|
Von Bertalanffy Function
The von Bertalanffy growth function (VBGF), or von Bertalanffy curve, is a type of growth curve for a time series and is named after Ludwig von Bertalanffy. It is a special case of the generalised logistic function. The growth curve is used to model mean length from age in animals. The function is commonly applied in ecology to model fish growth and in paleontology to model sclerochronological parameters of shell growth. The model can be written as the following: : L(a)= L_\infty(1-\exp(-k(a-t_0))) where a is age, k is the growth coefficient, t_0 is the theoretical age when size is zero, and L_\infty is asymptotic size. It is the solution of the following linear differential equation: : \frac = k (L_ - L ) Seasonally-adjusted von Bertalanffy The seasonally-adjusted von Bertalanffy is an extension of this function that accounts for organism growth that occurs seasonally. It was created by I. F. Somers in 1988. See also * Gompertz function * Monod equation The Monod equa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bulletin - Southern California Academy Of Sciences (2011) (20495253222)
Bulletin or The Bulletin may refer to: Periodicals (newspapers, magazines, journals) * Bulletin (online newspaper), a Swedish online newspaper * ''The Bulletin'' (Australian periodical), an Australian magazine (1880–2008) ** Bulletin Debate, a famous dispute from 1892 to 1893 between Henry Lawson and Banjo Paterson * ''The Bulletin'' (alternative weekly), an alternative weekly published in Montgomery County, Texas, U.S. * ''The Bulletin'' (Bend), a daily newspaper in Bend, Oregon, U.S. * ''The Bulletin'' (Belgian magazine), a weekly English-language magazine published in Brussels, Belgium * ''The Bulletin'' (Philadelphia newspaper), a newspaper in Philadelphia, Pennsylvania, U.S. (2004–2009) * ''The Bulletin'' (Norwich) * ''The Bulletin'' (Pittsburgh), a monthly community newspaper in Pittsburgh, Pennsylvania, U.S. * ''London Bulletin'', surrealist monthly magazine (1938–1940) * ''The Morning Bulletin'', a daily newspaper published in Rockhampton, Queensland, Austral ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Growth Curve (statistics)
The growth curve model in statistics is a specific multivariate linear model, also known as GMANOVA (Generalized Multivariate Analysis-Of-Variance). It generalizes MANOVA by allowing post-matrices, as seen in the definition. Definition Growth curve model: Let X be a ''p''×''n'' random matrix corresponding to the observations, A a ''p''×''q'' within design matrix with ''q'' ≤ ''p'', B a ''q''×''k'' parameter matrix, C a ''k''×''n'' between individual design matrix with rank(''C'') + ''p'' ≤ ''n'' and let Σ be a positive-definite ''p''×''p'' matrix. Then : X=ABC+\Sigma^E defines the growth curve model, where A and C are known, B and Σ are unknown, and E is a random matrix distributed as ''N''''p'',''n''(0,''I''''p'',''n''). This differs from standard MANOVA by the addition of C, a "postmatrix". History Many writers have considered the growth curve analysis, among them Wishart (1938), Box (1950) and Rao (1958). Potthoff and Roy in 1964 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time Series
In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Examples of time series are heights of ocean tides, counts of sunspots, and the daily closing value of the Dow Jones Industrial Average. A time series is very frequently plotted via a run chart (which is a temporal line chart). Time series are used in statistics, signal processing, pattern recognition, econometrics, mathematical finance, weather forecasting, earthquake prediction, electroencephalography, control engineering, astronomy, communications engineering, and largely in any domain of applied science and engineering which involves temporal measurements. Time series ''analysis'' comprises methods for analyzing time series data in order to extract meaningful statistics and other characteristics of the data. Time series ''forecasting' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ludwig Von Bertalanffy
Karl Ludwig von Bertalanffy (19 September 1901 – 12 June 1972) was an Austrian biologist known as one of the founders of general systems theory (GST). This is an interdisciplinary practice that describes systems with interacting components, applicable to biology, cybernetics and other fields. Bertalanffy proposed that the classical laws of thermodynamics might be applied to closed systems, but not necessarily to "open systems" such as living things. His mathematical model of an organism's growth over time, published in 1934, is still in use today. Bertalanffy grew up in Austria and subsequently worked in Vienna, London, Canada, and the United States. Biography Ludwig von Bertalanffy was born and grew up in the little village of Atzgersdorf (now Liesing) near Vienna. The Bertalanffy family had roots in the 16th century nobility of Hungary which included several scholars and court officials.T.E. Weckowicz (1989). Ludwig von Bertalanffy (1901-1972): A Pioneer of General Systems T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generalised Logistic Function
The generalized logistic function or curve is an extension of the logistic or sigmoid functions. Originally developed for growth modelling, it allows for more flexible S-shaped curves. The function is sometimes named Richards's curve after F. J. Richards, who proposed the general form for the family of models in 1959. Definition Richards's curve has the following form: :Y(t) = A + where Y = weight, height, size etc., and t = time. It has five parameters: *A: the lower (left) asymptote; *K: the upper (right) asymptote when C=1. If A=0 and C=1 then K is called the carrying capacity; *B: the growth rate; *\nu > 0 : affects near which asymptote maximum growth occurs. *Q: is related to the value Y(0) *C: typically takes a value of 1. Otherwise, the upper asymptote is A + The equation can also be written: :Y(t) = A + where M can be thought of as a starting time, at which Y(M) = A + . Including both Q and M can be convenient: :Y(t) = A + this representation simplifies the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Growth Curve (biology)
A growth curve is an empirical model of the evolution of a quantity over time. Growth curves are widely used in biology for quantities such as population size or biomass (in population ecology and demography, for population growth analysis), individual body height or biomass (in physiology, for growth analysis of individuals). Values for the measured property can be plotted on a graph as a function of time; see Figure 1 for an example... Bacterial growth In this example (Figure 1, see Lac operon for details) the number of bacteria present in a nutrient-containing broth was measured during the course of an 8-hour cell growth experiment. The observed pattern of bacterial growth is bi-phasic because two different sugars were present, glucose and lactose. The bacteria prefer to consume glucose (Phase I) and only use the lactose (Phase II) after the glucose has been depleted. Analysis of the molecular basis for this bi-phasic growth curve led to the discovery of the basic mechanis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ecology
Ecology () is the study of the relationships between living organisms, including humans, and their physical environment. Ecology considers organisms at the individual, population, community, ecosystem, and biosphere level. Ecology overlaps with the closely related sciences of biogeography, evolutionary biology, genetics, ethology, and natural history. Ecology is a branch of biology, and it is not synonymous with environmentalism. Among other things, ecology is the study of: * The abundance, biomass, and distribution of organisms in the context of the environment * Life processes, antifragility, interactions, and adaptations * The movement of materials and energy through living communities * The successional development of ecosystems * Cooperation, competition, and predation within and between species * Patterns of biodiversity and its effect on ecosystem processes Ecology has practical applications in conservation biology, wetland management, natural resource managemen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paleontology
Paleontology (), also spelled palaeontology or palæontology, is the scientific study of life that existed prior to, and sometimes including, the start of the Holocene epoch (roughly 11,700 years before present). It includes the study of fossils to classify organisms and study their interactions with each other and their environments (their paleoecology). Paleontological observations have been documented as far back as the 5th century BC. The science became established in the 18th century as a result of Georges Cuvier's work on comparative anatomy, and developed rapidly in the 19th century. The term itself originates from Greek (, "old, ancient"), (, ( gen. ), "being, creature"), and (, "speech, thought, study"). Paleontology lies on the border between biology and geology, but differs from archaeology in that it excludes the study of anatomically modern humans. It now uses techniques drawn from a wide range of sciences, including biochemistry, mathematics, and engineering. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sclerochronology
Sclerochronology is the study of periodic physical and chemical features in the hard tissues of animals that grow by accretion, including invertebrates and coralline red algae, and the temporal context in which they formed. It is particularly useful in the study of marine paleoclimatology. The term was coined in 1974 following pioneering work on nuclear test atolls by Knutson and Buddemeier and comes from the three Greek words ''skleros'' (hard), ''chronos'' (time) and ''logos'' (science), which together refer to the use of the hard parts of living organisms to order events in time. It is, therefore, a form of stratigraphy. Sclerochronology focuses primarily upon growth patterns reflecting annual, monthly, fortnightly, tidal, daily, and sub-daily (ultradian) increments of time. The regular time increments are controlled by biological clocks, which, in turn, are caused by environmental and astronomical pacemakers. Familiar examples include: *annual bandings in reef coral sk ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gompertz Function
The Gompertz curve or Gompertz function is a type of mathematical model for a time series, named after Benjamin Gompertz (1779–1865). It is a sigmoid function which describes growth as being slowest at the start and end of a given time period. The right-side or future value asymptote of the function is approached much more gradually by the curve than the left-side or lower valued asymptote. This is in contrast to the simple logistic function in which both asymptotes are approached by the curve symmetrically. It is a special case of the generalised logistic function. The function was originally designed to describe human mortality, but since has been modified to be applied in biology, with regard to detailing populations. History Benjamin Gompertz (1779–1865) was an actuary in London who was privately educated. He was elected a fellow of the Royal Society in 1819. The function was first presented in his June 16, 1825 paper at the bottom of page 518. The Gompertz function r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monod Equation
The Monod equation is a mathematical model for the growth of microorganisms. It is named for Jacques Monod (1910 – 1976, a French biochemist, Nobel Prize in Physiology or Medicine in 1965), who proposed using an equation of this form to relate microbial growth rates in an aqueous environment to the concentration of a limiting nutrient. The Monod equation has the same form as the Michaelis–Menten equation, but differs in that it is empirical while the latter is based on theoretical considerations. The Monod equation is commonly used in environmental engineering. For example, it is used in the activated sludge model for sewage treatment. Equation The empirical Monod equation is: : \mu = \mu_\max where: * ''μ'' is the growth rate of a considered microorganism * ''μ''max is the maximum growth rate of this microorganism * 'S''is the concentration of the limiting substrate ''S'' for growth * ''K''''s'' is the "half-velocity constant"—the value of 'S''when ''μ''/''Π... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
.jpg "Click for more on -> Ecology")
