , μ ^ D ) , {\displaystyle {\hat {\mu }}_{D}\in \arg \max _{\mu _{D}}\min _{\mu _{G}}L(\mu _{G},\mu _{D}),\quad {\hat {\mu }}_{G}\in \arg \min _{\mu _{G}}L(\mu _{G},{\hat {\mu }}_{D}),} Nash equilibrium ( μ ^ D , μ ^ G ) {\displaystyle ({\hat {\mu }}_{D},{\hat {\mu }}_{G})} , which is stable under simultaneous move order: μ ^ D ∈ arg max μ D L ( μ ^ G , μ D ) , μ ^ G ∈ arg min μ G L ( μ G , μ ^ D ) {\displaystyle {\hat {\mu }}_{D}\in \arg \max _{\mu _{D}}L({\hat {\mu }}_{G},\mu _{D}),\quad {\hat {\mu }}_{G}\in \arg \min _{\mu _{G}}L(\mu _{G},{\hat {\mu }}_{D})} For general games, these equilibria do not have to agree, or even to exist. For the original GAN game, these equilibria all exist, and are all equal. However, for more general GAN games, these do not necessarily exist, or agree. === Main theorems for GAN game === The original GAN paper proved the following two theorems: Interpretation: For any fixed generator strategy μ G {\displaystyle \mu _{G}} , the optimal discriminator keeps track of the likelihood ratio between the reference distribution and the generator distribution: D ( x ) 1 − D ( x ) = d μ ref d μ G ( x ) = μ ref ( d x ) μ G ( d x ) ; D ( x ) = σ ( ln μ ref ( d x ) − ln μ G (
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d x ) ) {\displaystyle {\frac {D(x)}{1-D(x)}}={\frac {d\mu _{\text{ref}}}{d\mu _{G}}}(x)={\frac {\mu _{\text{ref}}(dx)}{\mu _{G}(dx)}};\quad D(x)=\sigma (\ln \mu _{\text{ref}}(dx)-\ln \mu _{G}(dx))} where σ {\displaystyle \sigma } is the logistic function. In particular, if the prior probability for an image x {\displaystyle x} to come from the reference distribution is equal to 1 2 {\displaystyle {\frac {1}{2}}} , then D ( x ) {\displaystyle D(x)} is just the posterior probability that x {\displaystyle x} came from the reference distribution: D ( x ) = Pr ( x came from reference distribution ∣ x ) . {\displaystyle D(x)=\Pr(x{\text{ came from reference distribution}}\mid x).} == Training and evaluating GAN == === Training === ==== Unstable convergence ==== While the GAN game has a unique global equilibrium point when both the generator and discriminator have access to their entire strategy sets, the equilibrium is no longer guaranteed when they have a restricted strategy set. In practice, the generator has access only to measures of form μ Z ∘ G θ − 1 {\displaystyle \mu _{Z}\circ G_{\theta }^{-1}} , where G θ {\displaystyle G_{\theta }} is a function computed by a neural network with parameters θ {\displaystyle \theta } , and μ Z {\displaystyle \mu _{Z}} is an easily sampled distribution, such as the uniform or normal distribution. Similarly, the discriminator has access only to functions of form D ζ {\displaystyle D_{\zeta }} , a function computed by a neural network with parameters ζ {\displaystyle \zeta } . These restricted strategy sets take up a vanishingly small proportion of their entire strategy sets. Further, even if an equilibrium still exists, it can only be found by searching in the high-dimensional space of all possible neural network functions. The standard strategy of using gradient descent to find the equilibrium often does not work for GAN, and often the
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game "collapses" into one of several failure modes. To improve the convergence stability, some training strategies start with an easier task, such as generating low-resolution images or simple images (one object with uniform background), and gradually increase the difficulty of the task during training. This essentially translates to applying a curriculum learning scheme. ==== Mode collapse ==== GANs often suffer from mode collapse where they fail to generalize properly, missing entire modes from the input data. For example, a GAN trained on the MNIST dataset containing many samples of each digit might only generate pictures of digit 0. This was termed "the Helvetica scenario". One way this can happen is if the generator learns too fast compared to the discriminator. If the discriminator D {\displaystyle D} is held constant, then the optimal generator would only output elements of arg max x D ( x ) {\displaystyle \arg \max _{x}D(x)} . So for example, if during GAN training for generating MNIST dataset, for a few epochs, the discriminator somehow prefers the digit 0 slightly more than other digits, the generator may seize the opportunity to generate only digit 0, then be unable to escape the local minimum after the discriminator improves. Some researchers perceive the root problem to be a weak discriminative network that fails to notice the pattern of omission, while others assign blame to a bad choice of objective function. Many solutions have been proposed, but it is still an open problem. Even the state-of-the-art architecture, BigGAN (2019), could not avoid mode collapse. The authors resorted to "allowing collapse to occur at the later stages of training, by which time a model is sufficiently trained to achieve good results". ==== Two time-scale update rule ==== The two time-scale update rule (TTUR) is proposed to make GAN convergence more
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stable by making the learning rate of the generator lower than that of the discriminator. The authors argued that the generator should move slower than the discriminator, so that it does not "drive the discriminator steadily into new regions without capturing its gathered information". They proved that a general class of games that included the GAN game, when trained under TTUR, "converges under mild assumptions to a stationary local Nash equilibrium". They also proposed using the Adam stochastic optimization to avoid mode collapse, as well as the Fréchet inception distance for evaluating GAN performances. ==== Vanishing gradient ==== Conversely, if the discriminator learns too fast compared to the generator, then the discriminator could almost perfectly distinguish μ G θ , μ ref {\displaystyle \mu _{G_{\theta }},\mu _{\text{ref}}} . In such case, the generator G θ {\displaystyle G_{\theta }} could be stuck with a very high loss no matter which direction it changes its θ {\displaystyle \theta } , meaning that the gradient ∇ θ L ( G θ , D ζ ) {\displaystyle \nabla _{\theta }L(G_{\theta },D_{\zeta })} would be close to zero. In such case, the generator cannot learn, a case of the vanishing gradient problem. Intuitively speaking, the discriminator is too good, and since the generator cannot take any small step (only small steps are considered in gradient descent) to improve its payoff, it does not even try. One important method for solving this problem is the Wasserstein GAN. === Evaluation === GANs are usually evaluated by Inception score (IS), which measures how varied the generator's outputs are (as classified by an image classifier, usually Inception-v3), or Fréchet inception distance (FID), which measures how similar the generator's outputs are to a reference set (as classified by a learned image featurizer, such as Inception-v3 without its final layer). Many
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papers that propose new GAN architectures for image generation report how their architectures break the state of the art on FID or IS. Another evaluation method is the Learned Perceptual Image Patch Similarity (LPIPS), which starts with a learned image featurizer f θ : Image → R n {\displaystyle f_{\theta }:{\text{Image}}\to \mathbb {R} ^{n}} , and finetunes it by supervised learning on a set of ( x , x ′ , p e r c e p t u a l d i f f e r e n c e ( x , x ′ ) ) {\displaystyle (x,x',\operatorname {perceptual~difference} (x,x'))} , where x {\displaystyle x} is an image, x ′ {\displaystyle x'} is a perturbed version of it, and p e r c e p t u a l d i f f e r e n c e ( x , x ′ ) {\displaystyle \operatorname {perceptual~difference} (x,x')} is how much they differ, as reported by human subjects. The model is finetuned so that it can approximate ‖ f θ ( x ) − f θ ( x ′ ) ‖ ≈ p e r c e p t u a l d i f f e r e n c e ( x , x ′ ) {\displaystyle \|f_{\theta }(x)-f_{\theta }(x')\|\approx \operatorname {perceptual~difference} (x,x')} . This finetuned model is then used to define LPIPS ( x , x ′ ) := ‖ f θ ( x ) − f θ ( x ′ ) ‖ {\displaystyle \operatorname {LPIPS} (x,x'):=\|f_{\theta }(x)-f_{\theta }(x')\|} . Other evaluation methods are reviewed in. == Variants == There is a veritable zoo of GAN variants. Some of the most prominent are as follows: === Conditional GAN === Conditional GANs are similar to standard GANs except they allow the
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model to conditionally generate samples based on additional information. For example, if we want to generate a cat face given a dog picture, we could use a conditional GAN. The generator in a GAN game generates μ G {\displaystyle \mu _{G}} , a probability distribution on the probability space Ω {\displaystyle \Omega } . This leads to the idea of a conditional GAN, where instead of generating one probability distribution on Ω {\displaystyle \Omega } , the generator generates a different probability distribution μ G ( c ) {\displaystyle \mu _{G}(c)} on Ω {\displaystyle \Omega } , for each given class label c {\displaystyle c} . For example, for generating images that look like ImageNet, the generator should be able to generate a picture of cat when given the class label "cat". In the original paper, the authors noted that GAN can be trivially extended to conditional GAN by providing the labels to both the generator and the discriminator. Concretely, the conditional GAN game is just the GAN game with class labels provided: L ( μ G , D ) := E c ∼ μ C , x ∼ μ ref ( c ) [ ln D ( x , c ) ] + E c ∼ μ C , x ∼ μ G ( c ) [ ln ( 1 − D ( x , c ) ) ] {\displaystyle L(\mu _{G},D):=\operatorname {E} _{c\sim \mu _{C},x\sim \mu _{\text{ref}}(c)}[\ln D(x,c)]+\operatorname {E} _{c\sim \mu _{C},x\sim \mu _{G}(c)}[\ln(1-D(x,c))]} where μ C {\displaystyle \mu _{C}} is a probability distribution over classes, μ ref ( c ) {\displaystyle \mu _{\text{ref}}(c)} is the probability distribution of real images of class c {\displaystyle c} , and μ G ( c ) {\displaystyle \mu _{G}(c)} the probability distribution of images generated by the
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generator when given class label c {\displaystyle c} . In 2017, a conditional GAN learned to generate 1000 image classes of ImageNet. === GANs with alternative architectures === The GAN game is a general framework and can be run with any reasonable parametrization of the generator G {\displaystyle G} and discriminator D {\displaystyle D} . In the original paper, the authors demonstrated it using multilayer perceptron networks and convolutional neural networks. Many alternative architectures have been tried. Deep convolutional GAN (DCGAN): For both generator and discriminator, uses only deep networks consisting entirely of convolution-deconvolution layers, that is, fully convolutional networks. Self-attention GAN (SAGAN): Starts with the DCGAN, then adds residually-connected standard self-attention modules to the generator and discriminator. Variational autoencoder GAN (VAEGAN): Uses a variational autoencoder (VAE) for the generator. Transformer GAN (TransGAN): Uses the pure transformer architecture for both the generator and discriminator, entirely devoid of convolution-deconvolution layers. Flow-GAN: Uses flow-based generative model for the generator, allowing efficient computation of the likelihood function. === GANs with alternative objectives === Many GAN variants are merely obtained by changing the loss functions for the generator and discriminator. Original GAN: We recast the original GAN objective into a form more convenient for comparison: { min D L D ( D , μ G ) = − E x ∼ μ G [ ln D ( x ) ] − E x ∼ μ ref [ ln ( 1 − D ( x ) ) ] min G L G ( D , μ G ) = − E x ∼ μ G [ ln ( 1 − D ( x ) ) ] {\displaystyle {\begin{cases}\min _{D}L_{D}(D,\mu _{G})=-\operatorname {E} _{x\sim \mu _{G}}[\ln D(x)]-\operatorname {E} _{x\sim \mu _{\text{ref}}}[\ln(1-D(x))]\\\min _{G}L_{G}(D,\mu _{G})=-\operatorname {E} _{x\sim \mu _{G}}[\ln(1-D(x))]\end{cases}}} Original GAN, non-saturating loss:
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This objective for generator was recommended in the original paper for faster convergence. L G = E x ∼ μ G [ ln D ( x ) ] {\displaystyle L_{G}=\operatorname {E} _{x\sim \mu _{G}}[\ln D(x)]} The effect of using this objective is analyzed in Section 2.2.2 of Arjovsky et al. Original GAN, maximum likelihood: L G = E x ∼ μ G [ ( exp ∘ σ − 1 ∘ D ) ( x ) ] {\displaystyle L_{G}=\operatorname {E} _{x\sim \mu _{G}}[({\exp }\circ \sigma ^{-1}\circ D)(x)]} where σ {\displaystyle \sigma } is the logistic function. When the discriminator is optimal, the generator gradient is the same as in maximum likelihood estimation, even though GAN cannot perform maximum likelihood estimation itself. Hinge loss GAN: L D = − E x ∼ p ref [ min ( 0 , − 1 + D ( x ) ) ] − E x ∼ μ G [ min ( 0 , − 1 − D ( x ) ) ] {\displaystyle L_{D}=-\operatorname {E} _{x\sim p_{\text{ref}}}\left[\min \left(0,-1+D(x)\right)\right]-\operatorname {E} _{x\sim \mu _{G}}\left[\min \left(0,-1-D\left(x\right)\right)\right]} L G = − E x ∼ μ G [ D ( x ) ] {\displaystyle L_{G}=-\operatorname {E} _{x\sim \mu _{G}}[D(x)]} Least squares GAN: L D = E x ∼ μ ref [ ( D ( x ) − b ) 2 ] + E x ∼ μ G [ ( D ( x ) − a ) 2 ] {\displaystyle L_{D}=\operatorname {E} _{x\sim \mu _{\text{ref}}}[(D(x)-b)^{2}]+\operatorname {E} _{x\sim \mu _{G}}[(D(x)-a)^{2}]} L G = E x ∼ μ G [ ( D ( x ) − c ) 2 ] {\displaystyle L_{G}=\operatorname {E} _{x\sim \mu _{G}}[(D(x)-c)^{2}]} where a , b , c {\displaystyle a,b,c} are parameters to be chosen. The authors recommended a = −
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1 , b = 1 , c = 0 {\displaystyle a=-1,b=1,c=0} . === Wasserstein GAN (WGAN) === The Wasserstein GAN modifies the GAN game at two points: The discriminator's strategy set is the set of measurable functions of type D : Ω → R {\displaystyle D:\Omega \to \mathbb {R} } with bounded Lipschitz norm: ‖ D ‖ L ≤ K {\displaystyle \|D\|_{L}\leq K} , where K {\displaystyle K} is a fixed positive constant. The objective is L W G A N ( μ G , D ) := E x ∼ μ G [ D ( x ) ] − E x ∼ μ ref [ D ( x ) ] {\displaystyle L_{WGAN}(\mu _{G},D):=\operatorname {E} _{x\sim \mu _{G}}[D(x)]-\mathbb {E} _{x\sim \mu _{\text{ref}}}[D(x)]} One of its purposes is to solve the problem of mode collapse (see above). The authors claim "In no experiment did we see evidence of mode collapse for the WGAN algorithm". === GANs with more than two players === ==== Adversarial autoencoder ==== An adversarial autoencoder (AAE) is more autoencoder than GAN. The idea is to start with a plain autoencoder, but train a discriminator to discriminate the latent vectors from a reference distribution (often the normal distribution). ==== InfoGAN ==== In conditional GAN, the generator receives both a noise vector z {\displaystyle z} and a label c {\displaystyle c} , and produces an image G ( z , c ) {\displaystyle G(z,c)} . The discriminator receives image-label pairs ( x , c ) {\displaystyle (x,c)} , and computes D ( x , c ) {\displaystyle D(x,c)} . When the training dataset is unlabeled, conditional GAN does not work directly. The idea of InfoGAN is to decree that every latent vector in the latent space can be decomposed as ( z , c ) {\displaystyle (z,c)} :
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an incompressible noise part z {\displaystyle z} , and an informative label part c {\displaystyle c} , and encourage the generator to comply with the decree, by encouraging it to maximize I ( c , G ( z , c ) ) {\displaystyle I(c,G(z,c))} , the mutual information between c {\displaystyle c} and G ( z , c ) {\displaystyle G(z,c)} , while making no demands on the mutual information z {\displaystyle z} between G ( z , c ) {\displaystyle G(z,c)} . Unfortunately, I ( c , G ( z , c ) ) {\displaystyle I(c,G(z,c))} is intractable in general, The key idea of InfoGAN is Variational Mutual Information Maximization: indirectly maximize it by maximizing a lower bound I ^ ( G , Q ) = E z ∼ μ Z , c ∼ μ C [ ln Q ( c ∣ G ( z , c ) ) ] ; I ( c , G ( z , c ) ) ≥ sup Q I ^ ( G , Q ) {\displaystyle {\hat {I}}(G,Q)=\mathbb {E} _{z\sim \mu _{Z},c\sim \mu _{C}}[\ln Q(c\mid G(z,c))];\quad I(c,G(z,c))\geq \sup _{Q}{\hat {I}}(G,Q)} where Q {\displaystyle Q} ranges over all Markov kernels of type Q : Ω Y → P ( Ω C ) {\displaystyle Q:\Omega _{Y}\to {\mathcal {P}}(\Omega _{C})} . The InfoGAN game is defined as follows:Three probability spaces define an InfoGAN game: ( Ω X , μ ref ) {\displaystyle (\Omega _{X},\mu _{\text{ref}})} , the space of reference images. ( Ω Z , μ Z ) {\displaystyle (\Omega _{Z},\mu _{Z})} , the fixed random noise generator. ( Ω C , μ C ) {\displaystyle (\Omega _{C},\mu _{C})} , the fixed random information generator. There are 3 players in 2 teams: generator, Q, and discriminator. The generator and Q are on one team,
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and the discriminator on the other team. The objective function is L ( G , Q , D ) = L G A N ( G , D ) − λ I ^ ( G , Q ) {\displaystyle L(G,Q,D)=L_{GAN}(G,D)-\lambda {\hat {I}}(G,Q)} where L G A N ( G , D ) = E x ∼ μ ref , [ ln D ( x ) ] + E z ∼ μ Z [ ln ( 1 − D ( G ( z , c ) ) ) ] {\displaystyle L_{GAN}(G,D)=\operatorname {E} _{x\sim \mu _{\text{ref}},}[\ln D(x)]+\operatorname {E} _{z\sim \mu _{Z}}[\ln(1-D(G(z,c)))]} is the original GAN game objective, and I ^ ( G , Q ) = E z ∼ μ Z , c ∼ μ C [ ln Q ( c ∣ G ( z , c ) ) ] {\displaystyle {\hat {I}}(G,Q)=\mathbb {E} _{z\sim \mu _{Z},c\sim \mu _{C}}[\ln Q(c\mid G(z,c))]} Generator-Q team aims to minimize the objective, and discriminator aims to maximize it: min G , Q max D L ( G , Q , D ) {\displaystyle \min _{G,Q}\max _{D}L(G,Q,D)} ==== Bidirectional GAN (BiGAN) ==== The standard GAN generator is a function of type G : Ω Z → Ω X {\displaystyle G:\Omega _{Z}\to \Omega _{X}} , that is, it is a mapping from a latent space Ω Z {\displaystyle \Omega _{Z}} to the image space Ω X {\displaystyle \Omega _{X}} . This can be understood as a "decoding" process, whereby every latent vector z ∈ Ω Z {\displaystyle z\in \Omega _{Z}} is a code for an image x ∈ Ω X {\displaystyle x\in \Omega _{X}} , and the generator performs the decoding. This naturally leads to the idea of training another network that performs "encoding", creating an autoencoder out of the encoder-generator pair. Already
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in the original paper, the authors noted that "Learned approximate inference can be performed by training an auxiliary network to predict z {\displaystyle z} given x {\displaystyle x} ". The bidirectional GAN architecture performs exactly this. The BiGAN is defined as follows: Two probability spaces define a BiGAN game: ( Ω X , μ X ) {\displaystyle (\Omega _{X},\mu _{X})} , the space of reference images. ( Ω Z , μ Z ) {\displaystyle (\Omega _{Z},\mu _{Z})} , the latent space. There are 3 players in 2 teams: generator, encoder, and discriminator. The generator and encoder are on one team, and the discriminator on the other team. The generator's strategies are functions G : Ω Z → Ω X {\displaystyle G:\Omega _{Z}\to \Omega _{X}} , and the encoder's strategies are functions E : Ω X → Ω Z {\displaystyle E:\Omega _{X}\to \Omega _{Z}} . The discriminator's strategies are functions D : Ω X → [ 0 , 1 ] {\displaystyle D:\Omega _{X}\to [0,1]} . The objective function is L ( G , E , D ) = E x ∼ μ X [ ln D ( x , E ( x ) ) ] + E z ∼ μ Z [ ln ( 1 − D ( G ( z ) , z ) ) ] {\displaystyle L(G,E,D)=\mathbb {E} _{x\sim \mu _{X}}[\ln D(x,E(x))]+\mathbb {E} _{z\sim \mu _{Z}}[\ln(1-D(G(z),z))]} Generator-encoder team aims to minimize the objective, and discriminator aims to maximize it: min G , E max D L ( G , E , D ) {\displaystyle \min _{G,E}\max _{D}L(G,E,D)} In the paper, they gave a more abstract definition of the objective as: L ( G , E , D ) = E ( x , z ) ∼ μ E , X [ ln D ( x ,
|
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z ) ] + E ( x , z ) ∼ μ G , Z [ ln ( 1 − D ( x , z ) ) ] {\displaystyle L(G,E,D)=\mathbb {E} _{(x,z)\sim \mu _{E,X}}[\ln D(x,z)]+\mathbb {E} _{(x,z)\sim \mu _{G,Z}}[\ln(1-D(x,z))]} where μ E , X ( d x , d z ) = μ X ( d x ) ⋅ δ E ( x ) ( d z ) {\displaystyle \mu _{E,X}(dx,dz)=\mu _{X}(dx)\cdot \delta _{E(x)}(dz)} is the probability distribution on Ω X × Ω Z {\displaystyle \Omega _{X}\times \Omega _{Z}} obtained by pushing μ X {\displaystyle \mu _{X}} forward via x ↦ ( x , E ( x ) ) {\displaystyle x\mapsto (x,E(x))} , and μ G , Z ( d x , d z ) = δ G ( z ) ( d x ) ⋅ μ Z ( d z ) {\displaystyle \mu _{G,Z}(dx,dz)=\delta _{G(z)}(dx)\cdot \mu _{Z}(dz)} is the probability distribution on Ω X × Ω Z {\displaystyle \Omega _{X}\times \Omega _{Z}} obtained by pushing μ Z {\displaystyle \mu _{Z}} forward via z ↦ ( G ( x ) , z ) {\displaystyle z\mapsto (G(x),z)} . Applications of bidirectional models include semi-supervised learning, interpretable machine learning, and neural machine translation. ==== CycleGAN ==== CycleGAN is an architecture for performing translations between two domains, such as between photos of horses and photos of zebras, or photos of night cities and photos of day cities. The CycleGAN game is defined as follows:There are two probability spaces ( Ω X , μ X ) , ( Ω Y , μ Y ) {\displaystyle (\Omega _{X},\mu _{X}),(\Omega _{Y},\mu _{Y})} , corresponding to the two domains needed for translations fore-and-back. There are 4 players in 2 teams: generators G X : Ω X → Ω Y , G Y : Ω Y →
|
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Ω X {\displaystyle G_{X}:\Omega _{X}\to \Omega _{Y},G_{Y}:\Omega _{Y}\to \Omega _{X}} , and discriminators D X : Ω X → [ 0 , 1 ] , D Y : Ω Y → [ 0 , 1 ] {\displaystyle D_{X}:\Omega _{X}\to [0,1],D_{Y}:\Omega _{Y}\to [0,1]} . The objective function is L ( G X , G Y , D X , D Y ) = L G A N ( G X , D X ) + L G A N ( G Y , D Y ) + λ L c y c l e ( G X , G Y ) {\displaystyle L(G_{X},G_{Y},D_{X},D_{Y})=L_{GAN}(G_{X},D_{X})+L_{GAN}(G_{Y},D_{Y})+\lambda L_{cycle}(G_{X},G_{Y})} where λ {\displaystyle \lambda } is a positive adjustable parameter, L G A N {\displaystyle L_{GAN}} is the GAN game objective, and L c y c l e {\displaystyle L_{cycle}} is the cycle consistency loss: L c y c l e ( G X , G Y ) = E x ∼ μ X ‖ G X ( G Y ( x ) ) − x ‖ + E y ∼ μ Y ‖ G Y ( G X ( y ) ) − y ‖ {\displaystyle L_{cycle}(G_{X},G_{Y})=E_{x\sim \mu _{X}}\|G_{X}(G_{Y}(x))-x\|+E_{y\sim \mu _{Y}}\|G_{Y}(G_{X}(y))-y\|} The generators aim to minimize the objective, and the discriminators aim to maximize it: min G X , G Y max D X , D Y L ( G X , G Y , D X , D Y ) {\displaystyle \min _{G_{X},G_{Y}}\max _{D_{X},D_{Y}}L(G_{X},G_{Y},D_{X},D_{Y})} Unlike previous work like pix2pix, which requires paired training data, cycleGAN requires no paired data. For example, to train a pix2pix model to turn a summer scenery photo to winter scenery photo and back, the dataset must contain pairs of the same place in summer and winter, shot at the same angle; cycleGAN would only need a set of summer scenery
|
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"page_id": 50073184,
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photos, and an unrelated set of winter scenery photos. === GANs with particularly large or small scales === ==== BigGAN ==== The BigGAN is essentially a self-attention GAN trained on a large scale (up to 80 million parameters) to generate large images of ImageNet (up to 512 x 512 resolution), with numerous engineering tricks to make it converge. ==== Invertible data augmentation ==== When there is insufficient training data, the reference distribution μ ref {\displaystyle \mu _{\text{ref}}} cannot be well-approximated by the empirical distribution given by the training dataset. In such cases, data augmentation can be applied, to allow training GAN on smaller datasets. Naïve data augmentation, however, brings its problems. Consider the original GAN game, slightly reformulated as follows: { min D L D ( D , μ G ) = − E x ∼ μ ref [ ln D ( x ) ] − E x ∼ μ G [ ln ( 1 − D ( x ) ) ] min G L G ( D , μ G ) = − E x ∼ μ G [ ln ( 1 − D ( x ) ) ] {\displaystyle {\begin{cases}\min _{D}L_{D}(D,\mu _{G})=-\operatorname {E} _{x\sim \mu _{\text{ref}}}[\ln D(x)]-\operatorname {E} _{x\sim \mu _{G}}[\ln(1-D(x))]\\\min _{G}L_{G}(D,\mu _{G})=-\operatorname {E} _{x\sim \mu _{G}}[\ln(1-D(x))]\end{cases}}} Now we use data augmentation by randomly sampling semantic-preserving transforms T : Ω → Ω {\displaystyle T:\Omega \to \Omega } and applying them to the dataset, to obtain the reformulated GAN game: { min D L D ( D , μ G ) = − E x ∼ μ ref , T ∼ μ trans [ ln D ( T ( x ) ) ] − E x ∼ μ G [ ln ( 1 − D ( x ) )
|
{
"page_id": 50073184,
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"title": "Generative adversarial network"
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] min G L G ( D , μ G ) = − E x ∼ μ G [ ln ( 1 − D ( x ) ) ] {\displaystyle {\begin{cases}\min _{D}L_{D}(D,\mu _{G})=-\operatorname {E} _{x\sim \mu _{\text{ref}},T\sim \mu _{\text{trans}}}[\ln D(T(x))]-\operatorname {E} _{x\sim \mu _{G}}[\ln(1-D(x))]\\\min _{G}L_{G}(D,\mu _{G})=-\operatorname {E} _{x\sim \mu _{G}}[\ln(1-D(x))]\end{cases}}} This is equivalent to a GAN game with a different distribution μ ref ′ {\displaystyle \mu _{\text{ref}}'} , sampled by T ( x ) {\displaystyle T(x)} , with x ∼ μ ref , T ∼ μ trans {\displaystyle x\sim \mu _{\text{ref}},T\sim \mu _{\text{trans}}} . For example, if μ ref {\displaystyle \mu _{\text{ref}}} is the distribution of images in ImageNet, and μ trans {\displaystyle \mu _{\text{trans}}} samples identity-transform with probability 0.5, and horizontal-reflection with probability 0.5, then μ ref ′ {\displaystyle \mu _{\text{ref}}'} is the distribution of images in ImageNet and horizontally-reflected ImageNet, combined. The result of such training would be a generator that mimics μ ref ′ {\displaystyle \mu _{\text{ref}}'} . For example, it would generate images that look like they are randomly cropped, if the data augmentation uses random cropping. The solution is to apply data augmentation to both generated and real images: { min D L D ( D , μ G ) = − E x ∼ μ ref , T ∼ μ trans [ ln D ( T ( x ) ) ] − E x ∼ μ G , T ∼ μ trans [ ln ( 1 − D ( T ( x ) ) ) ] min G L G ( D , μ G ) = − E x ∼ μ G , T ∼ μ trans [ ln ( 1 − D ( T ( x ) ) ) ] {\displaystyle {\begin{cases}\min _{D}L_{D}(D,\mu _{G})=-\operatorname
|
{
"page_id": 50073184,
"source": null,
"title": "Generative adversarial network"
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{E} _{x\sim \mu _{\text{ref}},T\sim \mu _{\text{trans}}}[\ln D(T(x))]-\operatorname {E} _{x\sim \mu _{G},T\sim \mu _{\text{trans}}}[\ln(1-D(T(x)))]\\\min _{G}L_{G}(D,\mu _{G})=-\operatorname {E} _{x\sim \mu _{G},T\sim \mu _{\text{trans}}}[\ln(1-D(T(x)))]\end{cases}}} The authors demonstrated high-quality generation using just 100-picture-large datasets. The StyleGAN-2-ADA paper points out a further point on data augmentation: it must be invertible. Continue with the example of generating ImageNet pictures. If the data augmentation is "randomly rotate the picture by 0, 90, 180, 270 degrees with equal probability", then there is no way for the generator to know which is the true orientation: Consider two generators G , G ′ {\displaystyle G,G'} , such that for any latent z {\displaystyle z} , the generated image G ( z ) {\displaystyle G(z)} is a 90-degree rotation of G ′ ( z ) {\displaystyle G'(z)} . They would have exactly the same expected loss, and so neither is preferred over the other. The solution is to only use invertible data augmentation: instead of "randomly rotate the picture by 0, 90, 180, 270 degrees with equal probability", use "randomly rotate the picture by 90, 180, 270 degrees with 0.1 probability, and keep the picture as it is with 0.7 probability". This way, the generator is still rewarded to keep images oriented the same way as un-augmented ImageNet pictures. Abstractly, the effect of randomly sampling transformations T : Ω → Ω {\displaystyle T:\Omega \to \Omega } from the distribution μ trans {\displaystyle \mu _{\text{trans}}} is to define a Markov kernel K trans : Ω → P ( Ω ) {\displaystyle K_{\text{trans}}:\Omega \to {\mathcal {P}}(\Omega )} . Then, the data-augmented GAN game pushes the generator to find some μ ^ G ∈ P ( Ω ) {\displaystyle {\hat {\mu }}_{G}\in {\mathcal {P}}(\Omega )} , such that K trans ∗ μ ref = K trans ∗ μ ^ G {\displaystyle K_{\text{trans}}*\mu _{\text{ref}}=K_{\text{trans}}*{\hat {\mu
|
{
"page_id": 50073184,
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}}_{G}} where ∗ {\displaystyle *} is the Markov kernel convolution. A data-augmentation method is defined to be invertible if its Markov kernel K trans {\displaystyle K_{\text{trans}}} satisfies K trans ∗ μ = K trans ∗ μ ′ ⟹ μ = μ ′ ∀ μ , μ ′ ∈ P ( Ω ) {\displaystyle K_{\text{trans}}*\mu =K_{\text{trans}}*\mu '\implies \mu =\mu '\quad \forall \mu ,\mu '\in {\mathcal {P}}(\Omega )} Immediately by definition, we see that composing multiple invertible data-augmentation methods results in yet another invertible method. Also by definition, if the data-augmentation method is invertible, then using it in a GAN game does not change the optimal strategy μ ^ G {\displaystyle {\hat {\mu }}_{G}} for the generator, which is still μ ref {\displaystyle \mu _{\text{ref}}} . There are two prototypical examples of invertible Markov kernels: Discrete case: Invertible stochastic matrices, when Ω {\displaystyle \Omega } is finite. For example, if Ω = { ↑ , ↓ , ← , → } {\displaystyle \Omega =\{\uparrow ,\downarrow ,\leftarrow ,\rightarrow \}} is the set of four images of an arrow, pointing in 4 directions, and the data augmentation is "randomly rotate the picture by 90, 180, 270 degrees with probability p {\displaystyle p} , and keep the picture as it is with probability ( 1 − 3 p ) {\displaystyle (1-3p)} ", then the Markov kernel K trans {\displaystyle K_{\text{trans}}} can be represented as a stochastic matrix: [ K trans ] = [ ( 1 − 3 p ) p p p p ( 1 − 3 p ) p p p p ( 1 − 3 p ) p p p p ( 1 − 3 p ) ] {\displaystyle [K_{\text{trans}}]={\begin{bmatrix}(1-3p)&p&p&p\\p&(1-3p)&p&p\\p&p&(1-3p)&p\\p&p&p&(1-3p)\end{bmatrix}}} and K trans {\displaystyle K_{\text{trans}}} is an invertible kernel iff [ K trans ] {\displaystyle [K_{\text{trans}}]} is an invertible matrix, that is, p
|
{
"page_id": 50073184,
"source": null,
"title": "Generative adversarial network"
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≠ 1 / 4 {\displaystyle p\neq 1/4} . Continuous case: The gaussian kernel, when Ω = R n {\displaystyle \Omega =\mathbb {R} ^{n}} for some n ≥ 1 {\displaystyle n\geq 1} . For example, if Ω = R 256 2 {\displaystyle \Omega =\mathbb {R} ^{256^{2}}} is the space of 256x256 images, and the data-augmentation method is "generate a gaussian noise z ∼ N ( 0 , I 256 2 ) {\displaystyle z\sim {\mathcal {N}}(0,I_{256^{2}})} , then add ϵ z {\displaystyle \epsilon z} to the image", then K trans {\displaystyle K_{\text{trans}}} is just convolution by the density function of N ( 0 , ϵ 2 I 256 2 ) {\displaystyle {\mathcal {N}}(0,\epsilon ^{2}I_{256^{2}})} . This is invertible, because convolution by a gaussian is just convolution by the heat kernel, so given any μ ∈ P ( R n ) {\displaystyle \mu \in {\mathcal {P}}(\mathbb {R} ^{n})} , the convolved distribution K trans ∗ μ {\displaystyle K_{\text{trans}}*\mu } can be obtained by heating up R n {\displaystyle \mathbb {R} ^{n}} precisely according to μ {\displaystyle \mu } , then wait for time ϵ 2 / 4 {\displaystyle \epsilon ^{2}/4} . With that, we can recover μ {\displaystyle \mu } by running the heat equation backwards in time for ϵ 2 / 4 {\displaystyle \epsilon ^{2}/4} . More examples of invertible data augmentations are found in the paper. ==== SinGAN ==== SinGAN pushes data augmentation to the limit, by using only a single image as training data and performing data augmentation on it. The GAN architecture is adapted to this training method by using a multi-scale pipeline. The generator G {\displaystyle G} is decomposed into a pyramid of generators G = G 1 ∘ G 2 ∘ ⋯ ∘ G N {\displaystyle G=G_{1}\circ G_{2}\circ \cdots \circ G_{N}} , with the lowest one generating
|
{
"page_id": 50073184,
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the image G N ( z N ) {\displaystyle G_{N}(z_{N})} at the lowest resolution, then the generated image is scaled up to r ( G N ( z N ) ) {\displaystyle r(G_{N}(z_{N}))} , and fed to the next level to generate an image G N − 1 ( z N − 1 + r ( G N ( z N ) ) ) {\displaystyle G_{N-1}(z_{N-1}+r(G_{N}(z_{N})))} at a higher resolution, and so on. The discriminator is decomposed into a pyramid as well. === StyleGAN series === The StyleGAN family is a series of architectures published by Nvidia's research division. ==== Progressive GAN ==== Progressive GAN is a method for training GAN for large-scale image generation stably, by growing a GAN generator from small to large scale in a pyramidal fashion. Like SinGAN, it decomposes the generator as G = G 1 ∘ G 2 ∘ ⋯ ∘ G N {\displaystyle G=G_{1}\circ G_{2}\circ \cdots \circ G_{N}} , and the discriminator as D = D 1 ∘ D 2 ∘ ⋯ ∘ D N {\displaystyle D=D_{1}\circ D_{2}\circ \cdots \circ D_{N}} . During training, at first only G N , D N {\displaystyle G_{N},D_{N}} are used in a GAN game to generate 4x4 images. Then G N − 1 , D N − 1 {\displaystyle G_{N-1},D_{N-1}} are added to reach the second stage of GAN game, to generate 8x8 images, and so on, until we reach a GAN game to generate 1024x1024 images. To avoid shock between stages of the GAN game, each new layer is "blended in" (Figure 2 of the paper). For example, this is how the second stage GAN game starts: Just before, the GAN game consists of the pair G N , D N {\displaystyle G_{N},D_{N}} generating and discriminating 4x4 images. Just after, the GAN game consists of the
|
{
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pair ( ( 1 − α ) + α ⋅ G N − 1 ) ∘ u ∘ G N , D N ∘ d ∘ ( ( 1 − α ) + α ⋅ D N − 1 ) {\displaystyle ((1-\alpha )+\alpha \cdot G_{N-1})\circ u\circ G_{N},D_{N}\circ d\circ ((1-\alpha )+\alpha \cdot D_{N-1})} generating and discriminating 8x8 images. Here, the functions u , d {\displaystyle u,d} are image up- and down-sampling functions, and α {\displaystyle \alpha } is a blend-in factor (much like an alpha in image composing) that smoothly glides from 0 to 1. ==== StyleGAN-1 ==== StyleGAN-1 is designed as a combination of Progressive GAN with neural style transfer. The key architectural choice of StyleGAN-1 is a progressive growth mechanism, similar to Progressive GAN. Each generated image starts as a constant 4 × 4 × 512 {\displaystyle 4\times 4\times 512} array, and repeatedly passed through style blocks. Each style block applies a "style latent vector" via affine transform ("adaptive instance normalization"), similar to how neural style transfer uses Gramian matrix. It then adds noise, and normalize (subtract the mean, then divide by the variance). At training time, usually only one style latent vector is used per image generated, but sometimes two ("mixing regularization") in order to encourage each style block to independently perform its stylization without expecting help from other style blocks (since they might receive an entirely different style latent vector). After training, multiple style latent vectors can be fed into each style block. Those fed to the lower layers control the large-scale styles, and those fed to the higher layers control the fine-detail styles. Style-mixing between two images x , x ′ {\displaystyle x,x'} can be performed as well. First, run a gradient descent to find z , z ′ {\displaystyle z,z'} such that G ( z
|
{
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) ≈ x , G ( z ′ ) ≈ x ′ {\displaystyle G(z)\approx x,G(z')\approx x'} . This is called "projecting an image back to style latent space". Then, z {\displaystyle z} can be fed to the lower style blocks, and z ′ {\displaystyle z'} to the higher style blocks, to generate a composite image that has the large-scale style of x {\displaystyle x} , and the fine-detail style of x ′ {\displaystyle x'} . Multiple images can also be composed this way. ==== StyleGAN-2 ==== StyleGAN-2 improves upon StyleGAN-1, by using the style latent vector to transform the convolution layer's weights instead, thus solving the "blob" problem. This was updated by the StyleGAN-2-ADA ("ADA" stands for "adaptive"), which uses invertible data augmentation as described above. It also tunes the amount of data augmentation applied by starting at zero, and gradually increasing it until an "overfitting heuristic" reaches a target level, thus the name "adaptive". ==== StyleGAN-3 ==== StyleGAN-3 improves upon StyleGAN-2 by solving the "texture sticking" problem, which can be seen in the official videos. They analyzed the problem by the Nyquist–Shannon sampling theorem, and argued that the layers in the generator learned to exploit the high-frequency signal in the pixels they operate upon. To solve this, they proposed imposing strict lowpass filters between each generator's layers, so that the generator is forced to operate on the pixels in a way faithful to the continuous signals they represent, rather than operate on them as merely discrete signals. They further imposed rotational and translational invariance by using more signal filters. The resulting StyleGAN-3 is able to solve the texture sticking problem, as well as generating images that rotate and translate smoothly. == Other uses == Other than for generative and discriminative modelling of data, GANs have been used for other
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"page_id": 50073184,
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things. GANs have been used for transfer learning to enforce the alignment of the latent feature space, such as in deep reinforcement learning. This works by feeding the embeddings of the source and target task to the discriminator which tries to guess the context. The resulting loss is then (inversely) backpropagated through the encoder. == Applications == === Science === Iteratively reconstruct astronomical images Simulate gravitational lensing for dark matter research. Model the distribution of dark matter in a particular direction in space and to predict the gravitational lensing that will occur. Model high energy jet formation and showers through calorimeters of high-energy physics experiments. Approximate bottlenecks in computationally expensive simulations of particle physics experiments. Applications in the context of present and proposed CERN experiments have demonstrated the potential of these methods for accelerating simulation and/or improving simulation fidelity. Reconstruct velocity and scalar fields in turbulent flows. GAN-generated molecules were validated experimentally in mice. === Medical === One of the major concerns in medical imaging is preserving patient privacy. Due to these reasons, researchers often face difficulties in obtaining medical images for their research purposes. GAN has been used for generating synthetic medical images, such as MRI and PET images to address this challenge. GAN can be used to detect glaucomatous images helping the early diagnosis which is essential to avoid partial or total loss of vision. GANs have been used to create forensic facial reconstructions of deceased historical figures. === Malicious === Concerns have been raised about the potential use of GAN-based human image synthesis for sinister purposes, e.g., to produce fake, possibly incriminating, photographs and videos. GANs can be used to generate unique, realistic profile photos of people who do not exist, in order to automate creation of fake social media profiles. In 2019 the state of California
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"page_id": 50073184,
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considered and passed on October 3, 2019, the bill AB-602, which bans the use of human image synthesis technologies to make fake pornography without the consent of the people depicted, and bill AB-730, which prohibits distribution of manipulated videos of a political candidate within 60 days of an election. Both bills were authored by Assembly member Marc Berman and signed by Governor Gavin Newsom. The laws went into effect in 2020. DARPA's Media Forensics program studies ways to counteract fake media, including fake media produced using GANs. === Fashion, art and advertising === GANs can be used to generate art; The Verge wrote in March 2019 that "The images created by GANs have become the defining look of contemporary AI art." GANs can also be used to inpaint photographs generate fashion models, shadows, photorealistic renders of interior design, industrial design, shoes, etc. Such networks were reported to be used by Facebook. Some have worked with using GAN for artistic creativity, as "creative adversarial network". A GAN, trained on a set of 15,000 portraits from WikiArt from the 14th to the 19th century, created the 2018 painting Edmond de Belamy, which sold for US$432,500. GANs were used by the video game modding community to up-scale low-resolution 2D textures in old video games by recreating them in 4k or higher resolutions via image training, and then down-sampling them to fit the game's native resolution (resembling supersampling anti-aliasing). In 2020, Artbreeder was used to create the main antagonist in the sequel to the psychological web horror series Ben Drowned. The author would later go on to praise GAN applications for their ability to help generate assets for independent artists who are short on budget and manpower. In May 2020, Nvidia researchers taught an AI system (termed "GameGAN") to recreate the game of Pac-Man
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"page_id": 50073184,
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simply by watching it being played. In August 2019, a large dataset consisting of 12,197 MIDI songs each with paired lyrics and melody alignment was created for neural melody generation from lyrics using conditional GAN-LSTM (refer to sources at GitHub AI Melody Generation from Lyrics). === Miscellaneous === GANs have been used to show how an individual's appearance might change with age. reconstruct 3D models of objects from images, generate novel objects as 3D point clouds, model patterns of motion in video. inpaint missing features in maps, transfer map styles in cartography or augment street view imagery. use feedback to generate images and replace image search systems. visualize the effect that climate change will have on specific houses. reconstruct an image of a person's face after listening to their voice. produces videos of a person speaking, given only a single photo of that person. recurrent sequence generation. == History == In 1991, Juergen Schmidhuber published "artificial curiosity", neural networks in a zero-sum game. The first network is a generative model that models a probability distribution over output patterns. The second network learns by gradient descent to predict the reactions of the environment to these patterns. GANs can be regarded as a case where the environmental reaction is 1 or 0 depending on whether the first network's output is in a given set. Other people had similar ideas but did not develop them similarly. An idea involving adversarial networks was published in a 2010 blog post by Olli Niemitalo. This idea was never implemented and did not involve stochasticity in the generator and thus was not a generative model. It is now known as a conditional GAN or cGAN. An idea similar to GANs was used to model animal behavior by Li, Gauci and Gross in 2013. Another inspiration for GANs
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was noise-contrastive estimation, which uses the same loss function as GANs and which Goodfellow studied during his PhD in 2010–2014. Adversarial machine learning has other uses besides generative modeling and can be applied to models other than neural networks. In control theory, adversarial learning based on neural networks was used in 2006 to train robust controllers in a game theoretic sense, by alternating the iterations between a minimizer policy, the controller, and a maximizer policy, the disturbance. In 2017, a GAN was used for image enhancement focusing on realistic textures rather than pixel-accuracy, producing a higher image quality at high magnification. In 2017, the first faces were generated. These were exhibited in February 2018 at the Grand Palais. Faces generated by StyleGAN in 2019 drew comparisons with Deepfakes. == See also == Artificial intelligence art – Visual media created with AI Deepfake – Realistic artificially generated media Deep learning – Branch of machine learning Diffusion model – Deep learning algorithm Generative artificial intelligence – Subset of AI using generative models Synthetic media – Artificial production, manipulation, and modification of data and media by automated means == References == == External links == Knight, Will. "5 Big Predictions for Artificial Intelligence in 2017". MIT Technology Review. Retrieved January 5, 2017. Karras, Tero; Laine, Samuli; Aila, Timo (2018). "A Style-Based Generator Architecture for Generative Adversarial Networks". arXiv:1812.04948 [cs.NE]. This Person Does Not Exist – photorealistic images of people who do not exist, generated by StyleGAN This Cat Does Not Exist Archived March 5, 2019, at the Wayback Machine – photorealistic images of cats who do not exist, generated by StyleGAN Wang, Zhengwei; She, Qi; Ward, Tomas E. (2019). "Generative Adversarial Networks in Computer Vision: A Survey and Taxonomy". arXiv:1906.01529 [cs.LG].
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The Leuckart reaction is the chemical reaction that converts aldehydes or ketones to amines. The reaction is an example of reductive amination. The reaction, named after Rudolf Leuckart, uses either ammonium formate or formamide as the nitrogen donor and reducing agent. It requires high temperatures, usually between 120 and 130 °C; for the formamide variant, the temperature can be greater than 165 °C. == History == The Leuckart reaction is named in honor of its developer, the German chemist Rudolf Leuckart (1854–1899). He discovered that heating benzaldehyde with formamide does not produce benzylidenediformamide as anticipated, but benzylamine. In 1891, a colleague of Leuckart at the University of Göttingen, Otto Wallach, performed further reactions using alicyclic and terpenoid ketones as well as aldehydes, demonstrating the general application. Over the course of the past century, chemists have discovered several methods to improve the yield of the reaction and carry it out under less strenuous conditions. Pollard and Young summarized various ways in which amines can be formed: using either formamide or ammonium formate, or both, or adding formic acid to formamide. However, using just ammonium formate as the reagent produces the best yields. Using formamide produces low yields compared to ammonium formate but yields can be increased by using large amount of formamide, or using ammonium formate, ammonium sulfate, and magnesium chloride as catalysts. == Mechanism == === Ammonium formate as reagent === Ammonium formate is a source of formic acid and ammonia. Starting with nucleophilic attack on the carbonyl by the ammonia, the carbonyl is converted to the iminium ion: NH4HCO2 ⇌ NH3 + HCO2H NH3 + R2C=O + HCO2H → R2C=NH+2 + HCO−2 The iminium is then reduced by the formate: R2C=NH+2 + HCO−2 → R2CH−NH2 + CO2 === Formamide as reagent === Formamide first nucleophilically attacks the carbonyl carbon.
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{
"page_id": 5901920,
"source": null,
"title": "Leuckart reaction"
}
|
The oxygen is protonated by abstracting hydrogen from the nitrogen atom, subsequently forming a water molecule that leaves, forming N-formyl derivative, which is resonance stabilized. Water hydrolyzes formamide to give ammonium formate, which acts as a reducing agent and adds on to the N-formyl derivative. Hydride shift occurs, resulting in loss of carbon dioxide. An ammonium ion is added forming an imine and releasing ammonia. The imine goes through hydrolysis to form the amine, which is depicted in the scheme below. == Applications == An example of the Leuckart reaction is its use in the synthesis of tetrahydro-1,4 benzodiazepin-5-one, a molecule that is part of the benzodiazepine family. == See also == Eschweiler–Clarke reaction == Further reading == Leuchart's finding that benzaldehyde and acetamide react to give tribenzylamine:Leuckart, R. (1885). "Ueber eine neue Bildungsweise von Tribenzylamin". Berichte der Deutschen Chemischen Gesellschaft. 18 (2): 2341–2344. doi:10.1002/cber.188501802113. Leuchart's use of ammonium formate:Leuckart, R.; Bach, E. (1886). "Ueber die Einwirkung von Ammoniumformiat auf Benzaldehyd und Benzophenon". Berichte der Deutschen Chemischen Gesellschaft. 19 (2): 2128–2131. doi:10.1002/cber.188601902105. == References ==
|
{
"page_id": 5901920,
"source": null,
"title": "Leuckart reaction"
}
|
The Atomic City is a 1952 American film noir thriller film directed by Jerry Hopper and starring Gene Barry and Lydia Clarke. The story takes place at Los Alamos, New Mexico, where a nuclear physicist (Barry) lives and works. Terrorists kidnap his son and demand that the physicist turn over the H-bomb formula. The film was nominated for an Academy Award for Best Writing (Story and Screenplay), Sydney Boehm being the nominee. == Plot == Frank and Martha Addison live in Los Alamos, where he does top-secret work as a physicist. They have a young son, Tommy, who goes with school mates to Santa Fe for a carnival with their teacher, Ellen Haskell. During a puppet show, he disappears. This is not noticed until his name is announced as the winner of a raffle for a bicycle at the end of the show. They await a phone call as they fear something has happened. They receive a ransom note assembled from words from different newspapers. They also get a phone call saying to stay silent. Ellen's boyfriend is an FBI agent, Russ Farley, and she passes along her concerns. Farley and partner Harold Mann begin tailing the Addisons. When a kidnapper instructs Frank to steal a file from the atomic lab and mail it to a Los Angeles hotel, he wants to inform the authorities, but Martha fears for their boy. A small-time thief, David Rogers, collects an envelope with the file at a post office, but they alert the FBI who follow him. He goes to a baseball game, followed by the FBI's agents who ask the TV cameras to zoom into him. After the match they are surprised when his car explodes, killing the man. However Rogers no longer has the envelope. The FBI watch the film footage
|
{
"page_id": 21433950,
"source": null,
"title": "The Atomic City"
}
|
as they presume he has passed the file to someone at the game. Watching the film footage the FBI spots a hot-dog vendor who is actually Donald Clark, a man with Communist ties. The FBI bring him in but are limited in what they can extract. However, Dr. Addison is left in an adjoining room alone. He beats up Clark to ascertain where his son is... in Santa Fe. Tommy is moved by kidnappers to the Puye Cliff Dwellings in New Mexico, where they briefly encounter the Fentons, a family of tourists. The mastermind turns out to be Dr. Rassett, a physicist. He studies the file Addison mailed and determines it to be a fake. Rassett orders the boy killed, but Tommy has escaped and is hiding in a cave. The son of the Fentons finds the raffle ticket at the ruins, and back in Santa Fe tries to exchange it for the raffle prize. The area is being watched by the FBI, and they ask where the ticket came from, receiving the vital clue to Tommy's whereabouts. FBI agents rush to the site, where Rassett is arrested after killing his accomplices, and Tommy is saved. == Cast == Gene Barry as Dr. Frank Addison Lydia Clarke as Martha Addison Michael Moore as Russ Farley Nancy Gates as Ellen Haskell Lee Aaker as Tommy Addison Milburn Stone as Insp. Harold Mann Bert Freed as Emil Jablons Frank Cady as F.B.I. Agent George Weinberg Houseley Stevenson Jr. as 'Greg' Gregson Leonard Strong as Donald Clark Jerry Hausner as John Pattiz John Damler as Dr. Peter Rassett George Lynn as Robert Kalnick (as George M. Lynn) Olan Soule as Mortie Fenton Anthony Warde as Arnie Molter == Production == This was the film debut for star Gene Barry and director Jerry Hopper.
|
{
"page_id": 21433950,
"source": null,
"title": "The Atomic City"
}
|
This was the first feature film allowed to be filmed on location inside the city of Los Alamos, during the period that the entire community was still closed to the public at large. It includes views of the residential neighborhoods, main entrance gate, and of the laboratory buildings (from a distance). Filming was also done at the Puye Cliff Dwellings. == References == == External links == The Atomic City at IMDb The Atomic City at the TCM Movie Database The Atomic City at the AFI Catalog of Feature Films The Atomic City at Rotten Tomatoes
|
{
"page_id": 21433950,
"source": null,
"title": "The Atomic City"
}
|
The molecular formula C21H27ClO3 (molar mass: 362.89028 g/mol, exact mass: 362.1649 u) may refer to: Chlormadinone Cismadinone, also known as 6α-chloro-17α-hydroxypregna-1,4-diene-3,20-dione
|
{
"page_id": 35982947,
"source": null,
"title": "C21H27ClO3"
}
|
In mathematics, the coset construction (or GKO construction) is a method of constructing unitary highest weight representations of the Virasoro algebra, introduced by Peter Goddard, Adrian Kent and David Olive (1986). The construction produces the complete discrete series of highest weight representations of the Virasoro algebra and demonstrates their unitarity, thus establishing the classification of unitary highest weight representations. == References == Goddard, P.; Kent, A.; Olive, D. (1986). "Unitary representations of the Virasoro and super-Virasoro algebras". Comm. Math. Phys. 103 (1): 105–119. Bibcode:1986CMaPh.103..105G. doi:10.1007/BF01464283. S2CID 91181508. Victor Kac (2001) [1994], "Virasoro algebra", Encyclopedia of Mathematics, EMS Press Kac, V. G.; Raina, A. K. (1987). Bombay lectures on highest weight representations. World Sci. ISBN 9971-5-0395-6. Wassermann, Antony. "Lecture Notes on the Kac-Moody and Virasoro algebras". Archived from the original on 2007-03-22.
|
{
"page_id": 9309794,
"source": null,
"title": "Coset construction"
}
|
The urbilaterian (from German ur- 'original') is the hypothetical last common ancestor of the bilaterian clade, i.e., all animals having a bilateral symmetry. == Appearance == Its appearance is a matter of debate, for no representative has been (or may or may not ever be) identified in the fossil record. Two reconstructed urbilaterian morphologies can be considered: first, the less complex ancestral form forming the common ancestor to Xenacoelomorpha and Nephrozoa; and second, the more complex (coelomate) urbilaterian ancestral to both protostomes and deuterostomes, sometimes referred to as the "urnephrozoan". Since most protostomes and deuterostomes share features — e.g. nephridia (and the derived kidneys), through guts, blood vessels and nerve ganglia— that are useful only in relatively large (macroscopic) organisms, their common ancestor ought also to have been macroscopic. However, such large animals should have left traces in the sediment in which they moved, and evidence of such traces first appear relatively late in the fossil record — long after the urbilaterian would have lived. This leads to suggestions of a small urbilaterian (around 1 mm) which is the supposed state of the ancestor of protostomes, deuterostomes and acoelomorphs. == Dating the urbilaterian == The first evidence of bilateria in the fossil record comes from trace fossils in sediments towards the end of the Ediacaran period (about 570 million years ago), and the first fully accepted fossil of a bilaterian organism is Kimberella, dating to 555 million years ago. There are earlier, controversial fossils: Vernanimalcula has been interpreted as a bilaterian, but may simply represent a fortuitously infilled bubble. Fossil embryos are known from around the time of Vernanimalcula (580 million years ago), but none of these have bilaterian affinities. This may reflect a genuine absence of bilateria, however it is likely this is the case as bilateria may not
|
{
"page_id": 19467882,
"source": null,
"title": "Urbilaterian"
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|
have laid their eggs in sediment, where they would be likely to fossilise. Molecular techniques can generate expected dates of the divergence between the bilaterian clades, and thus an assessment of when the urbilaterian lived. These dates have huge margins of error, though they are becoming more accurate with time. More recent estimates are compatible with an Ediacaran bilaterian, although it is possible, especially if early bilaterians were small, that the bilateria had a long cryptic history before they left any evidence in the fossil record. == Characteristics of the urbilaterian == === Eyes === Light detection (photosensitivity) is present in organisms as simple as seaweeds; the definition of a true eye varies, but in general eyes must have directional sensitivity, and thus have screening pigments so only light from the target direction is detected. Thus defined, they need not consist of more than one photoreceptor cell. The presence of genetic machinery (the Pax6 and Six genes) common to eye formation in all bilaterians suggests that this machinery - and hence eyes - was present in the urbilaterian. The most likely candidate eye type is the simple pigment-cup eye, which is the most widespread among the bilateria. Since two types of opsin, the c-type and r-type, are found in all bilaterians, the urbilaterian must have possessed both types - although they may not have been found in a centralised eye, but used to synchronise the body clock to daily or lunar variations in lighting. == Complexity == Proponents of a complex urbilaterian point to the shared features and genetic machinery common to all bilateria. They argue that (1) since these are similar in so many respects, they could have evolved only once; and (2) since they are common to all bilateria, they must have been present in the ancestral bilaterian
|
{
"page_id": 19467882,
"source": null,
"title": "Urbilaterian"
}
|
animal. However, as biologists' understanding of the major bilaterian lineages increases, it is beginning to appear that some of these features may have evolved independently in each lineage. Further, the bilaterian clade has recently been expanded to include the acoelomorphs — a group of relatively simple flatworms. This lineage lacks key bilaterian features, and if it truly does reside within the bilaterian "family", many of the features listed above are no longer common to all bilateria. Instead, some features — such as segmentation and possession of a heart — are restricted to a sub-set of the bilateria, the deuterostomes and protostomes. Their last common ancestor would still have to be large and complex, but the bilaterian ancestor could be much simpler. However, some scientists stop short of including the acoelomorph clade in the bilateria. This shifts the position of the cladistic node which is being discussed; consequently the urbilaterian in this context is farther out the evolutionary tree and is more derived than the common ancestor of deuterostomes, protostomes and acoelomorphs. Genetic reconstructions are unfortunately not much help. They work by considering the genes common to all bilateria, but problems arise because very similar genes can be co-opted for different functions. For instance, the gene Pax6 has a function in eye development, but is absent in some animals with eyes; some cnidaria have genes which in bilateria control the development of a layer of cells that the cnidaria do not have. This means that even if a gene can be identified as present in the urbilaterian, we cannot necessary tell what the gene's function was. Before this was realised, genetic reconstructions implied an implausibly complex urbilaterian. The evolutionary developmental biologist Lewis Held notes that both centipedes and snakes use the oscillating mechanism based on the Notch signaling pathway to produce
|
{
"page_id": 19467882,
"source": null,
"title": "Urbilaterian"
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|
segments from the growing tip at the rear of the embryo. Further, both groups make use of "the obtuse process of 'resegmentation', whereby the phase of their metameres shifts by half a unit of wavelength, i.e. somites splitting to make vertebrae or parasegments splitting to form segments." Held comments that all this makes it difficult to imagine that their urbilaterian common ancestor was not segmented. == Reconstructing the urbilaterian == The absence of a fossil record gives a starting point for the reconstruction — the urbilaterian must have been small enough not to leave any traces as it moved over or lived in the sediment surface. This means it must have been well below a centimetre in length. As all Cambrian animals are marine, one can reasonably assume that the urbilaterian was too. Furthermore, a reconstruction of the urbilateria must rest on identifying morphological similarities between all bilateria. While some bilateria live attached to a substrate, this appears to be a secondary adaptation, and the urbilaterian was probably mobile. Its nervous system was probably dispersed, but with a small central "brain". Since acoelomorphs lack a heart, coelom or organs, the urbilaterian probably did too — it would presumably have been small enough for diffusion to do the job of transporting compounds through the body. A small, narrow gut was probably present, which would have had only one opening — a combined mouth and anus. Functional considerations suggest that the surface of the bilaterian was probably covered with cilia, which it could have used for locomotion or feeding. As of 2018 there is still no consensus on whether the characteristics of the deuterostomes and protostomes evolved once or many times. Features such as a heart and a blood-circulation system may therefore not have been present even in the deuterostome-protostome ancestor, which
|
{
"page_id": 19467882,
"source": null,
"title": "Urbilaterian"
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|
would mean that this too could have been small (hence explaining the lack of fossil record). == Possible models of the Urbilaterian == It is possible that the common ancestor of all bilaterals looked similar to: === Colonial-Pennatulacean hypothesis: (Colonialy fusion of cnidarian-like) === The proposal that bilaterals arose from the fusion between pennatulacean-like cnidarian zooids was granted by Dewel, implies that the body plans of bilaterals originated from a colonial ancestor. This proposal has little or no support in the existing data, and has been commonly used as a justification against the sedentary/semi-sedentary models of urbilaterians as a whole. === Larval Hypothesis (Pelagic larvae and adult ancestor) === === Panarticulata hypothesis: (Segmentated annelid-like ancestor) === === Cloudinomorpha hypothesis: (Biphasic Sedentary sessile adult and Pelagic larvae) === The recent model by Alexander V. Martynov and Tatiana A. Korshunova revives the idea of a sessile sedentary biphasic ancestor. Consider that the urbilaterian is an organism whose adult life is sessile sedentary with a juvenile or free and pelagic larval phase. This hypothesis is a derivative of Nielsen's larval hypothesis, but now also considering the homology of the adult forms of choanozoans (except Ctenophora). It also considers various phylogenetic, paleontological and molecular data, relates the adult and ancestral form of anthozoans (from which jellyfish, placozoans, nephrozoans, and perhaps proarticulate are derived), in turn derived from an ancestral organization shared between choanoflagellates, sponges and parahoxozoans. The current strong bias towards a mobile urbilaterian is considered to cause problems with palaeontological and morphological data in relation to groups within and outside Bilateria. So members of Proarticulata are an evolutionary dead end rather than the ancestors of nephrozoans. It is possible that the Cloudinids (Cloudina, Conotubus and Multiconotubus) are basal (and therefore bilateral) nephrozoans, because they have considerable similarity with the tubariums of sedentary pterobranchs,
|
{
"page_id": 19467882,
"source": null,
"title": "Urbilaterian"
}
|
as well as with the shells of semi-mobile hyoliths and mobile mollusks, this taking into account the ontogeny of the cloudinids. This implies that the Cloudinomorpha is not a polyphyletic group as would have been proposed but rather is a paraphyletic grade from which several taxa derive that may or may not conserve the ancestral clonality of basal metazoans, but instead of cloudinids having an annelid-type gut, it would instead be a U-shaped digestive tube, in fact the relationship between Cloudina and annelids is denied. The hypothesis of annelid-like ancestor is rejected, due to the independent evolution of segmentation and complete metamerism of several groups of bilaterians (annelids, panarthropods, chordates and proarticulates); On the other hand, the urbilaterian would be an animal with a U-shaped gut, with deuterostomic characteristics that hemichordates and lophophorates among other groups conserve, a stolon that holds the organism inside a tube secreted from the embryonic form as a dome or protoconch, a semi-metamerism derived from the formation of mesoderm from the gastrovascular cavity of an anthozoan-like animal. This form of urbilaterian: Smooths the transition between anthozoan-like polypoids and various groups of bilaterians. Taking into account the paraphyly of Cycloneuralia, Lophophorata and potentially Deuterostomia. The basal location of priapulids among ecdysozoans. Followed by the zero similarity between the priapulids with the cephalozoans that at the time were pointed out as ancestors of the arthropods. The hastily rejected possible homology of ambulacrarian, bryozoan and brachiozoan tentacles. The qualities of the common ancestor of mollusks as an animal with a single shell rather than a qiton-like animal. The location of basal polychaetes such as Oweniidae with still conserved deuterostome characteristics. The similarities between hyoliths and mollusks. The derived and non-ancestral position of the annelids, flatworms and perhaps the xenacoelomorphs. The common ancestor of modern bilaterals would then be
|
{
"page_id": 19467882,
"source": null,
"title": "Urbilaterian"
}
|
more similar to modern pterobranchs, although they would not be completely identical to them. The location of Ctenophora (Myriazoa hypothesis) should not change the hypothesis since it has been left aside taking only into account the molecular and morphological development of Choanoflagellatea, Porifera and Cnidaria. == See also == == References == == External links == Solène Song, Viktor Starunov, Xavier Bailly, Christine Ruta, Pierre Kerner, Annemiek J. M. Cornelissen, Guillaume Balavoine: Globins in the marine annelid Platynereis dumerilii shed new light on hemoglobin evolution in bilaterians. In: BMC Evolutionary Biology Vol. 20, Issue 165. 29 December 2020. doi:10.1186/s12862-020-01714-4. See also: A single gene 'invented' haemoglobin several times . On: EurekAlert! 29 December 2020. Source: CNRS
|
{
"page_id": 19467882,
"source": null,
"title": "Urbilaterian"
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|
The eyespot apparatus (or stigma) is a photoreceptive organelle found in the flagellate or (motile) cells of green algae and other unicellular photosynthetic organisms such as euglenids. It allows the cells to sense light direction and intensity and respond to it, prompting the organism to either swim towards the light (positive phototaxis), or away from it (negative phototaxis). A related response ("photoshock" or photophobic response) occurs when cells are briefly exposed to high light intensity, causing the cell to stop, briefly swim backwards, then change swimming direction. Eyespot-mediated light perception helps the cells in finding an environment with optimal light conditions for photosynthesis. Eyespots are the simplest and most common "eyes" found in nature, composed of photoreceptors and areas of bright orange-red red pigment granules. Signals relayed from the eyespot photoreceptors result in alteration of the beating pattern of the flagella, generating a phototactic response. == Microscopic structure == Under the light microscope, eyespots appear as dark, orange-reddish spots or stigmata. They get their color from carotenoid pigments contained in bodies called pigment granules. The photoreceptors are found in the plasma membrane overlaying the pigmented bodies. The eyespot apparatus of Euglena comprises the paraflagellar body connecting the eyespot to the flagellum. In electron microscopy, the eyespot apparatus appears as a highly ordered lamellar structure formed by membranous rods in a helical arrangement. In Chlamydomonas, the eyespot is part of the chloroplast and takes on the appearance of a membranous sandwich structure. It is assembled from chloroplast membranes (outer, inner, and thylakoid membranes) and carotenoid-filled granules overlaid by plasma membrane. The stacks of granules act as a quarter-wave plate, reflecting incoming photons back to the overlying photoreceptors, while shielding the photoreceptors from light coming from other directions. It disassembles during cell division and reforms in the daughter cells in an asymmetric
|
{
"page_id": 10096234,
"source": null,
"title": "Eyespot apparatus"
}
|
fashion in relation to the cytoskeleton. This asymmetric positioning of the eyespot in the cell is essential for proper phototaxis. == Eyespot proteins == The most critical eyespot proteins are the photoreceptor proteins that sense light. The photoreceptors found in unicellular organisms fall into two main groups: flavoproteins and retinylidene proteins (rhodopsins). Flavoproteins are characterized by containing flavin molecules as chromophores, whereas retinylidene proteins contain retinal. The photoreceptor protein in Euglena is likely a flavoprotein. In contrast, Chlamydomonas phototaxis is mediated by archaeal-type rhodopsins. Besides photoreceptor proteins, eyespots contain a large number of structural, metabolic and signaling proteins. The eyespot proteome of Chlamydomonas cells consists of roughly 200 different proteins. == Photoreception and signal transduction == The Euglena photoreceptor was identified as a blue-light-activated adenylyl cyclase. Excitation of this receptor protein results in the formation of cyclic adenosine monophosphate (cAMP) as a second messenger. Chemical signal transduction ultimately triggers changes in flagellar beat patterns and cell movement. The archaeal-type rhodopsins of Chlamydomonas contain an all-trans retinylidene chromatophore which undergoes photoisomerization to a 13-cis isomer. This activates a photoreceptor channel, leading to a change in membrane potential and cellular calcium ion concentration. Photoelectric signal transduction ultimately triggers changes in flagellar strokes and thus cell movement. == See also == Evolution of the eye Ocelloid == References ==
|
{
"page_id": 10096234,
"source": null,
"title": "Eyespot apparatus"
}
|
Animal science is described as "studying the biology of animals that are under the control of humankind". It can also be described as the production and management of farm animals. Historically, the degree was called animal husbandry and the animals studied were livestock species, like cattle, sheep, pigs, poultry, and horses. Today, courses available look at a broader area, including companion animals, like dogs and cats, and many exotic species. Degrees in Animal Science are offered at a number of colleges and universities. Animal science degrees are often offered at land-grant universities, which will often have on-campus farms to give students hands-on experience with livestock animals. == Education == Professional education in animal science prepares students for careers in areas such as animal breeding, food and fiber production, nutrition, animal agribusiness, animal behavior, and welfare. Courses in a typical Animal Science program may include genetics, microbiology, animal behavior, nutrition, physiology, and reproduction. Courses in support areas, such as genetics, soils, agricultural economics and marketing, legal aspects, and the environment also are offered. === Bachelor degree === At many universities, a Bachelor of Science (BS) degree in Animal Science allows emphasis in certain areas. Typical areas are species-specific or career-specific. Species-specific areas of emphasis prepare students for a career in dairy management, beef management, swine management, sheep or small ruminant management, poultry production, or the horse industry. Other career-specific areas of study include pre-veterinary medicine studies, livestock business and marketing, animal welfare and behavior, animal nutrition science, animal reproduction science, or genetics. Youth programs are also an important part of animal science programs. ==== Pre-veterinary emphasis ==== Many schools that offer a degree option in Animal Science also offer a pre-veterinary emphasis such as Iowa State University, the University of Nebraska–Lincoln, and the University of Minnesota, for example. This option provides
|
{
"page_id": 2035308,
"source": null,
"title": "Animal science"
}
|
knowledge of the biological and physical sciences including nutrition, reproduction, physiology, and genetics. This can prepare students for graduate studies in animal science, veterinary school, and pharmaceutical or animal science industries. === Graduate studies === In a Master of Science degree option, students take required courses in areas that support their main interest. These courses are above courses normally required for a Bachelor of Science degree in the Animal Science major. For example, in a Ph.D. degree program students take courses related to their major that are more in-depth than those for the Master of Science degree, with an emphasis on research or teaching. Graduate studies in animal sciences are considered preparation for upper-level positions in production, management, education, research, or agri-services. Professional study in veterinary medicine, law, and business administration are among the most commonly chosen programs by graduates. Other areas of study include growth biology, physiology, nutrition, and production systems. == Careers in Animal Science == There are a variety of careers available to someone with an animal science degree. Including, but not limited to, Academic researcher, Animal nutritionist, Animal physiotherapist technician, Nature conservation officer, Zookeeper, and Zoologist. == Areas of study == === Animal Behavior === Animal behavior is the study of how animals interact with their environment, interact with each other socially, and how they may achieve understanding of their environment. Animal behavior is examined with the framework of its development, mechanism, adaptive value, and evolution. === Animal Genetics === Animal genetics is the study of an animal genes and how they effect an animal's appearance, health, and function. The information gained from such studies is often applied to livestock breeding. === Veterinary Medicine === Veterinary medicine is a specialization within the field of medicine focusing on the diagnosis, prevention, control, and treatment of diseases that
|
{
"page_id": 2035308,
"source": null,
"title": "Animal science"
}
|
effect both wild and domesticated animals. There are three main medical positions within veterinary medicine, veterinarians, veterinary technicians, and veterinary assistants. == See also == American Registry of Professional Animal Scientists List of animal science degree-granting institutions Zoology, the interest of all animals. Veterinary science == References == == External links == "Career Information." American Society of Animal Science. ASAS, 2009. Web. 29 September 2011. http://www.asas.org American Society of Animal Science "UNL Animal Science Department." University of Nebraska-Lincoln. UNL Institute of Agriculture and Natural Resources, 27 January 2015. "MSU Department of Animal Science." Michigan State University. Michigan State University Department of Animal Science, 28 December 2013. "Animal Industry Careers." Purdue University. Purdue University, 11 August 2005. Web. 5 October 2011. http://www.ansc.purdue.edu Purdue University Animal Science
|
{
"page_id": 2035308,
"source": null,
"title": "Animal science"
}
|
Cytochrome P450, family 23, also known as CYP23, is a nematoda cytochrome P450 monooxygenase family. The first gene identified in this family is the CYP23A1 from the Caenorhabditis elegans, is a homolog of the human gene CYP7B1. == References ==
|
{
"page_id": 69275247,
"source": null,
"title": "CYP23 family"
}
|
The molecular formula C23H30O4 (molar mass: 370.48 g/mol, exact mass: 370.2144 u) may refer to: Nomegestrol acetate (NOMAC) Segesterone acetate (SGA)
|
{
"page_id": 35982961,
"source": null,
"title": "C23H30O4"
}
|
The Albright–Goldman oxidation is a name reaction of organic chemistry, first described by the American chemists J. Donald Albright and Leon Goldman in 1965. The reaction is particularly suitable for the synthesis of aldehydes from primary alcohols. Analogously, secondary alcohols can be oxidized to form ketones. Dimethyl sulfoxide/acetic anhydride serves as oxidizing agent. The reaction does not proceed further to the carboxylic acid. == Reaction mechanism == The following figure shows the reaction mechanism: First, dimethyl sulfoxide (1) reacts with acetic anhydride to form a sulfonium ion. It reacts with the primary alcohol in an addition reaction. Furthermore, acetic acid is cleaved, so that intermediate 2 is formed. The latter reacts upon elimination of acetic acid and dimethyl sulphide to the aldehyde. == Example == The Albright–Goldman oxidation is a particularly mild oxidation process. Thus, it is suitable for the oxidation of compounds which are sensitive to nonselective oxidizing agents, such as indole alkaloids. This reaction can also be used for sterically hindered hydroxyl groups. An example for its application is the synthesis of the indole alkaloid yohimbine: == Alternative reactions == An alternative method for the oxidation of primary alcohols to aldehydes is the Swern oxidation. == References ==
|
{
"page_id": 55250546,
"source": null,
"title": "Albright–Goldman oxidation"
}
|
The intermembral index is a ratio used to compare limb proportions, expressed as a percentage. It is equal to the length of forelimbs (humerus plus radius) divided by the length of the hind limbs (femur plus tibia) multiplied by 100, otherwise written mathematically as: ( h u m e r u s + r a d i u s ) ( f e m u r + t i b i a ) × 100 {\displaystyle {\tfrac {(humerus+radius)}{(femur+tibia)}}\times 100} The intermembral index is used frequently in primatology, since it helps predict primate locomotor patterns. For scores lower than 100, the forelimbs are shorter than the hind limbs, which is common in leaping primates and bipedal hominids. Quadrupedal primates tend to have scores around 100, while brachiating primates have scores significantly higher than 100. This information can also be used to predict locomotion patterns for extinct primates in cases where forelimb and hind limb fossils have been found. == Primate species == == Variation == In a diverse ethnic sample of 314 modern human skeletons covering African Pygmies, Andaman Islanders, Khoesan, Zulu, African Americans, Sami and Inuit the intermembral index was found to vary between 64 and 74. A study published in 1937 found a range of variation between 64.5 and 79.2. This study found no link with humans of different groups with individuals from different ethnic groups showing similar scatter of variation. Variation has also beem found in chimapanzees (100.1 - 113.7), gorillas (110.3 - 125.0), orangutan (135.0 -150.9), siamang (145.0 - 155.2), gibbon (120.5 - 137.1), and macque monkeys (83.0 - 91.0). == References ==
|
{
"page_id": 26283638,
"source": null,
"title": "Intermembral index"
}
|
Jannie Hofmeyr published the first catalog of control patterns in metabolic control analysis (MCA). His doctoral research. concerned the use of graphical patterns to elucidate chains of interaction in metabolic regulation, later published in the European Journal of Biochemistry. In his thesis, he cataloged 25 patterns for various biochemical networks. In later work, his research group, together with Carl D Christensen and Johann Rohwer, developed a Python based tool called SymCA that was part of the PySCeSToolbox toolkit that could generate patterns automatically and symbolically from a description of the network. This software was used to generate the patterns shown below. The control equations, especially the numerators of the equations, can give information on the relative importance and routes by which perturbations travel through a biochemical network == Notation == Control patterns describe how a perturbation to a given parameter affects the steady-state level of a given variable. For example, a concentration control coefficient can describe how the overexpression of a specific enzyme can influence steady-state metabolite concentrations. Flux control coefficients are similar in that they describe how a perturbation in a given enzyme affects steady-state flux through a pathway. Such coefficients can be written in terms of elasticity coefficients. Elasticity coefficients are local properties that describe how a single reaction is influenced by changes in the substrates and products that might influence the rate. For example, given a reaction such as: S ⟶ v P {\displaystyle S{\stackrel {v}{\longrightarrow }}P} we will assume it has a rate of reaction of v {\displaystyle v} . This reaction rate can be influenced by changes in the concentrations of substrate S {\displaystyle S} or product P {\displaystyle P} . This influence is measured by an elasticity which is defined as: ε s v = ∂ v ∂ s s v {\displaystyle \varepsilon _{s}^{v}={\frac
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"page_id": 74387063,
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{\partial v}{\partial s}}{\frac {s}{v}}} To make the notation manageable, a specific numbering scheme is used in the following patterns. If a substrate has an index of i {\displaystyle i} , then the reaction index will be v i + 1 {\displaystyle v_{i+1}} . The product elasticity will also have an index of i + 1 {\displaystyle i+1} . This means that a product elasticity will have identical subscripts and superscripts making them easy to identify. The source boundary species is always labeled zero as well as the label for the first reaction. For example, the following fragment of a network illustrates this labeling: X o ⟶ v 1 S 1 ⟶ v 2 S 2 ⟶ v 3 {\displaystyle X_{o}{\stackrel {v_{1}}{\longrightarrow }}S_{1}{\stackrel {v_{2}}{\longrightarrow }}S_{2}{\stackrel {v_{3}}{\longrightarrow }}} then ε 1 2 = ∂ v 2 ∂ s 1 s 1 v 2 , ε 2 2 = ∂ v 2 ∂ s 2 s 2 v 2 , ε 2 3 = ∂ v 3 ∂ s 2 s 2 v 3 {\displaystyle \varepsilon _{1}^{2}={\frac {\partial v_{2}}{\partial s_{1}}}{\frac {s_{1}}{v_{2}}},\quad \varepsilon _{2}^{2}={\frac {\partial v_{2}}{\partial s_{2}}}{\frac {s_{2}}{v_{2}}},\quad \varepsilon _{2}^{3}={\frac {\partial v_{3}}{\partial s_{2}}}{\frac {s_{2}}{v_{3}}}} == Linear Chains == === Two-Step Pathway === X o ⟶ v 1 S 1 ⟶ v 2 X 1 {\displaystyle X_{o}{\stackrel {v_{1}}{\longrightarrow }}S_{1}{\stackrel {v_{2}}{\longrightarrow }}X_{1}} ==== Assuming both steps are Irreversible ==== C e 1 J = 1 C e 2 J = 0 {\displaystyle C_{e_{1}}^{J}=1\qquad C_{e_{2}}^{J}=0} C e 1 s 1 = 1 ε 1 2 C e 2 s 1 = − 1 ε 1 2 {\displaystyle C_{e_{1}}^{s_{1}}={\frac {1}{\varepsilon _{1}^{2}}}\qquad C_{e_{2}}^{s_{1}}={\frac {-1}{\varepsilon _{1}^{2}}}} ==== Assuming both steps are Reversible ==== C v 1 J = ε 1 2 ε 1 2 − ε 1 1 C v 2 J = − ε 1 1 ε 1 2
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− ε 1 1 {\displaystyle C_{v_{1}}^{J}={\frac {\varepsilon _{1}^{2}}{\varepsilon _{1}^{2}-\varepsilon _{1}^{1}}}\qquad C_{v_{2}}^{J}={\frac {-\varepsilon _{1}^{1}}{\varepsilon _{1}^{2}-\varepsilon _{1}^{1}}}} C v 1 s 1 = 1 ε 1 2 − ε 1 1 C v 2 s 1 = − 1 ε 1 2 − ε 1 1 {\displaystyle C_{v_{1}}^{s_{1}}={\frac {1}{\varepsilon _{1}^{2}-\varepsilon _{1}^{1}}}\qquad C_{v_{2}}^{s_{1}}={\frac {-1}{\varepsilon _{1}^{2}-\varepsilon _{1}^{1}}}} === Three-Step Pathway === X o ⟶ v 1 S 1 ⟶ v 2 S 2 ⟶ v 3 X 1 {\displaystyle X_{o}{\stackrel {v_{1}}{\longrightarrow }}S_{1}{\stackrel {v_{2}}{\longrightarrow }}S_{2}{\stackrel {v_{3}}{\longrightarrow }}X_{1}} ==== Assuming the three steps are Irreversible ==== Denominator: d = ε 1 2 ε 2 3 {\displaystyle d=\varepsilon _{1}^{2}\varepsilon _{2}^{3}} Assume that each of the following expressions is divided by d C e 1 J = 1 C e 2 J = 0 C e 3 J = 0 {\displaystyle {\begin{array}{lll}C_{e_{1}}^{J}=1&C_{e_{2}}^{J}=0&C_{e_{3}}^{J}=0\end{array}}} C e 1 s 1 = ε 2 3 C e 1 s 2 = ε 1 2 C e 2 s 1 = − ε 2 3 C e 2 s 2 = 0 C e 2 s 2 = 0 C e 3 s 2 = − ε 1 2 {\displaystyle {\begin{array}{ll}C_{e_{1}}^{s_{1}}=\varepsilon _{2}^{3}&C_{e_{1}}^{s_{2}}=\varepsilon _{1}^{2}\\[6pt]C_{e_{2}}^{s_{1}}=-\varepsilon _{2}^{3}&C_{e_{2}}^{s_{2}}=0\\[6pt]C_{e_{2}}^{s_{2}}=0&C_{e_{3}}^{s_{2}}=-\varepsilon _{1}^{2}\end{array}}} ==== Assuming the three steps are Reversible ==== Denominator: d = ε 1 2 ε 2 3 − ε 1 1 ε 2 3 + ε 1 1 ε 2 2 {\displaystyle d=\varepsilon _{1}^{2}\varepsilon _{2}^{3}-\varepsilon _{1}^{1}\varepsilon _{2}^{3}+\varepsilon _{1}^{1}\varepsilon _{2}^{2}} Assume that each of the following expressions is divided by d {\displaystyle d} C e 1 J = ε 1 2 ε 2 3 C e 2 J = − ε 1 1 ε 2 3 C e 3 J = ε 1 1 ε 2 2 {\displaystyle {\begin{array}{lll}C_{e_{1}}^{J}=\varepsilon _{1}^{2}\varepsilon _{2}^{3}&C_{e_{2}}^{J}=-\varepsilon _{1}^{1}\varepsilon _{2}^{3}&C_{e_{3}}^{J}=\varepsilon _{1}^{1}\varepsilon _{2}^{2}\\[6pt]\end{array}}} C e 1 s 1 = ε 2 3 − ε 2 2 C
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"page_id": 74387063,
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e 1 s 2 = ε 1 2 C e 2 s 1 = − ε 2 3 C e 2 s 2 = − ε 1 1 C e 3 s 1 = ε 2 2 C e 3 s 2 = ε 1 1 − ε 1 2 {\displaystyle {\begin{array}{ll}C_{e_{1}}^{s_{1}}=\varepsilon _{2}^{3}-\varepsilon _{2}^{2}&C_{e_{1}}^{s_{2}}=\varepsilon _{1}^{2}\\[6pt]C_{e_{2}}^{s_{1}}=-\varepsilon _{2}^{3}&C_{e_{2}}^{s_{2}}=-\varepsilon _{1}^{1}\\[6pt]C_{e_{3}}^{s_{1}}=\varepsilon _{2}^{2}&C_{e_{3}}^{s_{2}}=\varepsilon _{1}^{1}-\varepsilon _{1}^{2}\end{array}}} === Four-Step Pathway === X o ⟶ v 1 S 1 ⟶ v 2 S 2 ⟶ v 3 S 3 ⟶ v 4 X 1 {\displaystyle X_{o}{\stackrel {v_{1}}{\longrightarrow }}S_{1}{\stackrel {v_{2}}{\longrightarrow }}S_{2}{\stackrel {v_{3}}{\longrightarrow }}S_{3}{\stackrel {v_{4}}{\longrightarrow }}X_{1}} Denominator: d = ε 1 1 ε 2 2 ε 3 3 − ε 1 1 ε 2 2 ε 3 4 + ε 1 1 ε 2 3 ε 3 4 − ε 1 2 ε 2 3 ε 3 4 {\displaystyle d=\varepsilon _{1}^{1}\varepsilon _{2}^{2}\varepsilon _{3}^{3}-\varepsilon _{1}^{1}\varepsilon _{2}^{2}\varepsilon _{3}^{4}+\varepsilon _{1}^{1}\varepsilon _{2}^{3}\varepsilon _{3}^{4}-\varepsilon _{1}^{2}\varepsilon _{2}^{3}\varepsilon _{3}^{4}} Assume that each of the following expressions is divided by d {\displaystyle d} . C e 1 J = − ε 1 2 ε 2 3 ε 3 4 C e 2 J = ε 1 1 ε 2 3 ε 3 4 C e 3 J = − ε 1 1 ε 2 2 ε 3 4 C e 4 J = ε 1 1 ε 2 2 ε 3 3 C e 1 s 1 = − ε 2 2 ε 3 3 + ε 2 2 ε 3 4 − ε 2 3 ε 3 4 C e 2 s 1 = − ε 2 3 ε 3 4 C e 3 s 1 = − ε 2 2 ε 3 4 C e 4 s 1 = ε 2 2 ε 3 3 C e 1 s 2 = ε 1 2 ε 3
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"page_id": 74387063,
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3 − ε 1 2 ε 3 4 C e 2 s 2 = − ε 1 1 ε 3 3 + ε 1 1 ε 3 4 C e 3 s 2 = − ε 1 1 ε 3 4 + ε 1 2 ε 3 4 C e 4 s 2 = ε 1 1 ε 3 3 − ε 1 2 ε 3 3 C e 1 s 3 = − ε 1 2 ε 2 3 C e 2 s 3 = ε 1 1 ε 2 3 C e 3 s 2 = − ε 1 1 ε 2 2 C e 4 s 2 = ε 1 1 ε 2 2 − ε 1 1 ε 2 3 + ε 1 2 ε 2 3 {\displaystyle {\begin{array}{lll}C_{e_{1}}^{J}=-\varepsilon _{1}^{2}\varepsilon _{2}^{3}\varepsilon _{3}^{4}&C_{e_{2}}^{J}=\varepsilon _{1}^{1}\varepsilon _{2}^{3}\varepsilon _{3}^{4}&C_{e_{3}}^{J}=-\varepsilon _{1}^{1}\varepsilon _{2}^{2}\varepsilon _{3}^{4}&C_{e_{4}}^{J}=\varepsilon _{1}^{1}\varepsilon _{2}^{2}\varepsilon _{3}^{3}\\[4pt]C_{e_{1}}^{s_{1}}=-\varepsilon _{2}^{2}\varepsilon _{3}^{3}+\varepsilon _{2}^{2}\varepsilon _{3}^{4}-\varepsilon _{2}^{3}\varepsilon _{3}^{4}&C_{e_{2}}^{s_{1}}=-\varepsilon _{2}^{3}\varepsilon _{3}^{4}&C_{e_{3}}^{s_{1}}=-\varepsilon _{2}^{2}\varepsilon _{3}^{4}&C_{e_{4}}^{s_{1}}=\varepsilon _{2}^{2}\varepsilon _{3}^{3}\\[4pt]C_{e_{1}}^{s_{2}}=\varepsilon _{1}^{2}\varepsilon _{3}^{3}-\varepsilon _{1}^{2}\varepsilon _{3}^{4}&C_{e_{2}}^{s_{2}}=-\varepsilon _{1}^{1}\varepsilon _{3}^{3}+\varepsilon _{1}^{1}\varepsilon _{3}^{4}&C_{e_{3}}^{s_{2}}=-\varepsilon _{1}^{1}\varepsilon _{3}^{4}+\varepsilon _{1}^{2}\varepsilon _{3}^{4}&C_{e_{4}}^{s_{2}}=\varepsilon _{1}^{1}\varepsilon _{3}^{3}-\varepsilon _{1}^{2}\varepsilon _{3}^{3}\\[4pt]C_{e_{1}}^{s_{3}}=-\varepsilon _{1}^{2}\varepsilon _{2}^{3}&C_{e_{2}}^{s_{3}}=\varepsilon _{1}^{1}\varepsilon _{2}^{3}&C_{e_{3}}^{s_{2}}=-\varepsilon _{1}^{1}\varepsilon _{2}^{2}&C_{e_{4}}^{s_{2}}=\varepsilon _{1}^{1}\varepsilon _{2}^{2}-\varepsilon _{1}^{1}\varepsilon _{2}^{3}+\varepsilon _{1}^{2}\varepsilon _{2}^{3}\end{array}}} == Linear Chains with Negative Feedback == === Three-Step Pathway === Denominator: d = ε 1 1 ε 2 2 − ε 1 1 ε 2 3 + ε 1 2 ε 2 3 − ε 2 1 ε 1 2 {\displaystyle d=\varepsilon _{1}^{1}\varepsilon _{2}^{2}-\varepsilon _{1}^{1}\varepsilon _{2}^{3}+\varepsilon _{1}^{2}\varepsilon _{2}^{3}-\varepsilon _{2}^{1}\varepsilon _{1}^{2}} Assume that each of the following expressions is divided by d {\displaystyle d} . C e 1 J = ε 1 2 ε 2 3 C e 2 J = − ε 1 1 ε 2 3 C e 3 J = ε 1 1 ε 2 2 − ε 2 1 ε 1 2 C e 1 s 1 = ε 2 3
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{
"page_id": 74387063,
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− ε 2 2 C e 2 s 1 = − ε 2 3 − ε 2 1 C e 3 s 1 = ε 2 2 − ε 2 1 C e 1 s 2 = ε 1 2 C e 2 s 2 = − ε 1 1 C e 3 s 2 = ε 1 1 − ε 1 2 {\displaystyle {\begin{array}{lll}C_{e_{1}}^{J}=\varepsilon _{1}^{2}\varepsilon _{2}^{3}&C_{e_{2}}^{J}=-\varepsilon _{1}^{1}\varepsilon _{2}^{3}&C_{e_{3}}^{J}=\varepsilon _{1}^{1}\varepsilon _{2}^{2}-\varepsilon _{2}^{1}\varepsilon _{1}^{2}\\[4pt]C_{e_{1}}^{s_{1}}=\varepsilon _{2}^{3}-\varepsilon _{2}^{2}&C_{e_{2}}^{s_{1}}=-\varepsilon _{2}^{3}-\varepsilon _{2}^{1}&C_{e_{3}}^{s_{1}}=\varepsilon _{2}^{2}-\varepsilon _{2}^{1}\\[4pt]C_{e_{1}}^{s_{2}}=\varepsilon _{1}^{2}&C_{e_{2}}^{s_{2}}=-\varepsilon _{1}^{1}&C_{e_{3}}^{s_{2}}=\varepsilon _{1}^{1}-\varepsilon _{1}^{2}\\[4pt]\end{array}}} === Four-Step Pathway === Denominator: d = ε 1 1 ε 2 2 ε 3 4 − ε 1 1 ε 2 3 ε 3 4 − ε 3 1 ε 1 2 ε 2 3 + ε 1 2 ε 2 3 ε 3 4 − ε 1 1 ε 2 2 ε 3 3 {\displaystyle d=\varepsilon _{1}^{1}\varepsilon _{2}^{2}\varepsilon _{3}^{4}-\varepsilon _{1}^{1}\varepsilon _{2}^{3}\varepsilon _{3}^{4}-\varepsilon _{3}^{1}\varepsilon _{1}^{2}\varepsilon _{2}^{3}+\varepsilon _{1}^{2}\varepsilon _{2}^{3}\varepsilon _{3}^{4}-\varepsilon _{1}^{1}\varepsilon _{2}^{2}\varepsilon _{3}^{3}} Assume that each of the following expressions is divided by d {\displaystyle d} . C v 1 J = ε 1 2 ε 2 3 ε 3 4 C v 2 J = − ε 1 1 ε 2 3 ε 3 4 C v 3 J = ε 1 1 ε 2 2 ε 3 4 C v 4 J = − ε 1 1 ε 2 2 ε 3 3 − ε 3 1 ε 1 2 ε 2 3 C v 1 S 1 = ε 2 2 ε 3 3 − ε 2 2 ε 3 4 + ε 2 3 ε 3 4 C v 2 S 1 = ε 3 1 ε 2 3 − ε 2 3 ε 3 4 C v 3 S 1 = − ε 3 1 ε 2 2 + ε 2 2
|
{
"page_id": 74387063,
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ε 3 4 C v 4 S 1 = ε 3 1 ε 2 2 − ε 3 1 ε 2 3 − ε 2 2 ε 3 3 C v 1 S 2 = − ε 1 2 ε 3 3 + ε 1 2 ε 3 4 C v 2 S 2 = ε 1 1 ε 3 3 − ε 1 1 ε 3 4 C v 3 S 2 = ε B 1 ε 3 4 + ε 3 1 ε 1 2 − ε 1 2 ε 3 4 C v 4 S 2 = − ε 1 1 ε 3 3 − ε 3 1 ε 1 2 + ε 1 2 ε 3 3 C v 1 S 3 = ε 1 2 ε 2 3 C v 2 S 3 = − ε 1 1 ε 2 3 C v 3 S 3 = ε 1 1 ε 2 2 C v 4 S 3 = − ε 1 1 ε 2 2 + ε 1 1 ε 2 3 − ε 1 2 ε 2 3 {\displaystyle {\begin{array}{llll}C_{v_{1}}^{J}=\varepsilon _{1}^{2}\varepsilon _{2}^{3}\varepsilon _{3}^{4}&C_{v_{2}}^{J}=-\varepsilon _{1}^{1}\varepsilon _{2}^{3}\varepsilon _{3}^{4}&C_{v_{3}}^{J}=\varepsilon _{1}^{1}\varepsilon _{2}^{2}\varepsilon _{3}^{4}&C_{v_{4}}^{J}=-\varepsilon _{1}^{1}\varepsilon _{2}^{2}\varepsilon _{3}^{3}-\varepsilon _{3}^{1}\varepsilon _{1}^{2}\varepsilon _{2}^{3}\\C_{v_{1}}^{S_{1}}=\varepsilon _{2}^{2}\varepsilon _{3}^{3}-\varepsilon _{2}^{2}\varepsilon _{3}^{4}+\varepsilon _{2}^{3}\varepsilon _{3}^{4}&C_{v_{2}}^{S_{1}}=\varepsilon _{3}^{1}\varepsilon _{2}^{3}-\varepsilon _{2}^{3}\varepsilon _{3}^{4}&C_{v_{3}}^{S_{1}}=-\varepsilon _{3}^{1}\varepsilon _{2}^{2}+\varepsilon _{2}^{2}\varepsilon _{3}^{4}&C_{v_{4}}^{S_{1}}=\varepsilon _{3}^{1}\varepsilon _{2}^{2}-\varepsilon _{3}^{1}\varepsilon _{2}^{3}-\varepsilon _{2}^{2}\varepsilon _{3}^{3}\\C_{v_{1}}^{S_{2}}=-\varepsilon _{1}^{2}\varepsilon _{3}^{3}+\varepsilon _{1}^{2}\varepsilon _{3}^{4}&C_{v_{2}}^{S_{2}}=\varepsilon _{1}^{1}\varepsilon _{3}^{3}-\varepsilon _{1}^{1}\varepsilon _{3}^{4}&C_{v_{3}}^{S_{2}}=\varepsilon _{B}^{1}\varepsilon _{3}^{4}+\varepsilon _{3}^{1}\varepsilon _{1}^{2}-\varepsilon _{1}^{2}\varepsilon _{3}^{4}&C_{v_{4}}^{S_{2}}=-\varepsilon _{1}^{1}\varepsilon _{3}^{3}-\varepsilon _{3}^{1}\varepsilon _{1}^{2}+\varepsilon _{1}^{2}\varepsilon _{3}^{3}\\C_{v_{1}}^{S_{3}}=\varepsilon _{1}^{2}\varepsilon _{2}^{3}&C_{v_{2}}^{S_{3}}=-\varepsilon _{1}^{1}\varepsilon _{2}^{3}&C_{v_{3}}^{S_{3}}=\varepsilon _{1}^{1}\varepsilon _{2}^{2}&C_{v_{4}}^{S_{3}}=-\varepsilon _{1}^{1}\varepsilon _{2}^{2}+\varepsilon _{1}^{1}\varepsilon _{2}^{3}-\varepsilon _{1}^{2}\varepsilon _{2}^{3}\end{array}}} == Branched Pathways == At steady-state v 1 = v 2 + v 3 {\displaystyle v_{1}=v_{2}+v_{3}} , therefore define the following two terms: α = v 2 v 1 1 − α = v 3 v 1 {\displaystyle \alpha ={\frac {v_{2}}{v_{1}}}\quad 1-\alpha ={\frac {v_{3}}{v_{1}}}} Denominator: d
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"page_id": 74387063,
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= ε s 2 α + ε s 3 ( 1 − α ) − ε s 1 {\displaystyle d=\varepsilon _{s}^{2}\alpha +\varepsilon _{s}^{3}(1-\alpha )-\varepsilon _{s}^{1}} Assume that each of the following expressions is divided by d {\displaystyle d} . C e 1 J 1 = ε s 3 ( 1 − α ) + ε s 2 α C e 1 J 1 = − ε s 1 α C e 1 J 1 = − ε s 1 ( 1 − α ) + ε s 2 α {\displaystyle {\begin{array}{lll}C_{e_{1}}^{J_{1}}=\varepsilon _{s}^{3}(1-\alpha )+\varepsilon _{s}^{2}\alpha \\C_{e_{1}}^{J_{1}}=-\varepsilon _{s}^{1}\alpha \\C_{e_{1}}^{J_{1}}=-\varepsilon _{s}^{1}(1-\alpha )+\varepsilon _{s}^{2}\alpha \end{array}}} == See also == Metabolic control analysis Branched pathways Elasticity coefficient Biochemical systems theory Control coefficient (biochemistry) Flux (metabolism) == References ==
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"page_id": 74387063,
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The acentric factor ω is a conceptual number introduced by Kenneth Pitzer in 1955, proven to be useful in the description of fluids. It has become a standard for the phase characterization of single and pure components, along with other state description parameters such as molecular weight, critical temperature, critical pressure, and critical volume (or critical compressibility). The acentric factor is also said to be a measure of the non-sphericity (centricity) of molecules. Pitzer defined ω from the relationship ω = − log 10 ( p r sat ) − 1 at T r = 0.7 , {\displaystyle \omega =-\log _{10}(p_{\text{r}}^{\text{sat}})-1{\text{ at }}T_{\text{r}}=0.7,} where p r sat = p sat / p c {\displaystyle p_{\text{r}}^{\text{sat}}=p^{\text{sat}}/p_{c}} is the reduced saturation vapor pressure, and T r = T / T c {\displaystyle T_{\text{r}}=T/T_{c}} is the reduced temperature. Pitzer developed this factor by studying the vapor-pressure curves of various pure substances. Thermodynamically, the vapor-pressure curve for pure components can be mathematically described using the Clausius–Clapeyron equation. The integrated form of equation is mainly used for obtaining vapor-pressure data mathematically. This integrated version shows that the relationship between the logarithm of vapor pressure and the reciprocal of absolute temperature is approximately linear. For a series of fluids, as the acentric factor increases the vapor curve is "pulled" down, resulting in higher boiling points. For many monatomic fluids, p r sat ≈ 0.1 {\displaystyle p_{\text{r}}^{\text{sat}}\approx 0.1} at T r = 0.7 , {\displaystyle T_{\text{r}}=0.7,} which leads to ω → 0 {\displaystyle \omega \to 0} . In many cases, T r = 0.7 {\displaystyle T_{\text{r}}=0.7} lies above the boiling temperature of liquids at atmosphere pressure. Values of ω can be determined for any fluid from accurate experimental vapor-pressure data. The definition of ω gives values close to zero for the noble gases argon, krypton, and
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{
"page_id": 2231930,
"source": null,
"title": "Acentric factor"
}
|
xenon. ω {\displaystyle \omega } is also very close to zero for molecules which are nearly spherical. Values of ω ≤ −1 correspond to vapor pressures above the critical pressure and are non-physical. The acentric factor can be predicted analytically from some equations of state. For example, it can be easily shown from the above definition that a van der Waals fluid has an acentric factor of about −0.302024, which if applied to a real system would indicate a small, ultra-spherical molecule. == Values of some common gases == == See also == Equation of state Reduced pressure Reduced temperature == References ==
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{
"page_id": 2231930,
"source": null,
"title": "Acentric factor"
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The mass number (symbol A, from the German word: Atomgewicht, "atomic weight"), also called atomic mass number or nucleon number, is the total number of protons and neutrons (together known as nucleons) in an atomic nucleus. It is approximately equal to the atomic (also known as isotopic) mass of the atom expressed in atomic mass units. Since protons and neutrons are both baryons, the mass number A is identical with the baryon number B of the nucleus (and also of the whole atom or ion). The mass number is different for each isotope of a given chemical element, and the difference between the mass number and the atomic number Z gives the number of neutrons (N) in the nucleus: N = A − Z. The mass number is written either after the element name or as a superscript to the left of an element's symbol. For example, the most common isotope of carbon is carbon-12, or 12C, which has 6 protons and 6 neutrons. The full isotope symbol would also have the atomic number (Z) as a subscript to the left of the element symbol directly below the mass number: 126C. == Mass number changes in radioactive decay == Different types of radioactive decay are characterized by their changes in mass number as well as atomic number, according to the radioactive displacement law of Fajans and Soddy. For example, uranium-238 usually decays by alpha decay, where the nucleus loses two neutrons and two protons in the form of an alpha particle. Thus the atomic number and the number of neutrons each decrease by 2 (Z: 92 → 90, N: 146 → 144), so that the mass number decreases by 4 (A = 238 → 234); the result is an atom of thorium-234 and an alpha particle (42He2+): On the other
|
{
"page_id": 659068,
"source": null,
"title": "Mass number"
}
|
hand, carbon-14 decays by beta decay, whereby one neutron is transmuted into a proton with the emission of an electron and an antineutrino. Thus the atomic number increases by 1 (Z: 6 → 7) and the mass number remains the same (A = 14), while the number of neutrons decreases by 1 (N: 8 → 7). The resulting atom is nitrogen-14, with seven protons and seven neutrons: Beta decay is possible because different isobars have mass differences on the order of a few electron masses. If possible, a nuclide will undergo beta decay to an adjacent isobar with lower mass. In the absence of other decay modes, a cascade of beta decays terminates at the isobar with the lowest atomic mass. Another type of radioactive decay without change in mass number is emission of a gamma ray from a nuclear isomer or metastable excited state of an atomic nucleus. Since all the protons and neutrons remain in the nucleus unchanged in this process, the mass number is also unchanged. == Mass number and isotopic mass == The mass number gives an estimate of the isotopic mass measured in atomic mass units (u). For 12C, the isotopic mass is exactly 12, since the atomic mass unit is defined as 1/12 of the mass of 12C. For other isotopes, the isotopic mass is usually within 0.1 u of the mass number. For example, 35Cl (17 protons and 18 neutrons) has a mass number of 35 and an isotopic mass of 34.96885. The difference of the actual isotopic mass minus the mass number of an atom is known as the mass excess, which for 35Cl is –0.03115. Mass excess should not be confused with mass defect which is the difference between the mass of an atom and its constituent particles (namely protons, neutrons
|
{
"page_id": 659068,
"source": null,
"title": "Mass number"
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|
and electrons). There are two reasons for mass excess: The neutron is slightly heavier than the proton. This increases the mass of nuclei with more neutrons than protons relative to the atomic mass unit scale based on 12C with equal numbers of protons and neutrons. Nuclear binding energy varies between nuclei. A nucleus with greater binding energy has a lower total energy, and therefore a lower mass according to Einstein's mass–energy equivalence relation E = mc2. For 35Cl, the isotopic mass is less than 35, so this must be the dominant factor. == Relative atomic mass of an element == The mass number should also not be confused with the standard atomic weight (also called atomic weight) of an element, which is the ratio of the average atomic mass of the different isotopes of that element (weighted by abundance) to the atomic mass constant. The atomic weight is a mass ratio, while the mass number is a counted number (and so an integer). This weighted average can be quite different from the near-integer values for individual isotopic masses. For instance, there are two main isotopes of chlorine: chlorine-35 and chlorine-37. In any given sample of chlorine that has not been subjected to mass separation there will be roughly 75% of chlorine atoms which are chlorine-35 and only 25% of chlorine atoms which are chlorine-37. This gives chlorine a relative atomic mass of 35.5 (actually 35.4527 g/mol). Moreover, the weighted average mass can be near-integer, but at the same time not corresponding to the mass of any natural isotope. For example, bromine has only two stable isotopes, 79Br and 81Br, naturally present in approximately equal fractions, which leads to the standard atomic mass of bromine close to 80 (79.904 g/mol), even though the isotope 80Br with such mass is unstable. ==
|
{
"page_id": 659068,
"source": null,
"title": "Mass number"
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|
References == == Further reading == Bishop, Mark. "The Structure of Matter and Chemical Elements (ch. 3)". An Introduction to Chemistry. Chiral Publishing. p. 93. ISBN 978-0-9778105-4-3. Retrieved 2008-07-08.
|
{
"page_id": 659068,
"source": null,
"title": "Mass number"
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|
The molecular formula C40H44N4O16 (molar mass: 836.79 g/mol, exact mass: 836.275231 u) may refer to: Uroporphyrinogen I Uroporphyrinogen III
|
{
"page_id": 24120961,
"source": null,
"title": "C40H44N4O16"
}
|
An EOSFET or electrolyte–oxide–semiconductor field-effect transistor is a FET, like a MOSFET, but with an electrolyte solution replacing the metal for the detection of neuronal activity. Many EOSFETs are integrated in a neurochip. == References ==
|
{
"page_id": 2035333,
"source": null,
"title": "EOSFET"
}
|
Beyond Einstein: The Cosmic Quest for the Theory of the Universe is a book by Michio Kaku, a theoretical physicist from the City College of New York, and Jennifer Trainer Thompson. It focuses on the development of superstring theory, which might become the unified field theory of the strong force, the weak force, electromagnetism and gravity. The book was initially published on February 1, 1987, by Bantam Books. == Overview == Beyond Einstein tries to explain the basics of superstring theory. Michio Kaku analyzes the history of theoretical physics and the struggle to formulate a unified field theory. He posits that the superstring theory might be the only theory that can unite quantum mechanics and general relativity in one theory. == References ==
|
{
"page_id": 13045388,
"source": null,
"title": "Beyond Einstein (book)"
}
|
A pyridinecarboxylic acid is any member of a group of organic compounds which are monocarboxylic derivatives of pyridine. Pyridinecarboxylic acid comes in three isomers: Picolinic acid (2-pyridinecarboxylic acid) Nicotinic acid (3-pyridinecarboxylic acid), also known as Niacin Isonicotinic acid (4-pyridinecarboxylic acid) All isomers share the molecular weight 123,11 g/mol and the chemical formula C6H5NO2. == See also == Pyridinedicarboxylic acid
|
{
"page_id": 5639821,
"source": null,
"title": "Pyridinecarboxylic acid"
}
|
Molecular diagnostics is a collection of techniques used to analyze biological markers in the genome and proteome, and how their cells express their genes as proteins, applying molecular biology to medical testing. In medicine the technique is used to diagnose and monitor disease, detect risk, and decide which therapies will work best for individual patients,: foreword and in agricultural biosecurity similarly to monitor crop- and livestock disease, estimate risk, and decide what quarantine measures must be taken. By analysing the specifics of the patient and their disease, molecular diagnostics offers the prospect of personalised medicine. These tests are useful in a range of medical specialties, including infectious disease, oncology, human leucocyte antigen typing (which investigates and predicts immune function), coagulation, and pharmacogenomics—the genetic prediction of which drugs will work best.: v-vii They overlap with clinical chemistry (medical tests on bodily fluids). == History == The field of molecular biology grew in the late twentieth century, as did its clinical application. In 1980, Yuet Wai Kan et al. suggested a prenatal genetic test for Thalassemia that did not rely upon DNA sequencing—then in its infancy—but on restriction enzymes that cut DNA where they recognised specific short sequences, creating different lengths of DNA strand depending on which allele (genetic variation) the fetus possessed. In the 1980s, the phrase was used in the names of companies such as Molecular Diagnostics Incorporated and Bethseda Research Laboratories Molecular Diagnostics. During the 1990s, the identification of newly discovered genes and new techniques for DNA sequencing led to the appearance of a distinct field of molecular and genomic laboratory medicine; in 1995, the Association for Molecular Pathology (AMP) was formed to give it structure. In 1999, the AMP co-founded The Journal of Medical Diagnostics. Informa Healthcare launched Expert Reviews in Medical Diagnostics in 2001. From 2002 onwards,
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{
"page_id": 40439442,
"source": null,
"title": "Molecular diagnostics"
}
|
the HapMap Project aggregated information on the one-letter genetic differences that recur in the human population—the single nucleotide polymorphisms—and their relationship with disease.: ch 37 In 2012, molecular diagnostic techniques for Thalassemia use genetic hybridization tests to identify the specific single nucleotide polymorphism causing an individual's disease. As the commercial application of molecular diagnostics has become more important, so has the debate about patenting of the genetic discoveries at its heart. In 1998, the European Union's Directive 98/44/ECclarified that patents on DNA sequences were allowable. In 2010 in the US, AMP sued Myriad Genetics to challenge the latter's patents regarding two genes, BRCA1, BRCA2, which are associated with breast cancer. In 2013, the U.S. Supreme Court partially agreed, ruling that a naturally occurring gene sequence could not be patented. == Techniques == === Development from research tools === The industrialisation of molecular biology assay tools has made it practical to use them in clinics.: foreword Miniaturisation into a single handheld device can bring medical diagnostics into the clinic and into the office or home.: foreword The clinical laboratory requires high standards of reliability; diagnostics may require accreditation or fall under medical device regulations. As of 2011, some US clinical laboratories nevertheless used assays sold for "research use only". Laboratory processes need to adhere to regulations, such as the Clinical Laboratory Improvement Amendments, Health Insurance Portability and Accountability Act, Good Laboratory Practice, and Food and Drug Administration specifications in the United States. Laboratory Information Management Systems help by tracking these processes. Regulation applies to both staff and supplies. As of 2012, twelve US states require molecular pathologists to be licensed; several boards such as the American Board of Medical Genetics and the American Board of Pathology certify technologists, supervisors, and laboratory directors. Automation and sample barcoding maximise throughput and reduce the
|
{
"page_id": 40439442,
"source": null,
"title": "Molecular diagnostics"
}
|
possibility of error or contamination during manual handling and results reporting. Single devices to do the assay from beginning to end are now available. === Assays === Molecular diagnostics uses in vitro biological assays such as PCR-ELISA or Fluorescence in situ hybridization. The assay detects a molecule, often in low concentrations, that is a marker of disease or risk in a sample taken from a patient. Preservation of the sample before analysis is critical. Manual handling should be minimised. The fragile RNA molecule poses certain challenges. As part of the cellular process of expressing genes as proteins, it offers a measure of gene expression but it is vulnerable to hydrolysis and breakdown by ever-present RNAse enzymes. Samples can be snap-frozen in liquid nitrogen or incubated in preservation agents.: ch 39 Because molecular diagnostics methods can detect sensitive markers, these tests are less intrusive than a traditional biopsy. For example, because cell-free nucleic acids exist in human plasma, a simple blood sample can be enough to sample genetic information from tumours, transplants or an unborn fetus.: ch 45 Many, but not all, molecular diagnostics methods based on nucleic acids detection use polymerase chain reaction (PCR) to vastly increase the number of nucleic acid molecules, thereby amplifying the target sequence(s) in the patient sample.: foreword PCR is a method that a template DNA is amplified using synthetic primers, a DNA polymerase, and dNTPs. The mixture is cycled between at least 2 temperatures: a high temperature for denaturing double-stranded DNA into single-stranded molecules and a low temperature for the primer to hybridize to the template and for the polymerase to extend the primer. Each temperature cycle theoretically doubles the quantity of target sequence. Detection of sequence variations using PCR typically involves the design and use oligonucleotide reagents that amplify the variant of interest
|
{
"page_id": 40439442,
"source": null,
"title": "Molecular diagnostics"
}
|
more efficiently than wildtype sequence. PCR is currently the most widely used method for detection of DNA sequences. The detection of the marker might use real time PCR, direct sequencing,: ch 17 microarray chips—prefabricated chips that test many markers at once,: ch 24 or MALDI-TOF The same principle applies to the proteome and the genome. High-throughput protein arrays can use complementary DNA or antibodies to bind and hence can detect many different proteins in parallel. Molecular diagnostic tests vary widely in sensitivity, turn around time, cost, coverage and regulatory approval. They also vary in the level of validation applied in the laboratories using them. Hence, robust local validation in accordance with the regulatory requirements and use of appropriate controls is required especially where the result may be used to inform a patient treatment decision. Benefits === Prenatal === Conventional prenatal tests for chromosomal abnormalities such as Down Syndrome rely on analysing the number and appearance of the chromosomes—the karyotype. Molecular diagnostics tests such as microarray comparative genomic hybridisation test a sample of DNA instead, and because of cell-free DNA in plasma, could be less invasive, but as of 2013 it is still an adjunct to the conventional tests. === Treatment === Some of a patient's single nucleotide polymorphisms—slight differences in their DNA—can help predict how quickly they will metabolise particular drugs; this is called pharmacogenomics. For example, the enzyme CYP2C19 metabolises several drugs, such as the anti-clotting agent Clopidogrel, into their active forms. Some patients possess polymorphisms in specific places on the 2C19 gene that make poor metabolisers of those drugs; physicians can test for these polymorphisms and find out whether the drugs will be fully effective for that patient. Advances in molecular biology have helped show that some syndromes that were previously classed as a single disease are actually
|
{
"page_id": 40439442,
"source": null,
"title": "Molecular diagnostics"
}
|
multiple subtypes with entirely different causes and treatments. Molecular diagnostics can help diagnose the subtype—for example of infections and cancers—or the genetic analysis of a disease with an inherited component, such as Silver-Russell syndrome. === Infectious disease === Molecular diagnostics are used to identify infectious diseases such as chlamydia, influenza virus and tuberculosis; or specific strains such as H1N1 virus or SARS-CoV-2. Genetic identification can be swift; for example a loop-mediated isothermal amplification test diagnoses the malaria parasite and is rugged enough for developing countries. But despite these advances in genome analysis, in 2013 infections are still more often identified by other means—their proteome, bacteriophage, or chromatographic profile. Molecular diagnostics are also used to understand the specific strain of the pathogen—for example by detecting which drug resistance genes it possesses—and hence which therapies to avoid. In addition, assays based on metagenomic next generation sequencing can be implemented to identify pathogenic organisms without bias. === Disease risk management === A patient's genome may include an inherited or random mutation which affects the probability of developing a disease in the future. For example, Lynch syndrome is a genetic disease that predisposes patients to colorectal and other cancers; early detection can lead to close monitoring that improves the patient's chances of a good outcome. Cardiovascular risk is indicated by biological markers and screening can measure the risk that a child will be born with a genetic disease such as Cystic fibrosis. Genetic testing is ethically complex: patients may not want the stress of knowing their risk. In countries without universal healthcare, a known risk may raise insurance premiums. === Cancer === Cancer is a change in the cellular processes that cause a tumour to grow out of control. Cancerous cells sometimes have mutations in oncogenes, such as KRAS and CTNNB1 (β-catenin). Analysing the
|
{
"page_id": 40439442,
"source": null,
"title": "Molecular diagnostics"
}
|
molecular signature of cancerous cells—the DNA and its levels of expression via messenger RNA—enables physicians to characterise the cancer and to choose the best therapy for their patients. As of 2010, assays that incorporate an array of antibodies against specific protein marker molecules are an emerging technology; there are hopes for these multiplex assays that could measure many markers at once. Other potential future biomarkers include micro RNA molecules, which cancerous cells express more of than healthy ones. Cancer is a disease with excessive molecular causes and constant evolution. There's also heterogeneity of disease even in an individual. Molecular studies of cancer have proved the significance of driver mutations in the growth and metastasis of tumors. Many technologies for detection of sequence variations have been developed for cancer research. These technologies generally can be grouped into three approaches: polymerase chain reaction (PCR), hybridization, and next-generation sequencing (NGS). Currently, a lot of PCR and hybridization assays have been approved by FDA as in vitro diagnostics. NGS assays, however, are still at an early stage in clinical diagnostics. To do the molecular diagnostic test for cancer, one of the significant issue is the DNA sequence variation detection. Tumor biopsy samples used for diagnostics always contain as little as 5% of the target variant as compared to wildtype sequence. Also, for noninvasive applications from peripheral blood or urine, the DNA test must be specific enough to detect mutations at variant allele frequencies of less than 0.1%. Currently, by optimizing the traditional PCR, there's a new invention, amplification-refractory mutation system (ARMS) is a method for detecting DNA sequence variants in cancer. The principle behind ARMS is that the enzymatic extension activity of DNA polymerases is highly sensitive to mismatches near the 3' end of primer. Many different companies have developed diagnostics tests based on
|
{
"page_id": 40439442,
"source": null,
"title": "Molecular diagnostics"
}
|
ARMS PCR primers. For instance, Qiagen therascreen, Roche cobas and Biomerieux THxID have developed FDA approved PCR tests for detecting lung, colon cancer and metastatic melanoma mutations in the KRAS, EGFR and BRAF genes. Their IVD kits were basically validated on genomic DNA extracted from FFPE tissue. There are also microarrays that utilize hybridization mechanism to diagnose cancer. More than a million of different probes can be synthesized on an array with Affymetrix's Genechip technology with a detection limit of one to ten copies of mRNA per well. Optimized microarrays are typically considered to produce repeatable relative quantitation of different targets. Currently, FDA have already approved a number of diagnostics assays utilizing microarrays: Agendia's MammaPrint assays can inform the breast cancer recurrence risk by profiling the expression of 70 genes related to breast cancer; Autogenomics INFNITI CYP2C19 assay can profile genetic polymorphisms, whose impacts on therapeutic response to antidepressants are great; and Affymetrix's CytoScan Dx can evaluate intellectual disabilities and congenital disorders by analyzing chromosomal mutation. In the future, the diagnostic tools for cancer will likely to focus on the Next Generation Sequencing (NGS). By utilizing DNA and RNA sequencing to do cancer diagnostics, technology in the field of molecular diagnostics tools will develop better. Although NGS throughput and price have dramatically been reduced over the past 10 years by roughly 100-fold, we remain at least 6 orders of magnitude away from performing deep sequencing at a whole genome level. Currently, Ion Torrent developed some NGS panels based on translational AmpliSeq, for example, the Oncomine Comprehensive Assay. They are focusing on utilizing deep sequencing of cancer-related genes to detect rare sequence variants. Molecular diagnostics tool can be used for cancer risk assessment. For example, the BRCA1/2 test by Myriad Genetics assesses women for lifetime risk of breast cancer. Also, some
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{
"page_id": 40439442,
"source": null,
"title": "Molecular diagnostics"
}
|
cancers are not always employed with clear symptoms. It is useful to analyze people when they do not show obvious symptoms and thus can detect cancer at early stages. For example, the ColoGuard test may be used to screen people over 55 years old for colorectal cancer. Cancer is a longtime-scale disease with various progression steps, molecular diagnostics tools can be used for prognosis of cancer progression. For example, the OncoType Dx test by Genomic Health can estimate risk of breast cancer. Their technology can inform patients to seek chemotherapy when necessary by examining the RNA expression levels in breast cancer biopsy tissue. With rising government support in DNA molecular diagnostics, it is expected that an increasing number of clinical DNA detection assays for cancers will become available soon. Currently, research in cancer diagnostics are developing fast with goals for lower cost, less time consumption and simpler methods for doctors and patients. == See also == Molecular medicine (the broader field of the molecular understanding of disease) Molecular pathology Laboratory Developed Test Pathogenesis Pathogenomics Pathology Precision medicine Personalized medicine == References ==
|
{
"page_id": 40439442,
"source": null,
"title": "Molecular diagnostics"
}
|
The uterine microbiome refers to the community of commensal, nonpathogenic microorganisms—including bacteria, viruses, and yeasts/fungi—present in a healthy uterus, as well as in the amniotic fluid and endometrium. These microorganisms coexist in a specific environment within the uterus, playing a vital role in maintaining reproductive health. In the past, the uterus was believed to be a sterile environment, free of any microbial life. Recent advancements in microbiological research, particularly the improvement of 16S rRNA gene sequencing techniques, have challenged this long-held belief. These advanced techniques have made it possible to detect bacteria and other microorganisms present in very low numbers. Using this procedure that allows the detection of bacteria that cannot be cultured outside the body, studies of microbiota present in the uterus are expected to increase. == Uterine microbiome and fertility == In the past, the uterine cavity had been traditionally considered to be sterile, but potentially susceptible to be affected by vaginal bacteria. However, this idea has been disproved. Moreover, it's been shown that endometrial and vaginal microbiota can differ in structure and composition in some women. The microbiome of the innermost layer of the uterus, the endometrium, may influence its capacity to allow an embryo to implant. The existence of more than 10% of non-Lactobacillus bacteria in the endometrium is correlated with negative impacts on reproductive function and should be considered as an emerging cause of implantation failure and pregnancy loss. == Characteristics == Bacteria, viruses and one genus of yeasts are a normal part of the uterus before and during pregnancy. The uterus has been found to possess its own characteristic microbiome that differs significantly from the vaginal microbiome, consisting primarily of lactobacillus species, and at far fewer numbers. In addition, the immune system is able to differentiate between those bacteria normally found in the uterus
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{
"page_id": 50925207,
"source": null,
"title": "Uterine microbiome"
}
|
and those that are pathogenic. Hormonal changes have an effect on the microbiota of the uterus. == Taxa == === Commensals === The organisms listed below have been identified as commensals in the healthy uterus. Some also have the potential for growing to the point of causing disease: === Pathogens === Other taxa can be present, without causing disease or an immune response. Their presence is associated with negative birth outcomes. == Clinical significance == Prophylactic antibiotics have been injected into the uterus to treat infertility. This has been done before the transfer of embryos with the intent to improve implantation rates. No association exists between successful implantation and antibiotic treatment. Infertility treatments often progress to the point where a microbiological analysis of the uterine microbiota is performed. Preterm birth is associated with certain species of bacteria that are not normally part of the healthy uterine microbiome. The uterine microbiome appears to be altered in female patients who experience endometrial cancer, endometriosis, chronic endometriosis, and related gynecological pathologies, suggesting the clinical relevance of the uterine microbiome’s composition. Next-generation sequencing has revealed the presence of certain bacterial taxa, such as Alteromonas, to be present in patients presenting with gynecological conditions. Clinically speaking, there is no universal protocol on how to treat uterine dysbiosis. However, use of antibiotics has been widespread. In the context of infertility, researchers have studied the effects of a treatment plan of antibiotics in conjunction with prebiotics and probiotics to increase Lactobacillus colonization in the endometrium. It was found that, while there was a Lactobacillus-dominated endometrium correlated with increased pregnancy rates, the data was not statistically significant. Antibiotics have also been used to treat chronic endometritis and endometriosis. Interestingly, a link between the oral microbiome and the uterine microbiome has been uncovered. Fusobacterium nucleatum, a Gram-negative bacteria commensal
|
{
"page_id": 50925207,
"source": null,
"title": "Uterine microbiome"
}
|
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