But what that did was that it made it so that your advantage went up logarithmically rather than linearly.
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Hot spots observed in the new study, with size corresponding logarithmically to intensity (a spot twice as large is ten times brighter).
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More than a decade later, such de-anonymizing is becoming ever-easier, with more data points to triangulate and logarithmically more computing power.
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Plotted logarithmically, however, it transforms into a straight line — which means that deviations from the exponential spread of the virus become much easier to discern.
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From one crumple to the next, he observed that a piece of paper never stopped forming new creases, although the rate of their formation slowed logarithmically.
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Speaking to CNN, Geoscience Australia Senior Duty Seismologist Hugh Glanville said while the 2011 earthquake had only been two degrees of magnitude higher than Tuesday's, a quake's impact increased logarithmically for every point of magnitude.
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In "Frequency," in which 3D acrylic columns represent where he's been, and grow logarithmically taller in places he's visited more, the contrast between the many short columns and the few ceiling-high data points made me think about the select locations that have an outsized importance in my own life.
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The Bell numbers form a logarithmically convex sequence. Dividing them by the factorials, Bn/n!, gives a logarithmically concave sequence.
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In other words, the amount of memory needed to store N grows logarithmically with N.
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Therefore, the diameter of Ramanujan graphs are also bounded logarithmically in terms of the number of vertices.
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If only the ordinate or abscissa is scaled logarithmically, the plot is referred to as a semi- logarithmic plot.
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In mathematics, a function f is logarithmically convex or superconvexKingman, J.F.C. 1961. A convexity property of positive matrices. Quart. J. Math. Oxford (2) 12,283-284.
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More precisely, McVeillance was defined as the ratio (linearly) or difference (logarithmically) of surveillance to sousveillance. McVeillance is one of the topics of the IEEE conference.
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Plot on log–log scale of equation of a line If both the vertical and horizontal axes of a plot are scaled logarithmically, the plot is referred to as a log–log plot.
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This result is known as Hölder's theorem. A definite and generally applicable characterization of the gamma function was not given until 1922. Harald Bohr and Johannes Mollerup then proved what is known as the Bohr–Mollerup theorem: that the gamma function is the unique solution to the factorial recurrence relation that is positive and logarithmically convex for positive and whose value at 1 is 1 (a function is logarithmically convex if its logarithm is convex). Another characterisation is given by the Wielandt theorem.
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The most efficient way to analyze log-normally distributed data consists of applying the well-known methods based on the normal distribution to logarithmically transformed data and then to back-transform results if appropriate.
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Self-balancing binary search trees may provide an acceptable compromise, where access time is not equal for all members of a collection, but the maximum time to retrieve a given member grows only logarithmically with its size.
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However, data that are linear or even logarithmically non-linear and include a continuous range for the independent variable with sparse measurements across each value (e.g., scatter-plot) may be amenable to single CV calculation using a maximum-likelihood estimation approach.
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On the other hand, the global symmetry group is an observable so it is essential that it is the same, SU(M), in both descriptions. The dual magnetic theory is free in the infrared, the coupling constant shrinks logarithmically, and so by the Dirac quantization condition the electric coupling constant grows logarithmically in the infrared. This implies that the potential between two electric charges, at long distances, scales as the logarithm of their distance divided by the distance. When M is between 3N/2 and 3N, in the theory has an infrared fixed point where it becomes a nontrivial conformal field theory.
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It is a predecessor of the slide rule, a calculating aid used from the 17th century until the 1970s. Gunter's line, or line of numbers refers to the logarithmically divided scale, like the most common scales used on slide rules for multiplication and division.
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Mathematically speaking, the normalized floating-point numbers of a given sign are roughly logarithmically spaced, and as such any finite-sized normal float cannot include zero. The denormal floats are a linearly spaced set of values, which span the gap between the negative and positive normal floats.
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It states that when the condition that be logarithmically convex (or "super-convex") is added, it uniquely determines for positive, real inputs. From there, the gamma function can be extended to all real and complex values (except the negative integers and zero) by using the unique analytic continuation of .
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The scale discards color as being part of a color wheel and ignores musical/logarithmic perception so it can overstep the limits of human perception. The introduction of the new scale to the eyeborg in 2010, allows users to decide whether they want to perceive colors logarithmically or not.
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The scale discards color as being part of a color wheel and ignores musical/logarithmic perception so it can overstep the limits of human perception. The introduction of the new scale to the eyeborg in 2010, allows users to decide whether they want to perceive colors logarithmically or not.
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A function is said to grow logarithmically if is (exactly or approximately) proportional to the logarithm of . (Biological descriptions of organism growth, however, use this term for an exponential function., chapter 19, p. 298) For example, any natural number N can be represented in binary form in no more than bits.
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Unlike the trade balance, the trade ratio can be logarithmically transformed regardless of whether a trade deficit or trade surplus exists.Hacker, RS and Hatemi-J, A. (2004) The effect of exchange rate changes on trade balances in the short and long run: Evidence from German trade with transitional Central European Economies. Economics of Transition. 12(4) 777-799.
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The attenuation values of ND filters are specified logarithmically. A ND 3 filter transmits 10−3 of the incident beam power. Placing the largest attenuator last before the CCD sensor will result in the best rejection of ghost images due to multiple reflections. Reflective filters are made with a thin metallic coating and hence operate over a larger bandwidth.
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The log- Cauchy distribution is an example of a heavy-tailed distribution. Some authors regard it as a "super-heavy tailed" distribution, because it has a heavier tail than a Pareto distribution-type heavy tail, i.e., it has a logarithmically decaying tail. As with the Cauchy distribution, none of the non-trivial moments of the log-Cauchy distribution are finite.
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A glide sweep (or chirp) is a continuous signal in which the frequency increases or decreases logarithmically with time. This provides the complete range of testing frequencies between the start and stop frequency. An advantage over the stepped sweep is that the signal duration can be reduced by the user without any loss of frequency resolution in the results. This allows for rapid testing.
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Another critical application was the slide rule, a pair of logarithmically divided scales used for calculation. The non-sliding logarithmic scale, Gunter's rule, was invented shortly after Napier's invention. William Oughtred enhanced it to create the slide rule—a pair of logarithmic scales movable with respect to each other. Numbers are placed on sliding scales at distances proportional to the differences between their logarithms.
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Wilhelm Wundt (seated) with colleagues in his psychological laboratory, the first of its kind. Gustav Fechner began conducting psychophysics research in Leipzig in the 1830s, articulating the principle (Weber–Fechner law) that human perception of a stimulus varies logarithmically according to its intensity.Leahey, History of Modern Psychology (2001), p. 61. Fechner's 1860 Elements of Psychophysics challenged Kant's stricture against quantitative study of the mind.Fechner, G. T. (1860).
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At low energy, the energy loss according to the Bethe formula therefore decreases approximately as v−2 with increasing energy. It reaches a minimum for approximately E = 3Mc2, where M is the mass of the particle (for protons, this would be about at 3000 MeV). For highly relativistic cases β ≈ 1, the energy loss increases again, logarithmically due to the transversal component of the electric field.
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The XY model is a two-dimensional vector spin model that possesses U(1) or circular symmetry. This system is not expected to possess a normal second-order phase transition. This is because the expected ordered phase of the system is destroyed by transverse fluctuations, i.e. the Nambu-Goldstone modes (see Goldstone boson) associated with this broken continuous symmetry, which logarithmically diverge with system size.
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25, p.245 Hipparchus, in the 1st century B.C., introduced the magnitude scale. He allocated first magnitude to the 20 brightest stars and the sixth magnitude to the faintest stars visible to the naked eye. In the 19th Century, this ancient scale of apparent magnitude was logarithmically defined—so that a star of 1.00 mag is exactly 100 times brighter than a star of 6.00 magnitude.
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Senapathy analyzed the distribution of the ORF lengths in computer-generated random DNA sequences first. Surprisingly, this study revealed that there actually existed an upper limit of about 200 codons (600 bases) in the lengths of ORFs. The shortest ORF (zero base in length) was the most frequent. At increasing lengths of ORFs, their frequency decreased logarithmically, reaching almost zero at about 600 bases.
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The propagation constant's value is expressed logarithmically, almost universally to the base e, rather than the more usual base 10 that is used in telecommunications in other situations. The quantity measured, such as voltage, is expressed as a sinusoidal phasor. The phase of the sinusoid varies with distance which results in the propagation constant being a complex number, the imaginary part being caused by the phase change.
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The Brunn–Minkowski inequality asserts that the Lebesgue measure is log- concave. The restriction of the Lebesgue measure to any convex set is also log-concave. By a theorem of Borell, a measure is log-concave if and only if it has a density with respect to the Lebesgue measure on some affine hyperplane, and this density is a logarithmically concave function. Thus, any Gaussian measure is log-concave.
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The reason the Lorenz beam principle was necessary, with its overlapping beams, was because the sharpness of a beam increases approximately logarithmically with the length of the aerial array with which it is generated. A law of diminishing returns operates, such that to attain the sharpness achieved by the Lorenz system with a single beam (approximately 1 mile wide over a range of two hundred miles), an array of prohibitive size would be required.
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This low error margin comes from the controlled sizing and spacing of Ag nanoparticles and the large number of such hotspots on the nanocapsule. Previously there existed only randomly placed hotspots, which produced more variation between nanocapsule sensitivity and therefore increased the error margin. The nanocapsules can detect Raman spectra at small concentrations (for example, 1,2-bi-(4-pyridyl) ethylene (BPE) at 10-12 M) and as concentration increases, the detection sensitivity increases logarithmically.
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Detailed information on measurement of aircraft acoustic signature to meet the requirements of Annex 16 is found in ICAO Document 9501Environmental Technical Manual, Volume I. Procedures for the Noise Certification of Aircraft. (2012) International Civil Aviation Committee on Aviation Environmental Protection. and IEC 61265. Data acquisition in one- third-octave bands is required, followed by processing to yield a logarithmically-scaled value in decibels relative to a sound pressure of 20 micropascals for each one-third-octave band.
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Neotame is sweet because it binds to TAS1R2-receptors of mouth as an agonist. Aspartame binds to the same receptor. Water solutions of neotame, that are equivalent in sweetness to sucrose water solutions, increase logarithmically in relative sweetness as the sucrose concentration of a comparably sweet sucrose solution increases, until a plateau is reached. Maximum sweetness is reached at neotame solution concentrations that are relatively as sweet as a water solution that is 15.1 percentage sucrose by weight, i.e.
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More bits also encouraged the storage of light as linear values, where the number directly corresponds to the amount of light emitted. Linear levels makes calculation of light (in the context of computer graphics) much easier. However, linear color results in disproportionately more samples near white and fewer near black, so the quality of 16-bit linear is about equal to 12-bit sRGB. Floating point numbers can represent linear light levels spacing the samples semi-logarithmically.
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It is customary to transform data logarithmically to fit symmetrical distributions (like the normal and logistic) to data obeying a distribution that is positively skewed (i.e. skew to the right, with mean > mode, and with a right hand tail that is longer than the left hand tail), see lognormal distribution and the loglogistic distribution. A similar effect can be achieved by taking the square root of the data. To fit a symmetrical distribution to data obeying a negatively skewed distribution (i.e.
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Phred was able to calculate highly accurate quality scores that were logarithmically linked to the error probabilities. Phred was quickly adopted by all the major genome sequencing centers as well as many other laboratories; the vast majority of the DNA sequences produced during the Human Genome Project were processed with Phred. After Phred quality scores became the required standard in DNA sequencing, other manufacturers of DNA sequencing instruments, including Li-Cor and ABI, developed similar quality scoring metrics for their base calling software.
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Charpentier et al. suggested that competence for transformation probably evolved as a DNA damage response. Logarithmically growing bacteria differ from stationary phase bacteria with respect to the number of genome copies present in the cell, and this has implications for the capability to carry out an important DNA repair process. During logarithmic growth, two or more copies of any particular region of the chromosome may be present in a bacterial cell, as cell division is not precisely matched with chromosome replication.
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A quarter tone () is a pitch halfway between the usual notes of a chromatic scale or an interval about half as wide (aurally, or logarithmically) as a semitone, which itself is half a whole tone. Quarter tones divide the octave by 50 cents each, and have 24 different pitches. Trumpet with 3 normal valves and a quartering on the extension valve (right) Quarter tone has its roots in the music of the Middle East and more specifically in Persian traditional music.Hormoz Farhat (2004).
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While the Snellen chart remains the default, some authors have argued that the logMAR chart is superior. The logMAR chart presents the same number of symbols on each line, uses a typeface with letters that are equally legible at various sizes, and by varying the symbol size logarithmically, it is easier to use at nonstandard distances. As a consequence of these improvements, the logMAR chart has been proposed as a more reliable tool for measuring visual acuity. However, the logMAR chart has not yet been widely adopted.
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EMCCD. The high voltages used in these serial transfers induce the creation of additional charge carriers through impact ionisation. EMCCD there is a dispersion (variation) in the number of electrons output by the multiplication register for a given (fixed) number of input electrons (shown in the legend on the right). The probability distribution for the number of output electrons is plotted logarithmically on the vertical axis for a simulation of a multiplication register. Also shown are results from the empirical fit equation shown on this page.
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These rivers also tend to be more turbulent, however, and particles in the water increasingly attenuate light as depth increases. Seasonal and diurnal factors might also play a role in light availability because the angle of incidence, the angle at which light strikes water can lead to light lost from reflection. Known as Beer's Law, the shallower the angle, the more light is reflected and the amount of solar radiation received declines logarithmically with depth. Additional influences on light availability include cloud cover, altitude, and geographic position.
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The gain of an amplifier is the ratio of output to input power or amplitude, and is usually measured in decibels. When measured in decibels it is logarithmically related to the power ratio: G(dB)=10 log(Pout /Pin). RF amplifiers are often specified in terms of the maximum power gain obtainable, while the voltage gain of audio amplifiers and instrumentation amplifiers will be more often specified. For example, an audio amplifier with a gain given as 20 dB will have a voltage gain of ten.
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The NFW profile is called 'universal' because it works for a large variety of halo masses, spanning four orders of magnitude, from individual galaxies to the halos of galaxy clusters. This profile has a finite gravitational potential even though the integrated mass still diverges logarithmically. It has become conventional to refer to the mass of a halo at a fiducial point that encloses an overdensity 200 times greater than the critical density of the universe, though mathematically the profile extends beyond this notational point.
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Most PAHs are insoluble in water, which limits their mobility in the environment, although PAHs sorb to fine-grained organic-rich sediments. Aqueous solubility of PAHs decreases approximately logarithmically as molecular mass increases. Two- ringed PAHs, and to a lesser extent three-ringed PAHs, dissolve in water, making them more available for biological uptake and degradation. Further, two- to four-ringed PAHs volatilize sufficiently to appear in the atmosphere predominantly in gaseous form, although the physical state of four-ring PAHs can depend on temperature.
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Perceived "loudness" varies approximately logarithmically with acoustical output power. The change in perceived loudness as a function of change in acoustical power is dependent on the reference power level. It is both useful and technically accurate to express perceived loudness in the logarithmic decibel (dB) scale that is independent of the reference power, with a somewhat straight-line relationship between 10 dB changes and doublings of perceived loudness. The approximately logarithmic relationship between power and perceived loudness is an important factor in audio system design.
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A network is said to be scalable if its performance does not deteriorate even if the network is very large. The scalability of Freenet is being evaluated, but similar architectures have been shown to scale logarithmically. This work indicates that Freenet can find data in O(\log^2 n) hops on a small-world network (which includes both opennet and darknet style Freenet networks), when ignoring the caching which could improve the scalability for popular content. However, this scalability is difficult to test without a very large network.
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A logarithmic timeline is a timeline laid out according to a logarithmic scale. This necessarily implies a zero point and an infinity point, neither of which can be displayed. The most natural zero point is the Big Bang, looking forward, but the most common is the ever-changing present, looking backward. (Also possible is a zero point in the present, looking forward to the infinite future.) The idea of presenting history logarithmically goes back at least to 1932, when John B. Sparks copyrighted his chart "Histomap of Evolution".
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The values stored for HDR images are often gamma compressed (power law) or logarithmically encoded, or floating-point linear values, since fixed-point linear encodings are increasingly inefficient over higher dynamic ranges. HDR images often don't use fixed ranges per color channel—other than traditional images—to represent many more colors over a much wider dynamic range. For that purpose, they do not use integer values to represent the single color channels (e.g., 0-255 in an 8 bit per pixel interval for red, green and blue) but instead use a floating point representation.
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Although the harmonic series does diverge, it does so very slowly. Another problem involving the harmonic series is the Jeep problem, which (in one form) asks how much total fuel is required for a jeep with a limited fuel-carrying capacity to cross a desert, possibly leaving fuel drops along the route. The distance that can be traversed with a given amount of fuel is related to the partial sums of the harmonic series, which grow logarithmically. And so the fuel required increases exponentially with the desired distance.
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Cancellation of the Higgs boson quadratic mass renormalization between fermionic top quark loop and scalar top squark Feynman diagrams in a supersymmetric extension of the Standard Model The original motivation for proposing the MSSM was to stabilize the Higgs mass to radiative corrections that are quadratically divergent in the Standard Model (hierarchy problem). In supersymmetric models, scalars are related to fermions and have the same mass. Since fermion masses are logarithmically divergent, scalar masses inherit the same radiative stability. The Higgs vacuum expectation value is related to the negative scalar mass in the Lagrangian.
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DALI lighting levels are specified by an 8-bit value, where 0 means off, 1 means 0.1% of full brightness, 254 means full brightness, and other values are logarithmically interpolated between, giving a 2.77% increase per step. That is, a (non-zero) control byte denotes a power level of . (A value of 255 is reserved for freezing the current lighting level without changing it.) This is designed to match human eye sensitivity so that perceived brightness steps will have uniform brightness change, and to achieve a uniform brightness between units from different manufacturers.
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Graphic equalizers also divide signals into bands logarithmically and report power by octaves; audio engineers put pink noise through a system to test whether it has a flat frequency response in the spectrum of interest. Systems that do not have a flat response can be equalized by creating an inverse filter using a graphic equalizer. Because pink noise has a tendency to occur in natural physical systems, it is often useful in audio production. Pink noise can be processed, filtered, and/or effects can be added to produce desired sounds.
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The conduction band has now been "logarithmically discretized". The Hamiltonian is now in a position to be transformed into so-called linear chain form, in which the impurity is coupled to only one conduction band state, which is coupled to one other conduction band state and so on. Crucially, these couplings decrease exponentially along the chain, so that, even though the transformed Hamiltonian is for an infinite chain, one can consider a chain of finite length and still obtain useful results. The only restriction to the conduction-band is that it is non-interacting.
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Advances in assisted reproductive technology (ART) have revolutionized the ability to help men with even the severest forms of male infertility to become fathers. This field began in earnest in 1978 when the first successful in vitro fertilization (IVF) cycle was performed. This technique involves controlled ovarian stimulation followed by egg retrieval, in vitro fertilization, and embryo transfer to the uterus. In the United States, the number of babies born to infertile couples with IVF has risen logarithmically from 260 babies in 1985 to almost 50,000 in 2003.
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Emil Julius Gumbel codified this theory in his 1958 book Statistics of Extremes, including the Gumbel distributions that bear his name. These results can be extended to allowing for slight correlations between variables, but the classical theory does not extend to strong correlations of the order of the variance. One universality class of particular interest is that of log-correlated fields, where the correlations decay logarithmically with the distance. A summary of historically important publications relating to extreme value theory can be found in the article List of publications in statistics.
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The frequency axis of this symbolic diagram may be linearly or logarithmically scaled. Except in special cases, the peak response will not align precisely with the center frequency. In electrical engineering and telecommunications, the center frequency of a filter or channel is a measure of a central frequency between the upper and lower cutoff frequencies. It is usually defined as either the arithmetic mean or the geometric mean of the lower cutoff frequency and the upper cutoff frequency of a band-pass system or a band-stop system.
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The viscosity of a multi-grade oil still varies logarithmically with temperature, but the slope representing the change is lessened. The SAE designation for multi-grade oils includes two viscosity grades; for example, 10W-30 designates a common multi-grade oil. The first number '10W' is the equivalent grade of the single grade oil that has the oil's viscosity at cold temperature and the second number is the grade of the equivalent single-grade oil that describes its viscosity at . Note that both numbers are grades and not viscosity values.
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Vladimir Gribov noted that the Froissart bound combined with the assumption of maximum possible scattering implied there was a Regge trajectory that would lead to logarithmically rising cross sections, a trajectory nowadays known as the pomeron. He went on to formulate a quantitative perturbation theory for near beam line scattering dominated by multi-pomeron exchange. From the fundamental observation that hadrons are composite, there grew two points of view. Some correctly advocated that there were elementary particles, nowadays called quarks and gluons, which made a quantum field theory in which the hadrons were bound states.
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Hick's law, or the Hick–Hyman law, named after British and American psychologists William Edmund Hick and Ray Hyman, describes the time it takes for a person to make a decision as a result of the possible choices: increasing the number of choices will increase the decision time logarithmically. The Hick–Hyman law assesses cognitive information capacity in choice reaction experiments. The amount of time taken to process a certain amount of bits in the Hick–Hyman law is known as the rate of gain of information. Hick's law is sometimes cited to justify menu design decisions.
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The eye senses brightness approximately logarithmically over a moderate range and stellar magnitude is measured on a logarithmic scale. This magnitude scale was invented by the ancient Greek astronomer Hipparchus in about 150 B.C. He ranked the stars he could see in terms of their brightness, with 1 representing the brightest down to 6 representing the faintest, though now the scale has been extended beyond these limits; an increase in 5 magnitudes corresponds to a decrease in brightness by a factor of 100. Modern researchers have attempted to incorporate such perceptual effects into mathematical models of vision.
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The freezing point is the temperature at which the liquid solvent and solid solvent are at equilibrium, so that their vapour pressures are equal. When a non-volatile solute is added to a volatile liquid solvent, the solution vapour pressure will be lower than that of the pure solvent. As a result, the solid will reach equilibrium with the solution at a lower temperature than with the pure solvent. This explanation in terms of vapor pressure is equivalent to the argument based on chemical potential, since the chemical potential of a vapor is logarithmically related to pressure.
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Although the power law exponent approximation is convenient, it has no theoretical basis. When the temperature profile is adiabatic, the wind speed should vary logarithmically with height, Measurements over open terrain in 1961 showed good agreement with the logarithmic fit up to 100 m or so, with near constant average wind speed up through 1000 m. The shearing of the wind is usually three-dimensional, that is, there is also a change in direction between the 'free' pressure-driven geostrophic wind and the wind close to the ground. This is related to the Ekman spiral effect.
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The LogMAR chart is designed to enable more accurate estimates of acuity as compared to other acuity charts (e.g., the Snellen chart). Each line of the LogMAR chart comprises the same number of test letters (effectively standardizing the test across letter size); the Sloan font is used (Sloan letters are approximately equally legible one from another); letter size from line to line varies logarithmically, as does the spacing between lines (making the chart easy to use at nonstandard viewing distances). Zero LogMAR indicates standard vision, positive values indicates poor vision, and negative values indicates good visions.
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For instance, the plot provides information on the difference between the number of zeros and poles of the transfer function by the angle at which the curve approaches the origin. When drawn by hand, a cartoon version of the Nyquist plot is sometimes used, which shows the linearity of the curve, but where coordinates are distorted to show more detail in regions of interest. When plotted computationally, one needs to be careful to cover all frequencies of interest. This typically means that the parameter is swept logarithmically, in order to cover a wide range of values.
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The main source of new genes in S. pneumoniae was Streptococcus mitis from which genes were transferred horizontally. The pan-genome size of S. pneumoniae increased logarithmically with the number of strains and linearly with the number of polymorphic sites of the sampled genomes, suggesting that acquired genes accumulate proportionately to the age of clones. Another example for the latter can be seen in a comparison of the sizes of the core and the pan-genome of Prochlorococcus. The core genome set is logically much smaller than the pangenome, which is used by different ecotypes of Prochlorococcus.
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The mathematics of this approach were rather simple, since Phred quality scores are logarithmically linked to error probabilities. This means that the quality scores of confirming reads can simply be added, as long as the error distributions are sufficiently independent. To satisfy this independence criterion, reads must typically be in different direction, since peak patterns that cause base calling errors are often identical when a region is sequenced several times in the same direction. If a consensus base is covered by both high-quality sequence and (discrepant) low-quality sequence, Phrap's selection of the higher quality sequence will in most cases be correct.
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Subtitled Explorations into Microtonal Tuning, Volume 1, the album is recorded in quarter tone tuning, where an octave is divided into 24 (logarithmically) equal-distanced quarter tones; it was originally conceived to play on a baglama, so the band members used instruments specifically modified for microtonal tuning, as well as other Middle-Eastern instruments like the zurna. The name "Flying Microtonal Banana" comes from Stu Mackenzie's custom-built yellow guitar, fitted with additional microtonal frets. The album has been described as psychedelic rock, acid rock and experimental rock, with elements of krautrock and Middle Eastern/Turkish music.
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The wall of the house was a 96-foot long logarithmically curved spiral, made from 200 tons of local "ironrock" sandstone dynamited (by Eugene) from a piece of purchased farmland near Robin Hill School, a few miles away from the house and hauled back on Eugene's 48 Chevy flatbed truck. The structure was anchored by a recycled oil field drill stem that was reused to make a central mast more than 55 feet high. The house had no interior walls; instead there were a series of platforms at different heights, some with curtains that could be drawn for privacy. The ground floor was covered with pools and planted areas.
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While other trajectories lead to falling cross sections, the pomeron can lead to logarithmically rising cross sections — which, experimentally, are approximately constant ones. The identification of the pomeron and the prediction of its properties was a major success of the Regge theory of strong interaction phenomenology. In later years, a BFKL pomeron was derived in further kinematic regimes from perturbative calculations in QCD, but its relationship to the pomeron seen in soft high energy scattering is still not fully understood. One consequence of the pomeron hypothesis is that the cross sections of proton–proton and proton–antiproton scattering should be equal at high enough energies.
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Sliding the upper scale appropriately amounts to mechanically adding logarithms, as illustrated here: alt=A slide rule: two rectangles with logarithmically ticked axes, arrangement to add the distance from 1 to 2 to the distance from 1 to 3, indicating the product 6. For example, adding the distance from 1 to 2 on the lower scale to the distance from 1 to 3 on the upper scale yields a product of 6, which is read off at the lower part. The slide rule was an essential calculating tool for engineers and scientists until the 1970s, because it allows, at the expense of precision, much faster computation than techniques based on tables.
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The effect is produced by adding a small and even level of exposure to the entire image. Since exposure levels increase logarithmically, this tiny level of additional exposure has no practical effect on an image's mid-tones or highlights, while it shifts the darker areas of the image into the practical sensitivity range, thus allowing darker areas of the image to show visual detail rather than uniform blackness. Flashing can be applied to the film stock before, during, or after principal photography of a motion picture, although always before the film is processed. When applied before or after shooting, this is generally done by a film laboratory.
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In the traditional view, the enormous gap in energy between the mass scales of ordinary particles and the Planck mass is reflected in the fact that virtual processes involving black holes or gravity are strongly suppressed. The suppression of these terms is the principle of renormalizability in order to see an interaction at low energy, it must have the property that its coupling only changes logarithmically as a function of the Planck scale. Nonrenormalizable interactions are weak only to the extent that the Planck scale is large. Virtual gravitational processes don't conserve anything except gauge charges, because black holes decay into anything with the same charge.
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Adomi Bridge steel arch supporting two- lane roadway Adomi Bridge hangers from arch to the transverse beams The single-span arch bridge was designed by William Brown of the engineers Freeman Fox & Partners. It is a two-hinged silver latticed steel crescent-shaped arch bridge with a two-lane road deck suspended by cables. The lower-chord arch rises above the hinges and the main span is long. To make an aesthetically pleasing crescent-shaped arch, the lower curve formed by the lower chords is a parabola, and the upper curve is derived from it by offsets decreasing logarithmically from the center to the hinges.
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The algorithm begins by finding the minimum-weight edge incident to each vertex of the graph, and adding all of those edges to the forest. Then, it repeats a similar process of finding the minimum-weight edge from each tree constructed so far to a different tree, and adding all of those edges to the forest. Each repetition of this process reduces the number of trees, within each connected component of the graph, to at most half of this former value, so after logarithmically many repetitions the process finishes. When it does, the set of edges it has added forms the minimum spanning forest.
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A Neel wall is a narrow transition region between magnetic domains, named after the French physicist Louis Neel. In the Neel wall, the magnetization smoothly rotates from the direction of magnetization within the first domain to the direction of magnetization within the second. In contrast to Bloch walls, the magnetization rotates about a line that is orthogonal to the normal of the domain wall (in other words, it rotates such that it points out of the domain wall plane in a 3D system). It consists of a core with fast varying rotation (where the magnetization points nearly orthogonal to the two domains) and two tails where the rotation logarithmically decays.
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Human ear drums are sensitive to variations in the sound pressure, and can detect pressure changes from as small as a few micropascals (µPa) to greater than For this reason, sound pressure level is also measured logarithmically, with all pressures referenced to (or 1.97385×10−10 atm). The lower limit of audibility is therefore defined as but the upper limit is not as clearly defined. The upper limit is more a question of the limit where the ear will be physically harmed or with the potential to cause noise-induced hearing loss. A more rigorous exploration of the lower limits of audibility determines that the minimum threshold at which a sound can be heard is frequency dependent.
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In quantum electrodynamics, the more thorough quantum field theory underlying the electromagnetic coupling, the renormalization group dictates how the strength of the electromagnetic interaction grows logarithmically as the relevant energy scale increases. The value of the fine-structure constant is linked to the observed value of this coupling associated with the energy scale of the electron mass: the electron is a lower bound for this energy scale, because it (and the positron) is the lightest charged object whose quantum loops can contribute to the running. Therefore, is the asymptotic value of the fine-structure constant at zero energy. At higher energies, such as the scale of the Z boson, about 90 GeV, one measures an effective , instead.
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The intensity of radiation was logarithmically proportional to the Lorentz factor of the particle. After the first observation of the transition radiation in the optical region P.Goldsmith and J.V.Jelley,"Optical transition radiation from protons entering metal surfaces", Philos.Mag. 4 (1959) 836, many early studies indicated that the application of the optical transition radiation for the detection and identification of individual particles seemed to be severely limited due to the inherent low intensity of the radiation. Interest in transition radiation was renewed when Garibian showed that the radiation should also appear in the x-ray region for ultrarelativistic particles. His theory predicted some remarkable features for transition radiation in the x-ray region G.M.Garibyan "Contribution to the Theory of Transition Radiation", JETP (USSR) 33 (1957) 1403; Sov.Phys.
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He is now a professor of Mathematics at the Weizmann Institute and at the Courant Institute, and was from 2002 to 2013 a part-time professor at the University of Minnesota. His research deals with stochastic processes and filtering theory with applications to control theory (electrical engineering), the spectral theory of random matrices, the theory of large deviations in probability theory, motion in random media, and extremes of logarithmically correlated fields. He was Invited Speaker with the talk Random Walks in Random Environments at the ICM in Beijing in 2002. Zeitouni was elected a Fellow of the American Mathematical Society in 2017, member of the American Academy of Arts and Sciences in 2019, and member of the National Academy of Sciences in 2020.
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File:Gamelan gender Wayang ensemble accompanying Balinese Wayang puppetry.wav Like other Balinese gamelan, gender wayang are only approximately standardized in relative pitch, though instruments of each group are precisely tuned with masterful pitch pairing and register stretching. Absolute pitch varies according to the bronzesmith's preference. As a result, individual instruments are rarely exchangeable with those from any group other than its original. One instrument in the each pitch register, pengisup (sucker), are tuned a hair higher than their mates, pengumbang (waver); due to our logarithmically scaled sense of hearing, the lowest notes need to be paired further apart in absolute pitches than the highest to achieve the same, ideal rate of “shimmer” at unison. Further, octave intervals are stretched to be slightly more than double the hertz to achieve a similar “shimmer” at octaves.
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In 1940, Paul Erdős showed that there is a constant c < 1 and infinitely many primes p such that where p′ denotes the next prime after p. What this means is that we can find infinitely many intervals that contain two primes as long as we let these intervals grow slowly in size as we move to bigger and bigger primes. Here, "grow slowly" means that the length of these intervals can grow logarithmically. This result was successively improved; in 1986 Helmut Maier showed that a constant c < 0.25 can be used. In 2004 Daniel Goldston and Cem Yıldırım showed that the constant could be improved further to c = 0.085786… In 2005, Goldston, János Pintz and Yıldırım established that c can be chosen to be arbitrarily small,. i.e.
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The TNR measures ~4–256 kHz electric fields in up to 5 logarithmically spaced frequency bands, though typically only set at 3 bands, from 32 or 16 channels per band, with a 7 nV/(Hz)1/2 sensitivity, 400 Hz to 6.4 kHz bandwidth, and total dynamic range in excess of 100 dB. The data are taken by two multi- channel receivers which nominally sample for 20 ms at a 1 MHz sampling rate (see Bougeret 1995 for more information). The TNR is often used to determine the local plasma density by observing the plasma line, an emission at the local upper hybrid frequency due to a thermal noise response of the wire dipole antenna. One should note that observation of the plasma line requires the dipole antenna to be longer than the local Debye length, λDe.
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If concrete is fully dried, it does not creep, but it is next to impossible to dry concrete fully without severe cracking. Fig. 1 Changes of pore water content due to drying or wetting processes cause significant volume changes of concrete in load-free specimens. They are called the shrinkage (typically causing strains between 0.0002 and 0.0005, and in low strength concretes even 0.0012) or swelling (< 0.00005 in normal concretes, < 0.00020 in high strength concretes). To separate shrinkage from creep, the compliance function J(t, t'), defined as the stress-produced strain \epsilon (i.e., the total strain minus shrinkage) caused at time t by a unit sustained uniaxial stress \sigma = 1 applied at age t', is measured as the strain difference between the loaded and load-free specimens. The multi-year creep evolves logarithmically in time (with no final asymptotic value), and over the typical structural lifetimes it may attain values 3 to 6 times larger than the initial elastic strain.
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