Slope other uses In vector calculus , the gradient of a scalar field is a vector field which points ... magnitude is the greatest rate of change. A generalization of the gradient for functions on a Euclidean ..., the scalar field is in black and white, black representing higher values, and its corresponding gradient ...,z math we will assume that the temperature does not change in time . At each point in the room, the gradient ... of the gradient will determine how fast the temperature rises in that direction. Consider a surface whose height above sea level at a point math x, y math is math H x, y math . The gradient ... grade at that point. The steepness of the slope at that point is given by the magnitude of the gradient vector. The gradient can also be used to measure how a scalar field changes in other directions ... will also be 40 . If, instead, the road goes around the hill at an angle the gradient vector , then it will have ... height function math H math is differentiable function differentiable , then the gradient of math ... of the vector. More precisely, when math H math is differentiable, the dot product of the gradient ... H math in the direction of that unit vector. Definition Image Gradient99.png thumb 350px The gradient ... as a projected vector field on the bottom plane The gradient or gradient vector field of a scalar ... math operatorname grad f math is also used for the gradient. The gradient of f is defined to be the vector ... f left frac partial f partial x 1 , dots, frac partial f partial x n right . math Here the gradient ... on a parameter such as time, the gradient often refers simply to the vector of its spatial derivatives only. The gradient of a vector math mathbf f f 1 , f 2 , f 3 math is math nabla mathbf f frac ... partial f 1 , f 2 , f 3 partial x 1 , x 2 , x 3 math . More generally, the gradient may be defined ... dimensional rectangular coordinates The form of the gradient depends on the coordinate system used ... z hat mathbf k math Example For example, the gradient of the function in Cartesian coordinates math ... more details
Wiktionarypar gradientGradient may refer to Gradient , in vector calculus, a vector field representing the maximum rate of increase of the scalar field direction of the maximum change. 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 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 nl Gradi nt ja pl Gradient simple Gradient disambiguation ... 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 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 ch560 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
A potential gradient is the local space derivative rate of change of the potential with respect to displacement. In electrostatics then, it is the local space rate of change of the electric potential math mathbf E delta V delta s math http niuhep.physics.niu.edu willis phys251 chapter 19 day 2.html Units are volt s per meter V m . The electric field is the same as the potential gradient but with opposite sign. In biology , potential gradient is the net difference in electric charge across a cell membrane . Category Electronics terms electronics stub pl Gradient potencja u ... more details
to indicate the direction of the gradient An image gradient is a directional change in the intensity ... software for digital image editing , the term gradient is used for a gradual blend of color which can ... to black in the images to the right. Another name for this is color progression . Mathematically, the gradient ... 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 to the rate of change in that direction ... operator represents a rather inaccurate approximation of the image gradient, but is still of sufficient ... only in a 3× 3 region around each image point to approximate 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 for edge detection . 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 ... for this purpose. Each pixel of a gradient image measures the change in intensity of that same point in the original image, in a given direction. To get the full range of direction, gradient images in the x and y directions are computed. One of the most common uses is in edge detection. After gradient ... more details
Stream gradient is the grade slope measured by the ratio of drop in a stream per unit distance, usually expressed as Foot length feet per mile or meter s per kilometer . 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 that cross a certain segment of a stream, multiplying this by the contour interval, and dividing that quantity by the length of the stream segment you can determine the stream gradient. Because stream gradient ... rises and the length of the stream segment in feet, then multiply feet per foot gradient by 1000. For example ... 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 river ... 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 See also Biome , cline biology , thermocline . DEFAULTSORT Environmental Gradient Ecology stub Category Ecology ... 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
Gradient Equation for Recovering Shape from Texture , IEEE Transactions on Pattern Analysis and Machine Intelligence. Retrieved 2010 2 15. ref See also Texture visual arts Image gradient Perspective ... Gradient Category Artistic techniques Art stub ... 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
Density gradient is a 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 cgi content ... gradient can refer to the change in density in an urban area from the center to the periphery ... more details
norefs date February 2010 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 url http oreilly.com catalog 9780596002237 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 Image 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 Image 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 Image gradient Color banding Posterization Wikibooks Colors Color gradient Category Computer graphics graphics software stub de Farbverlauf fr D grad de couleur nl Kleurengradi nt ... 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
Orphan date January 2011 Image Example of gradient copolymer.png 500px thumb Figure 1 Example of a a diblock copolymer, b gradient copolymer and c random copolymer Copolymer s are polymer s that are synthesized ... Kryszewski first M year 1998 title Gradient Polymers and Copolymers journal Polymers for Advanced ... first Uwe year 2008 title Gradient Copolymer journal Colloid Polym Sci publisher Springer volume 286 ... Michael J. Ziegler, Stephen V. Arehart, Dorota Greszta and Tadeusz Pakula year 2000 title Gradient ... CRC Press year 2008 edition Third pages 147 148 issn 8493 9813 ref In the gradient copolymer, as a result ... Kim, John M. Torkelson year 2008 title Gradient Copolymers with Broad Glass Transition Temperature ... study of the concepts and properties 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 ... preexisting copolymers. 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 ... gradient fraction math g X math is described by molar fraction of monomer 1 in the copolymer math F ... Prior to the development of controlled radical polymerization CRP , gradient copolymers as distinguished from statistical copolymers were not synthetically possible. While a gradient can be achieved ... journal last Davis first Kelly coauthors Krzysztof Matyjaszewski year 2002 title Statistical, Gradient ... opening polymerization 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 ... throughout the polymerization creates an inconsistent gradient along the polymer. Forced gradient ... composition adjustment to achieve the desired gradient composition. Properties The wide range of composition possible in a gradient polymer due to the variety of monomers incorporated and the change ... more details
Gradient descent is a First order approximation first order optimization mathematics 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 ... of the negative 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 ... Gradient descent has problems with pathological functions such as the Rosenbrock function shown here ... SteepDesc.gif 400px The Zig Zagging nature of the method is also evident below, where the gradient ... . 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 ... problems, gradient descent increasingly zigzags as the gradients point nearly orthogonally to the shortest direction to a minimum point. For more details, see Gradient descent Comments Comments below For non differentiable functions, gradient methods are ill defined. For locally Lipschitz problems and especially ... 10.1007 PL00011414 year 2001 id MR 1819784 ref Solution of a linear system Gradient descent can be used ... formulas for the locally optimal math gamma math are known. Solution of a non linear system Gradient ... 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
to a high drainage gradient. However, longitudinal highway slopes steeper than 0.5 are surprisingly ... drainage gradient are few and short. Still they account for an unacceptable number of skid ... maintained road networks ref . How to avoid or minimize skid risk caused by insufficient drainage gradient ... with too little drainage gradient 0.5 , resulting in unacceptable skid accident risk. When designing .... These synthetic longitudinal gradients can then be used to reach a sufficient drainage gradient ... Surface Drainage of Pavements Final Report DEFAULTSORT Drainage Gradient Category Pavement engineering ... 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 ... as wind gradient. Background seealso Ekman layer Ekman spiral Planetary boundary layer Surface layer Typically, due to aerodynamic drag force drag , there is a wind gradient in the wind flow just ... is called the wind profile or wind gradient. ref due to the no slip condition . ref name Brown ... terrain, the wind gradient effect could cause a reduction of 40 to 50 of the geostrophic wind speed ... pages 102 103 ref For engineering purposes, the wind gradient is modeled as a simple shear exhibiting ... 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 speed . ref name Crawley ref name Gupta cite book last Gupta first ... for the predicted gradient height are 457 m for large cities, 366 m for suburbs, 274 m for open ... last Ghosal first M. title Renewable Energy Resources chapter 7.8.5 Vertical Wind Speed Gradient publisher ... 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 ... ja no Temperaturgradient nn Temperaturgradient pl Pionowy gradient temperatury pt Gradiente ... more details
calculus cTopic Vector calculus The gradient theorem , also known as the fundamental theorem of calculus for line integrals , says that a line integral through a gradient field any irrotational vector field conservative vector field can be expressed as a gradient can be evaluated by evaluating the original scalar field at the endpoints of the curve math phi left mathbf q right phi left mathbf p right int L nabla phi cdot d mathbf r . math It is a generalization of the fundamental theorem of calculus to any curve in a plane or space generally n dimensional rather than just the real line. The gradient theorem implies that line integrals through irrotational vector fields are Conservative vector field Path independence path independent . In physics this theorem is one of the ways of defining a Conservative force conservative force . By placing math phi math as potential, math nabla phi math is a conservative field . Work done by conservative forces does not depend on the path followed by the object, but only the end points, as the above equation shows. Proof Let math phi math be a Differential form 0 form scalar field . Let L be a 1 segment curve from p to q . By Stokes theorem math int partial L phi int L d phi. math But because math partial L mathbf q mathbf p math , math phi left mathbf q right phi left mathbf p right int L d phi. math Restricting the curve to Euclidean space and expanding in Cartesian coordinates math d phi sum i frac partial phi partial x i dx i sum i left frac partial partial x i right phi cdot left dx i right nabla phi cdot d mathbf r . math See also state function Category Vector calculus Category Mathematical theorems Category Articles containing proofs mathanalysis stub bs Teorem gradijenta eo Gradienta teoremo fa fr Th or me du gradient it Teorema del gradiente ... 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 Mathematical theorems Mathanalysis stub ... more details
In mathematical morphology and digital image processing , morphological gradient is the difference between the dilation morphology dilation and the erosion morphology erosion of a given image. It is an image where each pixel value typically non negative indicates the contrast intensity in the close neighborhood of that pixel. It is useful for edge detection and segmentation applications. Mathematical definition and types Let math f E mapsto R math be a grayscale image, mapping points from a Euclidean space or discrete grid E such as R sup 2 sup or Z sup 2 sup into the real line. Let math b x math be a grayscale structuring element . Usually, b is symmetry symmetric and has short support, e.g., math b x left begin array ll 0,& x leq 1, infty,& mbox otherwise end array right. math . Then, the morphological gradient of f is given by math G f f oplus b f ominus b math , where math oplus math and math ominus math denote the dilation and the erosion, respectively. An internal gradient is given by math G i f f f ominus b math , and an external gradient is given by math G e f f oplus b f math . The internal and external gradients are thinner than the gradient, but the gradient peaks are located on the edges, whereas the internal and external ones are located at each side of the edges. Notice that math G i G e G math . If math b 0 geq 0 math , then all the three gradients have non negative values at all pixels. References cite id serra82 Image Analysis and Mathematical Morphology by Jean Serra, ISBN 0126372403 1982 cite Image Analysis and Mathematical Morphology, Volume 2 Theoretical Advances by Jean Serra, ISBN 0 12 637241 1 1988 An Introduction to Morphological Image Processing by Edward R. Dougherty, ISBN 0 8194 0845 X 1992 External links http cmm.ensmp.fr beucher publi morph grad.pdf Morphological gradients , Centre de Morphologie Math matique, cole des Mines de Paris Category Mathematical morphology Category Digital geometry compu graphics stub comp sci stub ... 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 ... 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 ..., for example electric current driven by a gradient of electric potential in the information ... to its neighbors. This idea motivated the approach through gradient networks which studies flow ... ref name grad Z. Toroczkai, B. Kozma, K.E. Bassler, N.W. Hengartner and G. Korniss. Gradient Networks, cond mat 0408262. ref Image Gradient.jpg thumb 300px left Fig.2. The gradient at node i is a directed .... 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, and the in degree .... The degree distributions of the gradient network and the substrate BA Model . ref name grad When ... 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 network ... rangle text network R 0 math where N sub receive sub is the number of nodes that receive gradient flow ... more details
Merge electrochemical potential date August 2010 An electrochemical gradient is a spatial variation of both electrical potential and chemical concentration across a membrane. Both components are often due to ion gradients , particularly proton gradients , and the result can be a type of potential energy available for work in a cell. This can be calculated as a thermodynamic measure, termed electrochemical potential , that combines the concepts of energy stored in the form of chemical potential , which accounts for an ion s concentration gradient across a cellular membrane , and electric charge electrostatics , which accounts for an ion s tendency to move relative to the membrane 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 ... gradient. In mitochondria and chloroplast s, proton gradients are used to generate a chemiosmotic ... of ATP by oxidative phosphorylation . An electrochemical gradient has two components ... across a membrane. An electrochemical gradient is analogous to the water pressure across a hydroelectric .... The enzyme NaKATPase Na K ATPase uses ATP to make a sodium ion gradient and a potassium ion gradient ... ions across biological membranes. Proton gradients The proton gradient can be used as intermediate ... cause it to create a transmembrane proton 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 ..., 2002 1 14 2005 , for Biology 113 at the Ohio State University DEFAULTSORT Electrochemical Gradient ... biology Category 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
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