of steepness of a line Slope other uses In vector calculus , the gradient of a scalar field is a vector ... magnitude mathematics magnitude is that rate of increase. A generalization of the gradient ... corresponding gradient is represented by blue arrows. Interpretations File Gradient of a Function.tif thumb 350px Gradient of the 2 d function math f x,y xe x 2 y 2 math is plotted as blue arrows over ... time. At each point in the room, the gradient of math T math at that point will show the direction the temperature rises most quickly. The magnitude of the gradient will determine how fast the temperature ..., y math is math H x, y math . The gradient of math H math at a point is a vector pointing in the direction ... is given by the magnitude of the gradient vector. The gradient can also be used to measure how ... as follows. If the hill height function math H math is differentiable function differentiable , then the gradient ..., the dot product of the gradient of math H math with a given unit vector is equal to the directional ... 350px The gradient of the function f x , y &minus cos sup 2 sup x cos sup 2 sup y sup 2 sup depicted as a projected vector field on the bottom plane The gradient or gradient ... , del . The notation math operatorname grad f math is also commonly used for the gradient. The gradient ... v f x . math In a rectangular coordinate system, the gradient is the vector field whose components ... directions. When a function also depends on a parameter such as time, the gradient often ... unit vectors. For example, the gradient of the function math f x,y,z 2x 3y 2 sin z math ... to represent the gradient as a row vector or column vector of its components in a rectangular coordinate system. Gradient and the derivative or differential Linear approximation to a function The gradient ... nabla f x 0 cdot x x 0 math for math x math close to math x 0 math , where math nabla f x 0 math is the gradient ... of math f math at math x math . The gradient is therefore related to the differential by the formula ... more details
Wiktionarypar gradient The Gradient is the rate of variation of a numerical quantity. It may refer to Slope or Grade slope grade , referring to the inclination of a road or other geographic features Image gradient , a gradual change or blending of color Color gradient Texture gradient Mathematics Gradient , in vector calculus, a vector field representing the maximum rate of increase of a scalar field or a multivariate function and the direction of this maximal rate. Gradient descent Gradient theorem Gradient method Conjugate gradient method Nonlinear conjugate gradient method Stochastic gradient descent Biology diffusion Concentration gradient , the ratio of solute concentration between two adjoining regions Potential gradient , the difference in electric charge between two adjoining regions Fluid dynamics and earth science Density gradient Pressure gradient Temperature gradient Geothermal gradient Sound speed gradient Wind gradient See also lookfrom gradient intitle gradient Graduation disambiguation Fade disambiguation disambig bs Gradijent vor cs Gradient de Gradient eo Gradiento io Gradiento homonimo ja pl Gradient simple Gradient disambiguation tl Gradient ... more details
In optimization mathematics optimization , gradient method is an algorithm to solve problems of the form math min x in mathbb R n f x math with the search directions defined by the gradient of the function at the current point. Examples of gradient method are the gradient descent and the conjugate gradient . See also col begin col break Gradient descent method Conjugate gradient method Derivation of the conjugate gradient method Nonlinear conjugate gradient method Biconjugate gradient method Biconjugate gradient stabilized method References cite book year 1997 title Optimization Algorithms and Consistent Approximations publisher Springer Verlag isbn 0 387 94971 2 author Elijah Polak Optimization algorithms DEFAULTSORT Gradient Method Category First order methods Category Optimization algorithms and methods Category Numerical linear algebra Category Gradient methods fr Algorithme du gradient ja ... more details
In vector calculus , the surface gradient is a Vector geometric vector differential operator that is similar to the conventional gradient . The distinction is that the surface gradient takes effect along a surface. For a surface math S math in a scalar field math u math , the surface gradient is defined and notated as ref R. Shankar Subramanian, http web2.clarkson.edu projects subramanian ch490 notes Boundary 20Conditions 20in 20Fluid 20Mechanics.pdf Boundary Conditions in Fluid Mechanics . ref math nabla S u nabla u mathbf hat n mathbf hat n cdot nabla u math where math mathbf hat n math is a unit Surface normal normal to the surface. Examining the definition shows that the surface gradient is the conventional gradient with the component normal to the surface removed subtracted , hence this gradient is tangent to the surface. In other words, the surface gradient is the orthographic projection of the gradient onto the surface. The surface gradient arises whenever the gradient of a quantity over a surface is important. In the study of capillary surface s for example, the gradient of spatially varying surface tension doesn t make much sense, however the surface gradient does and serves certain purposes. References Reflist Category Vector calculus bs Povr inski gradijent ... more details
Multiple issues unreferenced December 2009 orphan December 2009 wikify December 2009 Gradient related is a term used in multivariable calculus to describe a direction. A direction sequence math d k math is gradient related to math x k math if for any subsequence math x k k in K math that converges to a nonstationary point, the corresponding subsequence math d k k in K math is bounded and satisfies math limsup k rightarrow infty, k in K nabla f x k d k 0. math A gradient related direction is usually encountered in the gradient based iterative optimisation of a function math f math . At each iteration math k math the current vector is math x k math and we move in the direction math d k math , thus generating a sequence of directions. It is easy to guarantee that the directions we generate are gradient related, by for example setting them equal to the gradient at each point. DEFAULTSORT Gradient Related Category Vector calculus ... more details
In computer graphics, a color gradient sometimes called a color ramp or color progression specifies a range of position dependent color s, usually used to fill a region. ref cite book title SVG Essentials isbn 0596002238 last Eisenberg first J. David year 2002 publisher O Reilly Media pages 364 page 107 ref For example, many window managers allow the screen background to be specified as a gradient. The colors produced by a gradient vary continuously with position, producing smooth color transitions. Linear gradients File linear gradient.svg right A linear color gradient is specified by two points, and a color at each point. The colors along the line through those points are calculated using linear interpolation , then extended perpendicular to that line. In digital imaging systems, colors are typically interpolated in an RGB color space , often using gamma compression gamma compressed RGB color values, as opposed to linear. Circular gradients File radial gradient.svg right A circular gradient is specified as a circle that has one color and a focus the center of the circle that has another. Colors are calculated by linear interpolation based on distance from the focus. References reflist See also Wikibooks Colors Color gradient Image gradient Color banding Posterization Diffusion curve Category Computer graphics graphics software stub de Farbverlauf fr D grad de couleur nl Kleurengradi nt pl Gradient grafika ... more details
In mathematics , a skew gradient of a harmonic function over a simply connected domain with two real dimensions is a vector field that is everywhere orthogonal to the gradient of the function, and has the same Magnitude mathematics magnitude that the gradient has. Definition The skew gradient can be defined using complex analysis and the Cauchy Riemann equations . Let math f z x,y u x,y iv x,y math be a complex valued analytic function, where u , v are real valued scalar functions of the real variables x , y . A skew gradient is defined as math nabla perp u x,y nabla v x,y math and from the Cauchy Riemann equations , it is derived that math nabla perp u x,y frac partial u partial y , frac partial u partial x math Properties The skew gradient has two interesting properties. It is everywhere orthogonal to the gradient of u, and of the same length math nabla u x,y cdot nabla perp u x,y 0 , rVert nabla u rVert rVert nabla perp u rVert math References Refbegin Peter Olver, http www.math.umn.edu olver pdn.html Introduction to Partial Differential Equations, ch. 7, p. 232 Refend Category Differential calculus Category Generalizations of the derivative Category Linear operators in calculus Category Vector calculus ... more details
In atmospheric sciences meteorology , climatology and related fields , the pressure gradient typically ... gradient is a dimensional quantity expressed in Units of measurement units of pressure ... coordinate system coordinates of the location of interest, then the pressure gradient ... Strictly speaking, the concept of pressure gradient is a local characterization of the air more generally of the fluid under investigation . The pressure gradient is defined only at those spatial scales ... s including the Earth s atmosphere Earth s , the pressure gradient is a vector pointing roughly downwards ... or Norm mathematics norm of the pressure gradient in the troposphere is typically of the order 9 Pa m or 90 hPa km . The pressure gradient often has a small but critical horizontal component, which is largely responsible for the wind circulation. The horizontal pressure gradient is a 2 dimensional vector resulting from the projection of the pressure gradient onto a local horizontal plane. Near the Earth s surface , this horizontal pressure gradient is typically pointing towards high pressure ... on the weather situation. At mid latitude s, the typical horizontal pressure gradient may take on values ..., the pressure gradient constitutes one of the main forces acting on the air to make it move as wind. Note that the pressure gradient force points from high towards low pressure zones, it is thus oriented in the opposite direction from the pressure gradient itself. Sound waves and shock wave s are events ... also Gradient Isobar meteorology Isobar Geopotential height Geostrophic wind Primitive equations Temperature gradient References Edward N. Lorenz 1967 The nature and theory of the general circulation ... wg1 index.htm IPCC Third Assessment Report Category Atmospheric dynamics ca Gradient de pressi es Gradiente barom trico nl Drukgradi nt ja pl Gradient ci nienia pt Gradiente de press o ru simple Pressure gradient uk ... more details
Stream gradient is the grade slope grade measured by the ratio of drop in a stream per unit distance, usually expressed as Foot length feet per mile or metre s per kilometre . Hydrology and geology A high gradient indicates a steep slope and rapid volumetric flow rate flow of water i.e. more ability to erode whereas a low gradient indicates a more nearly level stream bed and sluggishly moving water, that may be able to carry only small amounts of very fine sediment . High gradient streams tend to have steep, narrow V shaped valley s, and are referred to as young streams. Low gradient streams have wider and less rugged valley s, with a tendency for the stream to meander . Fluvial Erosion A stream that flows upon a uniformly erosion erodible substrate will tend to have a steep gradient near its source, and a low gradient nearing zero as it reaches its base level . Of course, a uniform substrate would be rare in nature hard layers of rock geology rock along the way may establish a temporary base level, followed by a high gradient, or even a waterfall , as softer materials are encountered below the hard layer. Human dam s, glaciation , changes in sea level , and many other factors can also change the normal or natural gradient pattern. Topographic mapping On topographic map s, stream Grade slope gradient can be easily approximated if the scale of the map and the contour intervals are known. Contour lines form a V shape on the map, pointing upstream. By counting the number of lines ... by the length of the stream segment you can determine the stream gradient. Because stream gradient is customarily given in feet per 1000 feet, one should then measure the amount a stream segment rises and the length of the stream segment in feet, then multiply feet per foot gradient by 1000 ... crossed on a map with ten foot contours, the gradient is approximately 5.7 feet per 1000 feet, a fairly steep gradient. See also Channel types Relief ratio Rapid s waterfall Types Types of waterfall ... more details
to indicate the direction of the gradient. Dark areas indicate higher values An image gradient is a directional ... from images. In graphics software for digital image editing , the term gradient is used for a gradual ... progression . Mathematically, the gradient of a two variable function here the image intensity ... s in the horizontal and vertical directions. At each image point, the gradient vector points in the direction of largest possible intensity increase, and the length of the gradient vector corresponds ... gradient, but is still of sufficient quality to be of practical use in many applications. More precisely ... the corresponding image gradient, and it uses only integer values for the coefficients which weight the image intensities to produce the gradient approximation. The gradient of the image is one of the fundamental building blocks in image processing . For example the Canny edge detector uses image gradient ... Computer vision File Intensity image with gradient images.png thumb 400px alt Left Black and white picture of a cat. Center The same cat, displayed in a gradient image in the x direction. Appears similar to an embossed image. Right The same cat, displayed in a gradient image in the y direction. Appears similar to an embossed image. On the left, an intensity image of a cat. In the center, a gradient image in the x direction measuring horizontal change in intensity. On the right, a gradient image in the y direction measuring vertical change in intensity. Gray pixels have a small gradient black or white pixels have a large gradient. Image gradients can be used to extract information from images. Gradient images are created from the original image generally by convolving with a filter, one of the simplest being the Sobel filter for this purpose. Each pixel of a gradient image measures the change ... of direction, gradient images in the x and y directions are computed. One of the most common uses is in edge detection. After gradient images have been computed, pixels with large gradient values ... more details
Unreferenced stub auto yes date December 2009 An environmental gradient is a gradual change in abiotic factors through space or time . Environmental gradients can be related to factors such as altitude, temperature, depth, ocean proximity and soil humidity. Species Abundance ecology abundance s usually change along environmental gradients in a more or less predictive way. However, the species abundance along an envronmental gradient is not only determined by the abiotic factor but, also by the change in the biotic interaction s along the environmental gradient. At an ecotone , species Abundance ecology abundance s change relatively quick compared to the environmental gradient. The species distribution along environmental gradients has been studied intensively due to large databases of species presence data e.g. Global Biodiversity Information Facility GBIF Environmental Gradients are linked to Connectivity and natural disturbance when considering river systems. A river restoration scheme must consider all of these factors before undertaking a program as these three factors are what leads to a larger biodiversity. Each species are not found in every type of habitat or in every part of the world. Within the environment there are multiple factors which affects organisms. The organisms in the polar region can not survive the climate at the equator. See also Biome , cline biology , thermocline . DEFAULTSORT Environmental Gradient Ecology stub Category Ecology ... more details
Gradient descent is a First order approximation first order Mathematical optimization optimization algorithm . To find a local minimum of a function using gradient descent, one takes steps proportional to the negative of the gradient or of the approximate gradient of the function at the current point. If instead one takes steps proportional to the positive of the gradient , one approaches a local maximum of that function the procedure is then known as gradient ascent . Gradient descent is also known as steepest descent , or the method of steepest descent . When known as the latter, gradient descent ... Image gradient descent.png thumb right 350px Illustration of gradient descent Gradient descent ... of the negative gradient of math F math at math mathbf a math , math nabla F mathbf a math . It follows ... in this case gradient descent can converge to the global solution. This process is illustrated in the picture ... gradient at that point. Note that the negative gradient at a point is orthogonal to the contour line going through that point. We see that gradient descent leads us to the bottom of the bowl, that is, to the point where the value of the function math F math is minimal. Examples Gradient descent ... 400px The Zig Zagging nature of the method is also evident below, where the gradient ascent method is applied to math F x,y sin left frac 1 2 x 2 frac 1 4 y 2 3 right cos 2 x 1 e y math . Image gradient ascent contour .png 350px The gradient descent algorithm in action. 1 contour Image gradient ascent surface .png 450px The gradient descent algorithm in action. 2 surface Limitations For some of the above examples, gradient descent is relatively slow close to the minimum technically, its asymptotic ..., gradient descent increasingly zigzags as the gradients point nearly orthogonally to the shortest direction to a minimum point. For more details, see the Gradient descent Comments comments below. For non differentiable functions, gradient methods are ill defined. For locally Lipschitz continuity Lipschitz ... more details
with hilliness, road sections with risk for insufficient drainage gradient are few and short ... . How to avoid or minimize skid risk caused by insufficient drainage gradient Roads should be designed ... gradient 0.5 , resulting in unacceptable skid accident risk. When designing road curves in a flat ... gradients can then be used to reach a sufficient drainage gradient, in sections where the cross ... Final Report DEFAULTSORT Drainage Gradient Category Pavement engineering ... more details
Density gradient is a spatial variation in density over an area. The term is used in the natural sciences to describe varying density of matter , but can apply to any quantity whose density can be measured . ref cite web title Non Destructive Testing Resource Center Glossary url http www.ndt ed.org GeneralResources Glossary letter d.htm ref ref cite web title Chicago Wilderness Journal, Volume 1 Number 1 November, 2003 url http www.chicagowilderness.org pubprod cwjournal docs CWJournal1003.pdf ref Aerodynamics In the study of supersonic flight, Schlieren photography observes the density gradient of air as it interacts with aircraft. ref cite web title CFI Shadowgraph Schliren Photography for Aerodynamic Applications url http pdf.aiaa.org preview 1994 PV1994 2616.pdf ref Water A steep density gradient in a body of water can have the effect of trapping energy and preventing convection , such a gradient is employed in solar pond s. In the case of salt water, sharp gradients can lead to Stratification water stratification of different concentrations of salinity . This is called a Halocline . ref cite web title Effects of sill processes and tidal forcing on exchange in eastern Long Island Sound url http www.agu.org pubs crossref 1994 94JC00721.shtml ref Biology In the life sciences, a special technique called density gradient separation is used for isolating and purifying cells, viruses and subcellular particles. ref cite web title GE Healthcare Density Gradient Separation url http www6.amershambiosciences.com aptrix upp00919.nsf Content CellSep EduC dgs ref Variations of this include Isopycnic centrifugation , Differential centrifugation , and Sucrose gradient centrifugation . A blood donation technique called Pheresis involves density gradient separation. Geophysics The understanding ... is one theory by reason of density gradient and supported and espoused by http www.pnas.org ..., the density gradient can refer to the change in density in an urban area from the center to the periphery ... more details
Gradient noise is a type of noise commonly used as a procedural texture primitive in computer graphics. It is conceptually different, and often confused with value noise . This method consists of a creation of a lattice of random gradients , which are then interpolated to obtain values in between the lattices. An artifact of some implementations of this noise is that the returned value at the lattice points is 0. Unlike the value noise, gradient noise has more energy in the high frequencies. The first implementation of a gradient noise function is credited to Ken Perlin , who published the description of it in 1985. This noise is now commonly known as the Perlin noise . ref David Ebert, Kent Musgrave, Darwyn Peachey, Ken Perlin, and Worley. Texturing and Modeling A Procedural Approach. Academic Press, October 1994. ISBN 0 12 228760 6 ref See also Value noise Perlin noise Simplex noise Wavelet noise Worley noise References reflist Category Noise Category Computer graphic techniques graphics software stub ru ... more details
Image Example of gradient copolymer.png 500px thumb Figure 1 Example of a a diblock copolymer, b gradient ... 1998 title Gradient Polymers and Copolymers journal Polymers for Advanced Technologies publisher John ... Gradient Copolymer journal Colloid Polym Sci publisher Springer volume 286 pages 1465 1474 doi 10.1007 ..., Stephen V. Arehart, Dorota Greszta and Tadeusz Pakula year 2000 title Gradient Copolymers by Atom Transfer ... Third pages 147 148 issn 8493 9813 ref In the gradient copolymer, as a result of the gradual compositional ... 2008 title Gradient Copolymers with Broad Glass Transition Temperature Regions Design of Purely ... of gradient copolymers because the synthesis of this group of novel polymers was now straightforward. Due to the similar properties of gradient copolymers to that of block copolymers, they have .... ref name E Polymer Composition Image Gradient Polym Composition2.png thumb right 300px Figure 2 Graphical depiction of the composition of a gradient copolymer In the gradient copolymer, there is a continuous ... can be depicted in a mathematical expression.The local composition gradient fraction math g ... of controlled radical polymerization CRP , gradient copolymers as distinguished from statistical copolymers were not synthetically possible. While a gradient can be achieved through compositional drift ... Kelly coauthors Krzysztof Matyjaszewski year 2002 title Statistical, Gradient, Block, and Graft Copolymers ... have been used to synthesize gradient copolymers. ref name E cite journal ref The gradient can be formed through either a spontaneous or a forced gradient. Spontaneous gradient polymerization is due ... creates an inconsistent gradient along the polymer. Forced gradient polymerization involves ... to achieve the desired gradient composition. Properties The wide range of composition possible in a gradient ... with the homopolymers. Micelles of the gradient copolymer can form when the gradient copolymer ... b gradient copolymer blend with annealing For the compatiabilization of immiscible blends ... more details
In physics , chemistry and biology , a potential gradient is the local derivative rate of change of the potential with respect to displacement, i.e. spatial derivative, or gradient. This quantity frequently occurs in equations of physical processes because it leads to some form of flux . In electrical engineering it refers specifically to electric potential gradient, which is equal to the electric field . Definition Elementary algebra calculus Fundamentally the expression for a potential gradient F in one dimension takes the form ref Essential Principles of Physics, P.M. Whelan, M.J. Hodgeson, 2nd Edition, 1978, John Murray, ISBN 0 7195 3382 1 ref math F frac delta phi delta x , math where is some type of potential , and x is displacement not distance , in the x direction. In the limit of infinitesimal displacements, the ratio of differences becomes a ratio of differential of a function differentials math F frac rm d phi rm d x , math In three dimensions, the resultant potential gradient is the sum of the potential gradients in each direction, in Cartesian coordinates math bold F bold ..., which can be compactly and neatly written in terms of the gradient operator mathematics operator , math bold F nabla phi , math Vector calculus The mathematical nature of a potential gradient arises ... space. For any conservative vector field F , there exists a scalar field , such that the gradient ... can be shown to be conservative, it is equal to the gradient in gravitational potential math mathbf ... gradient and field are opposite in direction, as the potential gradient increases, the gravitational ... field has identical properties to the gravitational field it is the gradient of the electric potential ... to the gradient in electric potential, a time dependent term must be added ref Introduction to Electrodynamics ... standard conditions . The potential gradient is relatively abrupt, since there is an almost ... terms Category Fundamental physics concepts Category Vector calculus pl Gradient potencja u ... more details
distinguish gradient wind about the interaction of horizontal wind with the earth s surface a more general treatment of related phenomena wind shear In common usage, wind gradient , more specifically wind speed gradient ref name Hadlock cite book last Hadlock first Charles title Mathematical Modeling ... 088385709X pages quote Thus we have a wind speed gradient as we move vertically, and this has a tendency ... and below it. ref or wind velocity gradient , ref name Gorder1996 cite conference author Gorder, P.J. coauthors Kaufman, K. Greif, R. year 1996 title Effect of wind gradient on the trajectory synthesis ... wind velocity with altitude, the wind velocity gradient... ref or alternatively shear wind , ref cite ... 10.1111 j.1474 919x.2004.00295.x quote ...the shear wind gradient is rather weak....the energy gain...is due to a mechanism other than the wind gradient effect. ref is the vertical gradient of the mean ... pages 54 quote Therefore the vertical gradient of mean wind speed d dz is greatest over smooth terrain ... English publisher Routledge location New York year 2000 isbn 157958201X pages 104 quote wind gradient ... layer, increasing vertical wind shear near the surface, also known as wind gradient. Background seealso ... drag force drag , there is a wind gradient in the wind flow just a few hundred meters above the Earth ... or wind gradient. ref due to the no slip condition . ref name Brown cite book last Brown first G. title ... Berlin year 2003 isbn 354040340X pages 17 ref Over a city or rough terrain, the wind gradient effect ... purposes, the wind gradient is modeled as a simple shear exhibiting a vertical velocity profile ... above ground where surface friction has a negligible effect on wind speed is called the gradient height and the wind speed above this height is assumed to be a constant called the gradient wind ... year 2005 isbn 1402028504 pages 73 ref For example, typical values for the predicted gradient height ... Energy Resources chapter 7.8.5 Vertical Wind Speed Gradient publisher Alpha Science International ... more details
Gradient Analytics, Inc. , founded in 1996 by Donn Vickrey and Dr. Carr Bettis as Camelback Research Alliance, Inc. and based in Scottsdale, Arizona , is an independent securities research equity research company. ref http investing.businessweek.com research stocks private snapshot.asp?privcapId 11517448 Gradient Analytics, Inc. , profile at BusinessWeek ref References references External links http www.marketwatch.com news story story.aspx?guid 7B83FE0B79 0B4A 45DE AF4E 1C1E3EAEEEA2 7D Category Companies based in Scottsdale, Arizona Category Companies established in 1996 Category Financial services companies of the United States finance company stub ... more details
cleanup jargon date October 2011 An electrochemical gradient is a gradient of electrochemical potential , usually for an ion that can move across membrane . The gradient consist of two parts, the electrical potential and a difference in the chemical concentration across a membrane. The difference of electrochemical potential s can be interpreted as a type of potential energy available for work in a cell. The energy is stored in the form of chemical potential , which accounts for an ion s concentration gradient across a cell membrane , and electrostatic energy , which accounts for an ion s tendency to move under influence of the transmembrane potential . Overview Electrochemical potential is important in electroanalytical chemistry and industrial applications such as batteries and fuel cells. It represents one of the many interchangeable forms of potential energy through which energy may be conservation ... or active transport across a membrane is determined by the electrochemical gradient. In mitochondria ... . An electrochemical gradient has two components. First, the electrical component is caused ... gradient is analogous to the water pressure across a hydroelectric dam . Membrane transport ... ATP to make a sodium ion gradient and a potassium ion gradient. The electrochemical potential is used ... gradients The proton gradient can be used as intermediate energy storage for heat production ... gradient . This is used by fermenting bacteria which do not have an electron transport chain, and hydrolyze ATP to make a proton gradient for flagella and the transportation of nutrients into the cell ... 2005 , for Biology 113 at the Ohio State University DEFAULTSORT Electrochemical Gradient Category Cellular ... Physical quantities Category Thermodynamics ca Gradient electroqu mic da Elektrokemisk gradient de Elektrochemischer Gradient es Gradiente electroqu mico fr Gradient lectrochimique id Gaya gerak proton lt Elektrocheminis gradientas nl Elektrochemische gradi nt pl Gradient elektrochemiczny ... more details
Multiple issues orphan February 2009 context June 2009 cleanup June 2009 A gradient network is a directed subnetwork of an undirected substrate computer network network in which each node networking node has an associated scalar potential and one out link that point to the node with the smallest or largest potential in its neighborhood, defined as the reunion of itself and its nearest neighbors on the substrate networks. ref name grad2 Bogdan Danila, Congestion gradient driven transport on complex networks, PHYSICAL REVIEW E 74, 046114 2006 ref Let us consider that transport takes place on a fixed ... j V i,j E . Image gnt.jpg thumb 250px right Fig.3. An example of gradient network. ref name toro ... V, so that every node i has a scalar value h sub i sub associated to it. Gradient h sub i sub ... sup 1 sup i , and h sub sub has the maximum value in math h j j in S i 1 cup i math . Gradient network math G math math G math math V, F math where F is the set of gradient edges on G . In general ..., the gradient network math G math will be dynamic. Motivation Real world networks evolve to fulfill ... gradients of a scalar, for example electric current driven by a gradient of electric potential in the information ... from a node to its neighbors. This idea motivated the approach through gradient networks which .... Gradient Networks, cond mat 0408262. ref Image Gradient.jpg thumb 300px left Fig.2. The gradient ... s neighborhood. ref name toro In degree distribution of gradient networks In a gradient network, in degree of a node i, k sub i sub sup in sup is the number of gradient edges pointing into i ... 200px left Fig.5. The degree distributions of the gradient network and the substrate BA Model . ref ... the power law center math R l approx l 1 math center This shows in this limit, the gradient network of random network is scale free. If the subtstrate network G is scale free, like BA model, then the gradient ... gradient flow and N sub send sub is the number of nodes that send the flow. The value of J is in the range ... more details
A temperature gradient is a physical quantity that describes in which direction and at what rate the temperature changes the most rapidly around a particular location. The temperature gradient is a dimensional quantity expressed in Units of measurement units of degrees on a particular temperature scale per unit length. The International System of Units SI unit is kelvin per meter K m . Temperature gradients in the Earth s atmosphere atmosphere are important in the atmospheric sciences meteorology , climatology and related fields . Mathematical description Assuming that the temperature T is an intensive quantity , i.e., a single valued, Continuous function continuous and Derivative differentiable Function mathematics function of three dimensional space often called a scalar field , i.e., that math T T x,y,z math where x , y and z are the Cartesian coordinate system coordinates of the location of interest, then the temperature gradient is the vector geometric vector quantity defined as math nabla T begin pmatrix frac partial T partial x , frac partial T partial y , frac partial T partial z end pmatrix math ... Weather and climate relevance Differences in air temperature between different locations are critical in weather forecasting and climate. The absorption of solar light at or near the planetary surface increases the temperature gradient and may result in convection a major process of cloud formation, often associated with Precipitation meteorology precipitation . Similarly ... fronts are regions where the horizontal temperature gradient may reach relatively high values, as these are boundaries ... gradient may change substantially in time, as a result of diurnal or seasonal heating and cooling ... in space or time may cause discomfort and, in extreme cases, heat or cold stresses. See also Gradient ... IPCC Third Assessment Report Category Atmospheric dynamics Category Climatology ca Gradient t rmic ... pl Pionowy gradient temperatury pt Gradiente de temperatura zh ... more details
In mathematics , the gradient conjecture , due to Ren Thom , was proved in 2000 by 3 Polish mathematicians, Krzysztof Kurdyka University of Savoie , France , Tadeusz Mostowski Warsaw University , Poland and Adam Parusinski University of Angers , France . It states that given a real valued analytic function f defined on R sup n sup and a trajectory x t of the gradient vector field of f having a limit point x sub 0 sub R sup n sup , where f has an isolated critical point at x sub 0 sub , there exists a limit in the projective space PR sup n 1 sup for the secant lines from x t to x sub 0 sub , as t tends to zero. References A published statement of the conjecture R. Thom, Probl mes rencontr s dans mon parcours math matique un bilan, Publ. Math. IHES 70 1989 , 200 214. This gradient conjecture due to Ren Thom was in fact well known among specialists by the early 70 s, having been often discussed during that period by Thom during his weekly seminar on singularities at the IHES . The paper where it is proved Annals of Math. 152 2000 , 763 792. It is available http arxiv.org abs math.AG 9906212 here . Category Mathematical analysis Category Theorems in analysis Mathanalysis stub ... more details
Gradient boosting is a machine learning technique for Regression machine learning regression problems ... differentiable loss function . Gradient boosting method can be also used for classification machine ... Function Approximation A Gradient Boosting Machine. February 1999 ref introduced the method, and the second ... Stochastic Gradient Boosting. March 1999 ref described an important tweak to the algorithm, which improves its accuracy and performance. Gradient boosting In many supervised learning problems one has ... Gradient boosting method assumes a real valued y and seeks an approximation math hat F x math in the form ... allows us to generalize , we ll just choose the one that most closely approximates the gradient of L ... equation above. In pseudocode, the generic gradient boosting method is ref name Friedman1999a ref name ... F m x F m 1 x gamma m h m x . math Output math F M x . math frame footer Gradient tree boosting Gradient ... trees of a fixed size as base learners. For this special case Friedman proposes a modification to gradient boosting method which improves the quality of fit of each base learner. Generic gradient .... One natural regularization parameter is the number of gradient boosting iterations M i.e. the number ... other regularization techniques are used. Shrinkage An important part of gradient boosting method ... yields dramatic improvements in model s generalization ability over gradient boosting without shrinking ... both during training and querying lower learning rate requires more iterations. Stochastic gradient boosting Soon after the introduction of gradient boosting Friedman proposed a minor modification to the algorithm ... set. ref Friedman observed a substantional improvement in gradient boosting s accuracy ... to the gbm package. ref Number of observations in leaves Gradient tree boosting implementations often .... Usage Recently, gradient boosting method has gained some popularity in learning to rank field ... corporate blog entry about new ranking model Snezhinsk in Russian ref use variants of gradient boosting ... more details
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