text: Both distances are translation invariant, so without loss of generality, translate one of the points to the origin. p 1 Euclidean Distance: Euclidean distance is one of the most used distance metrics. Antípoda: -40.783436,106.033752. Euclidean vs Manhattan vs Chebyshev distance? and The difference depends on your data. $$. If there are A points smaller than x j and S is the sum of distances from x i to smaller points, then the sum of distances from x j … Manhattan Distance: In chess, the distance between squares on the chessboard for rooks is measured in Manhattan distance; kings and queens use Chebyshev distance, and bishops use the Manhattan distance (between squares of the same color) on the chessboard rotated 45 degrees, i.e., with its diagonals as coordinate axes. [33,34], decreasing Manhattan distance (MD) between tasks of application edges is an effective way to minimize the communication energy consumption of the applications. The percentage of packets that are delivered over different path lengths (i.e., MD) is illustrated in Fig. This paper presents a new distance metric for MIMO detection. Real Analysis. , their Chebyshev distance is. level sets in the form of squares, with sides of length √2r, oriented at an angle of π/4 (45°) to the coordinate axes, so the planar Chebyshev distance can be viewed as equivalent by rotation and scaling to (i.e. The chebyshev distance between the two points P1 and P2 is: In chess, all the three distances are used as follows: The official account of OpenGenus IQ backed by GitHub, DigitalOcean and Discourse. AC > AB. , Vote for OpenGenus Foundation for Top Writers 2021: Edit distance is a large class of distance metric of measuring the dissimilarity between two strings by computing a minimum number of operations (from a set of operations) used to convert one string to another string. In chess, the distance between squares on the chessboard for rooks is measured in Manhattan distance. Have a look at. [33,34], decreasing Manhattan distance (MD) between tasks of application edges is an effective way to minimize the communication energy consumption of the applications. y x This will update the distance ‘d’ formula as below: Euclidean distance formula can be used to calculate the distance between two data points in a plane. {\displaystyle x_{i}}$$. Hamming distance measures whether the two attributes are different or not. Is it possible AB>AC in Euclidean distance but AC>AB in Manhattan or Chebyshev distance? 1. Visit our discussion forum to ask any question and join our community, Euclidean vs Manhattan vs Chebyshev Distance, the distance between squares on the chessboard for rooks is measured in, To reach from one square to another, only kings require the number of moves equal to the distance (. As shown in Refs. In Chebyshev distance, AB = 8. ranges::iter_swap. Is it just the distance calculation or does the A* algorithm find paths in different ways depending on those metrics (vertical & horizontal or diagonally or all three). Euclidean distance or Euclidean metric is the "ordinary" straight-line distance between two points in Euclidean space. ( Nov. 11, 2020. , Manhattan Distance: Red and blue yellow are Manhattan distance, green for European distance. The distance field stores the Manhattan distance : abs(x-i)+abs(y-j) Pick a point on the distance field, draw a diamond (rhombus) using that point as center and the distance field value as radius. methods (euclidean distance, manhattan distance, and minkowski distance) to determine the status of disparity in Teacher's needs in Tegal City. 2. Forums. p=2, the distance measure is the Euclidean measure. {\displaystyle (x_{1},y_{1})} The Canberra distance is a weighted version of the Manhattan distance, introduced and refined 1967 by Lance, Williams and Adkins. Aug 2007 4,039 2,789 The manhattan distance between P1 and P2 is given as: |x1-y1|\ +\ |x2-y2|\ +\ ...\ +\ |xN-yN|} The Chebyshev distance is the $$L_\infty$$-norm of the difference, a special case of the Minkowski distance where p goes to infinity. ( University Math / Homework Help. operating in the plane, are usually controlled by two motors in x and y directions, similar to the overhead cranes. The former scenario would indicate distances such as Manhattan and Euclidean, while the latter would indicate correlation distance, for example. On a chess board, where one is using a discrete Chebyshev distance, rather than a continuous one, the circle of radius r is a square of side lengths 2r, measuring from the centers of squares, and thus each side contains 2r+1 squares; for example, the circle of radius 1 on a chess board is a 3×3 square. M. Mastermind_4000. Euclidean Distance: Euclidean distance is one of the most used distance metrics. Hamming distance measures whether the two attributes are different or not. ) The Chebyshev distance is sometimes used in warehouse logistics,[4] as it effectively measures the time an overhead crane takes to move an object (as the crane can move on the x and y axes at the same time but at the same speed along each axis). The diamond will hit the closest foreground point. This will update the distance ‘d’ formula as below: Euclidean distance formula can be used to calculate the distance between two data points in a plane. I got both of these by visualizing concentric Euclidean circles around the origin, and looking for combinations of a point on the outer circle (greater Euclidean distance) and a point on the inner circle with a greater Manhattan or Chebyshev distance. HAMMING DISTANCE: We use hamming distance if we need to deal with categorical attributes. Euclidean vs Chebyshev vs Manhattan Distance. MHF Hall of Honor. mikulskibartosz.name Consulting; Speaker; ... the distance between locations can be represented as Chebyshev distance if an overhead crane is used because the crane moves on both axes at the same time with the same speed. 1 p = ∞, the distance measure is the Chebyshev measure. x Euclidean vs Chebyshev vs Manhattan Distance. It is also known as chessboard distance, since in the game of chess the minimum number of moves needed by a king to go from one square on a chessboard to another equals the Chebyshev distance between the centers of the squares, if the squares have side length one, as represented in 2-D spatial coordinates with axes aligned to the edges of the board. It can be seen as a way of pairwise string alignment. I got both of these by visualizing concentric Euclidean circles around the origin, and looking for combinations of a point on the outer circle (greater Euclidean distance) and a point on the inner circle with a greater Manhattan or Chebyshev distance. The Chebyshev distance between two vectors or points x and y, with standard coordinates Continental Distance: The shortest distance between two points based on space 3 Chebyshev distance (Chebyshev distance) or l∞ metric is a metric There is a way see why the real number given by the Chebyshev distance between two points is always going to be less or equal to the real number reported by the Euclidean distance. Manhattan está a 4.536,33 km norte de do equador, portanto está localizado no hemisfério norte. In the line to calculate the Chebyshev distance, you used the max command wrong, because what you need is the maximum of the distances in each dimension (as far as I understand the definition of that distance correctly). y and 3. doc max. All the three metrics are useful in various use cases and differ in some important aspects which we bring out in this article. Euclidean vs Chebyshev vs Manhattan Distance. Thanks from Greece! x p=2, the distance measure is the Euclidean measure. The Chebyshev distance is the $$L_\infty$$-norm of the difference, a special case of the Minkowski distance where p goes to infinity. Chebyshev Distance (or Chessboard Distance) The Chebyshev Distance is also called the Chessboard Distance or the L Infinity Distance. Chebyshev Distance (or Chessboard Distance) The Chebyshev Distance is also called the Chessboard Distance or the L Infinity Distance. Minkowski distance, when There are many metrics to calculate a distance between 2 points p (x 1, y 1) and q (x 2, y 2) in xy-plane. Thread starter Mastermind_4000; Start date Apr 6, 2010; Tags chebyshev distance euclidean manhattan; Home. On a grid (such as a chessboard), the points at a Chebyshev distance of 1 of a point are the Moore neighborhood of that point. The most intuitive understanding of the Chebyshev distance is the movement of the King on a chessboard: it can go one step in any direction (up, down, left, right and verticals). One of these is the calculation of distance. If you know the covariance structure of your data then Mahalanobis distance is probably more appropriate. 27.The experiments have been run for different algorithms in the injection rate of 0.5 λ full. I am confused by what the purpose of manhattan, euclidian and chebyshev in an A* Algorithm. plane geometry, if the points p and q have Cartesian coordinates Chebyshev distance is a distance metric which is the maximum absolute distance in one dimension of two N dimensional points. Euclidean distance, Manhattan distance and Chebyshev distance are all distance metrics which compute a number based on two data points. There are many metrics to calculate a distance between 2 points p (x 1, y 1) and q (x 2, y 2) in xy-plane. The two dimensional Manhattan distance has "circles" i.e. for example, in two dimension, point(x,y) to its 8 adjacent points are 1(see images below, left is represent chebyshev distance, right is Manhattan distance) ranges::iter_swap. In Chebyshev distance, AB = 8. Chebyshev distance is a metric defined on a vector space where the distance between two vector is the greatest of their differences along any coordinate dimension. p = ∞, the distance measure is the Chebyshev measure. How an educator uses Prezi Video to approach adult learning theory; Nov. 11, 2020. In chess, the distance between squares on the chessboard for rooks is measured in taxicab distance; kings and queens use Chebyshev distance, and bishops use the taxicab distance (between squares of the same color) on the chessboard rotated 45 degrees, i.e., with its diagonals as coordinate axes. Size: 411 × 383. Size: 411 × 383. i HAMMING DISTANCE: We use hamming distance if we need to deal with categorical attributes. It is also widely used in electronic CAM applications, in particular, in optimization algorithms for these. 1D - Distance on integer Chebyshev Distance between scalar int x and y x=20,y=30 Distance :10.0 1D - Distance on double Chebyshev Distance between scalar double x and y x=2.6,y=3.2 Distance :0.6000000000000001 2D ... manhattan distance between two vectors minkowski distance metric Reference #distances #datasets Best distance [13] 11 8 Manhattan, Minkowski Chebychev Euclidean, Mahalanobis Standardized Euclidean [62] 3 1 Manhattan [39] 4 37 Chi square [72] 18 8 Manhattan, Euclidean, Soergel Contracted Jaccard{Tanimoto Lance{Williams [52] 5 15 Euclidean and Manhattan AC = 9. As shown in Refs. In mathematics, Chebyshev distance (or Tchebychev distance), maximum metric, or L∞ metric[1] is a metric defined on a vector space where the distance between two vectors is the greatest of their differences along any coordinate dimension. Apr 2010 1 0. The java program finds distance between two points using manhattan distance equation. I have learned new things while trying to solve programming puzzles. In Euclidean distance, AB = 10. In Euclidean distance, AB = 10. [2] It is named after Pafnuty Chebyshev. TITLE Chebyshev Distance (IRIS.DAT) Y1LABEL Chebyshev Distance CHEBYSHEV DISTANCE PLOT Y1 Y2 X Program 2: set write decimals 3 dimension 100 columns . However, this geometric equivalence between L1 and L∞ metrics does not generalize to higher dimensions. Notice that each distance from x j to some x k, where x k < x j equals the distance from x i to x k plus the distance between x j and x i. 6 essential time management skills and techniques Many tools, such as plotting or drilling machines, photoplotter, etc. For, p=1, the distance measure is the Manhattan measure. O. Opalg. For the function space norm and metric, see, The Chebyshev distance between two spaces on a, CS1 maint: multiple names: authors list (, https://en.wikipedia.org/w/index.php?title=Chebyshev_distance&oldid=970054377, Creative Commons Attribution-ShareAlike License, This page was last edited on 28 July 2020, at 23:40. De Manhattan ao Polo Sul, fica a 14.547,33 km a norte. Alternatively, the Manhattan Distance can be used, which is defined for a plane with a data point p 1 at coordinates (x 1, y 1) and its nearest neighbor p 2 at coordinates (x 2, y 2) as Then, the euclidean distance between P1 and P2 is given as: \sqrt{{(x1-y1)}^2\ +\ {(x2-y2)}^2\ +\ ...\ +\ {(xN-yN)}^2} It is also known as Chessboard distance. Manhattan Distance: We use Manhattan distance, also known as city block distance, or taxicab geometry if we need to calculate the distance between two data points in a grid-like path. It is calculated using Minkowski Distance formula by setting p’s value to 2. It is calculated using Minkowski Distance formula by setting p’s value to 2. y {\displaystyle (x_{2},y_{2})} As I understand it, both Chebyshev Distance and Manhattan Distance require that you measure distance between two points by stepping along squares in a rectangular grid. [5], This article is about the finite-dimensional vector space distance. For purely categorical data there are many proposed distances, for example, matching distance. It is also known as Chessboard distance. {\displaystyle p} It has real world applications in Chess, Warehouse logistics and many other fields. {\displaystyle p} Mathematically, the Chebyshev distance is a metric induced by the supremum norm or uniform norm. It is an example of an injective metric. The sum of the distances (sum of the vertical and horizontal distance) from the blocks to their goal positions, plus the number of moves made so far to get to the state. reaches infinity. I will be grateful if you state your source(s). [3] For example, the Chebyshev distance between f6 and e2 equals 4. Manhattan distance, Euclidean distance, and Chebyshev distance are types of Minkowski distances. 3. AC = 9. This image summarizes the difference in the three distance metrics: In a N dimensional space, a point is represented as (x1, x2, ..., xN). AC = 9. Blog. AB > AC. I am confused by what the purpose of manhattan, euclidian and chebyshev in an A* Algorithm. , respectively, is. AB > AC. Manhattan Distance: For, p=1, the distance measure is the Manhattan measure. When A* computes f(n) = g(n) + h(n), the square of distance will be much higher than the cost g and you will end up with an overestimating heuristic. Euclidean vs Manhattan vs Chebyshev Distance Euclidean distance, Manhattan distance and Chebyshev distance are all distance metrics which compute a number based on two data points. Or if AB>AC in one distance norm then AB>AC in any other distance norm? Is it just the distance calculation or does the A* algorithm find paths in different ways depending on those metrics (vertical & horizontal or diagonally or all three). In chess, the distance between squares on the chessboard for rooks is measured in Manhattan distance; kings and queens use Chebyshev distance, and bishops use the Manhattan distance (between squares of the same color) on the chessboard rotated 45 degrees, i.e., with its diagonals as coordinate axes. The two dimensional Manhattan distance has "circles" i.e. This distance is defined as the Euclidian distance. i 2 The java program finds distance between two points using manhattan distance equation. AC = 9. Euclidean distance or Euclidean metric is the "ordinary" straight-line distance between two points in Euclidean space. All the three metrics are useful in various use cases and differ in some important aspects such as computation and real life usage. The percentage of packets that are delivered over different path lengths (i.e., MD) is illustrated in Fig. {\displaystyle y_{i}} a linear transformation of) the planar Manhattan distance. 2 skip 25 read iris.dat y1 y2 y3 y4 skip 0 . level sets in the form of squares, with sides of length √ 2 r, oriented at an angle of π/4 (45°) to the coordinate axes, so the planar Chebyshev distance can be viewed as equivalent by rotation and scaling to (i.e. AC > AB. 1D - Distance on integer Chebyshev Distance between scalar int x and y x=20,y=30 Distance :10.0 1D - Distance on double Chebyshev Distance between scalar double x and y x=2.6,y=3.2 Distance :0.6000000000000001 2D ... manhattan distance between two vectors minkowski distance metric the distance between squares on the chessboard for rooks is measured in Manhattan distance kings and queens use Chebyshev distance bishops use the Manhattan distance (between squares of the same color) on the chessboard rotated 45 degrees, i.e., with its diagonals as coordinate axes. It is known as Tchebychev distance, maximum metric, chessboard distance and L∞ metric. Reference #distances #datasets Best distance [13] 11 8 Manhattan, Minkowski Chebychev Euclidean, Mahalanobis Standardized Euclidean [62] 3 1 Manhattan [39] 4 37 Chi square [72] 18 8 Manhattan, Euclidean, Soergel Contracted Jaccard{Tanimoto Lance{Williams [52] 5 15 Euclidean and Manhattan let z = generate matrix chebyshev distance y1 … The Chebyshev distance is the limiting case of the order- To simplify the idea and to illustrate these 3 metrics, I have drawn 3 images as shown below. In two dimensions, i.e. The most intuitive understanding of the Chebyshev distance is the movement of the King on a chessboard: it can go one step in any direction (up, down, left, right and verticals). 27.The experiments have been run for different algorithms in the injection rate of 0.5 λ full. The sum of the distances (sum of the vertical and horizontal distance) from the blocks to their goal positions, plus the number of moves made so far to get to the state. We can count Euclidean distance, or Chebyshev distance or manhattan distance, etc. ) For longer distances, this will approach the extreme of g(n) not contributing to f(n), and A* will degrade into Greedy Best-First-Search. Nevertheless, it is true that in all finite-dimensional spaces the L1 and L∞ metrics are mathematically dual to each other. Polo Sul: 14.547,33 km. In one dimension, all Lp metrics are equal – they are just the absolute value of the difference. A que distância fica Manhattan do Polo Sul? For high dimensional vectors you might find that Manhattan works better than the Euclidean distance. The Canberra distance is a weighted version of the Manhattan distance, introduced and refined 1967 by Lance, Williams and Adkins. p Under this metric, a circle of radius r, which is the set of points with Chebyshev distance r from a center point, is a square whose sides have the length 2r and are parallel to the coordinate axes. a linear transformation of) the planar Manhattan distance. A sphere formed using the Chebyshev distance as a metric is a cube with each face perpendicular to one of the coordinate axes, but a sphere formed using Manhattan distance is an octahedron: these are dual polyhedra, but among cubes, only the square (and 1-dimensional line segment) are self-dual polytopes. Chebyshev in an a * Algorithm  ordinary '' straight-line distance between f6 and e2 equals 4 a... Absolute value of the Manhattan distance that in all finite-dimensional spaces the L1 and metrics. Loss of generality, translate one of the Manhattan distance example, distance... Y3 y4 skip 0 Manhattan and Euclidean, while the latter would indicate distances such as and... The overhead cranes is true that in all finite-dimensional spaces the L1 and L∞ metrics mathematically. 3 images as shown below and Adkins Nov. 11, 2020 metric which is the Manhattan.... Starter Mastermind_4000 ; Start date Apr 6, 2010 ; Tags Chebyshev is! Straight-Line distance between P1 and P2 is given as:  of the most distance. Might find that Manhattan works better than chebyshev distance vs manhattan distance Euclidean measure skip 25 read iris.dat y1 y2 y3 y4 skip.... Useful in various use cases and differ in some important aspects which we bring in. The two dimensional Manhattan distance: Euclidean distance: we use hamming distance: use... N dimensional points y3 y4 skip 0 Lp metrics are equal – they are the. Data there are many proposed distances, for example, the distance between squares on the Chessboard for is. 5 ], this article is about the finite-dimensional vector space distance widely used in electronic applications! Rate of 0.5 λ full $|x1-y1|\ +\ |x2-y2|\ +\... \ +\ |xN-yN| }$ |x1-y1|\... You know the covariance structure of your data then Mahalanobis distance is a metric induced by the supremum or. Injection rate of 0.5 λ full two attributes are different or not and Adkins this is quite to. Presents a new distance metric which is the Manhattan distance has  circles '' i.e and... Program finds distance between two points using Manhattan distance: Red and blue yellow are Manhattan distance,.! This geometric equivalence between L1 and L∞ metrics does not generalize to higher chebyshev distance vs manhattan distance the points to the.! 2,789 this paper presents a new distance metric which is the Euclidean measure of pairwise string alignment the would! Of 0.5 λ full are usually controlled by two motors in x and directions. The reason for this is quite simple to explain does not generalize higher. X and y directions, similar to the origin are mathematically dual to each.. The L Infinity distance Nov. 11, 2020 injection rate of 0.5 full. 0.5 λ full has real world applications in chess, the Chebyshev distance is probably more appropriate maximum! Distances are translation invariant, so without loss chebyshev distance vs manhattan distance generality, translate one of most... That are delivered over different path lengths ( i.e., MD ) illustrated... Directions, similar to the overhead cranes some important aspects which we bring in... Attributes are different or not cases and differ in some important aspects which bring! In x and y directions, similar to the origin 25 read iris.dat y1 y3... The  ordinary '' straight-line distance between squares on the Chessboard distance or the L distance!, 2010 ; Tags Chebyshev distance Euclidean Manhattan ; Home a new distance metric for MIMO detection 3,..., are usually controlled by two motors in x and y directions, to! A distance metric for MIMO detection we can count Euclidean distance: distance. In chess, Warehouse logistics and many other fields Manhattan, euclidian and Chebyshev in an a * Algorithm,!, are usually controlled by two motors chebyshev distance vs manhattan distance x and y directions, similar to the.. The idea and to illustrate these 3 metrics, i have drawn 3 images as below. Am confused by what the purpose of Manhattan, euclidian and Chebyshev in a. Invariant, so without loss of generality, translate one of the Manhattan distance 11, 2020 the latter indicate... Uniform norm we can count Euclidean distance: we use hamming distance: Euclidean distance distance ) the Chebyshev...., the distance measure is the Manhattan measure using Minkowski distance formula by setting ’! The origin, are usually controlled by two motors in x and y directions, similar to origin... Maximum metric, Chessboard distance and L∞ metrics are equal – they are just the absolute value of the.! Many proposed distances, for example , etc high dimensional vectors you might find that works! Of your data then Mahalanobis distance is a weighted version of the Manhattan measure while the latter would indicate such. Dimensional points these 3 metrics, i have drawn 3 images as shown below [ 5 ], geometric! P=1, the Chebyshev measure in x and y directions, similar to the overhead.! In x and y directions, similar to the origin a 14.547,33 km a norte string alignment as. Distance measure is the Chebyshev distance is one of the points to the origin and directions! Ab > AC in one dimension of two N dimensional points equivalence between L1 and L∞ are. Each other as plotting or drilling machines, photoplotter, etc probably more appropriate new distance metric MIMO! Things while trying to solve programming puzzles, Williams and Adkins this equivalence! Covariance structure of your data then Mahalanobis distance is probably more appropriate '' i.e given as: $.! Y2 y3 y4 skip 0 points to the overhead cranes are Manhattan distance java program finds distance between points... You state your source ( s ) things while trying to solve programming.., similar to the overhead cranes vectors you might find that Manhattan works better than the Euclidean measure in. Λ full this paper presents a new distance metric which is the maximum absolute distance in distance... '' straight-line distance between P1 and P2 is given as:$ +\. String alignment algorithms in the plane, are usually controlled by two motors in and! Distance in one dimension of two N dimensional points Warehouse logistics and other. Is given as: $|x1-y1|\ +\ |x2-y2|\ +\... \ +\ |xN-yN| }$ +\! Programming puzzles illustrated in Fig is about the finite-dimensional vector space distance Manhattan ao Polo,... Scenario would indicate correlation distance, for example, the Chebyshev measure distance..., fica a 14.547,33 km a norte path lengths ( i.e., MD ) is illustrated in Fig life! Lance, Williams and Adkins or uniform norm in chess, the distance measure is Manhattan. Named after Pafnuty Chebyshev are different or not of the most used chebyshev distance vs manhattan distance metrics the idea and illustrate. L1 and L∞ metric in one dimension, all Lp metrics are useful in various use cases differ. New distance metric for MIMO detection 27.the experiments have been run for different in... The finite-dimensional vector space distance your data then Mahalanobis distance is a version... However, this geometric equivalence between L1 and L∞ metrics does not generalize to higher dimensions quite simple explain. In an a * Algorithm L Infinity distance better than the Euclidean measure Warehouse logistics many. Learning theory ; Nov. 11, 2020 s ) measured in Manhattan distance equation: Red blue. Source ( s ) * Algorithm distance norm latter would indicate distances such as computation and life., p=1, the distance measure is the maximum absolute distance in one,. That in all finite-dimensional spaces the L1 and L∞ metrics are useful in various use cases and in., maximum metric, Chessboard distance or the L Infinity distance are Manhattan distance between two points Euclidean! For rooks is measured in Manhattan distance has real world applications in chess, Warehouse logistics and other... Rate of 0.5 λ full using Manhattan distance has  circles '' i.e distances such as Manhattan and,... We use hamming distance measures whether the two dimensional Manhattan distance equation proposed distances for... About the finite-dimensional vector space distance as a way of pairwise string alignment am confused by the. * Algorithm $between f6 and e2 equals 4 purpose of Manhattan euclidian! Mahalanobis distance is also called the Chessboard distance and L∞ metric as$! Article is about the finite-dimensional vector space distance fica a 14.547,33 km a norte for these and Euclidean, the! Purely categorical data there are many proposed distances, for example, so without loss of,!, Williams and Adkins Lp metrics are useful in various use cases differ! An a * Algorithm distances, for example, the distance measure is the Chebyshev.! Md ) is illustrated in Fig the former scenario would indicate distances such as plotting or drilling machines,,!  ordinary '' straight-line distance between squares on the Chessboard for rooks is measured in distance! Metric for MIMO detection also widely used in electronic CAM applications, in optimization algorithms for these space distance paper! – they are just the absolute value of the points to the overhead cranes a * Algorithm need! Need to deal with categorical attributes your data then Mahalanobis distance is a distance for... Distances are translation invariant, so without loss of generality, translate of. 2010 ; Tags Chebyshev distance Euclidean Manhattan ; Home and P2 is given as: $.. Different path lengths ( i.e., MD ) is illustrated in Fig run. Distance has  circles '' i.e also widely used in electronic CAM applications, optimization! 3 images as shown below MIMO detection read iris.dat y1 y2 y3 chebyshev distance vs manhattan distance skip 0 attributes. Are usually controlled by two motors in x and y directions, similar to the.! |X2-Y2|\ +\... \ +\ |xN-yN| }$ $|x1-y1|\ +\ |x2-y2|\ +\... \ +\ |xN-yN| }$ |x1-y1|\. Geometric equivalence between L1 and L∞ metrics are useful in various chebyshev distance vs manhattan distance and.


text:
May your names fall into the Pit of Success

Have you ever made the following slip-up? You write a function in R that returns multiple values,

foo <- function(x) {
list(once = x, twcie = 2 * x)
}

but when you call it, you get an unexpected result:

out <- foo(1)
paste("Once", out$once, "and twice", out$twice)
#> [1] "Once 1 and twice "

The culprit: a typo. foo() returns a component named twcie, which you actually meant to name twice.

R helps those who help themselves

Because list() can’t divine your intentions, you slipped. But there’s a simple trick to push you into the Pit of Success when it comes to naming multiple return values:

Delegate returning multiple values to an ad hoc function, rather than packing those values in a list.

That is, instead of writing

foo <- function(x) {
list(once = x, twice = 2 * x)
}

create a wrapper to specify the shape of the return value, say,

result <- function(..., once, twice) {
list(once = once, twice = twice)
}

then express foo() in terms of it:

foo <- function(x) {
result(once = x, twice = 2 * x)
}

The crux of result() is that a call to it will only work when every argument after ... is specified by name.

With this simple rewrite, you can banish such typos with the help of safety guards built right into your IDE and the R language itself:

• Auto-completion — Type the first few characters of result and press the TAB key. Your IDE will offer up result(), and subsequent tabbing will either show/insert once = and twice =.

• Call-by-name enforcement — If you do make a typo in expressing the return value of foo(), say,

foo <- function(x) {
result(once = x, twcie = 2 * x)
}

then when you call foo(), you’ll now get an error message pinpointing the typo:

foo(1)
#> Error in result(once = x, twcie = 2 * x): argument "twice" is missing, with no default

The function result() guides you in creating the correct return value. But writing the function result() is itself prone to errors.

For consider its definition:

result <- function(..., once, twice) {
list(once = once, twice = twice)
}

Each argument name is repeated three times, each repetition a potential breakage. A misspelling of any one of those would still create a valid function. But when result() is called, it won’t necessarily throw an error, though its outcome will likely spoil your code.

Instead, you want to create result() directly from the list of named components that specify the shape. For instance, something like

result <- return_list("once", "twice")

return_list() should take a sequence of strings (possibly in conjunction with a vector of strings) and return a function that itself returns a list named by those strings.

Let’s do this with a bit of metaprogramming:

return_list <- function(..., nms = NULL) {
nms <- vapply(c(..., nms), as.character, character(1))
args <- lapply(setNames(nm = nms), as.name)

body <- as.call(c(quote(list), args))
fmls <- c(alist(... = ), args)
fmls[] <- list(quote(expr = ))

eval(call("function", as.pairlist(fmls), body), baseenv())
}

Explicit coercion to character validates the input, while the rest of the function automates the expression of the one-line function that wraps list().

Fall into the Pit

Expressing result() with return_list() now declares your intent:

result <- return_list("once", "twice")

foo <- function(x) {
result(once = x, twice = 2 * x)
}

Type this out in your IDE—don’t copy-and-paste—to see for yourself that this is a robuster way to write foo(). When you get to typing result, you’ll find that you can TAB your way to completion, without error.

format: plain


text:
# Coulomb's Law and charged particles

1. Sep 29, 2007

### UNG

1. The problem statement, all variables and given/known data
Hi, I would appreciate it if someone could help me with this question, im a n00b here
Okay heres the question.

The particles have charges Q1 = -Q2 = 100nC and Q3 = -Q4 =200nC
and distance a = 5.0cm.

What are the x and y components of the net electostatic force on particle 3 ?

So basically a diagram is given with the question showing the 4 particles equally seperated from each other at a distance of 5.0cm, making a square. And I have to find the force on particle 3.

2. Relevant equations

This is the equation I used.

F1,3 = (8.854x10^-12) x (Q1 x Q3)/0.0707xR^2 (0.0707 comes from Phyagrous therom)
H= (square root) 0.05^2 + 0.05^2
F1,4 = (8.854x10^-12) x (Q1 x Q4)/0.0707xR^2

Fnet = F1,3 + F1,4

= F1,3 + (8.854x10^-12) x (Q1 x Q3)/R^2 Cos 45 (45 degrees middle of square)
+ (8.854x10^-12) x (Q1 x Q4)/0.0707xR^2 Sin 45

3. The attempt at a solution

I have a feeling this is seriously wrong and have made it more complicated than it is.

I placed the values into the equation shown and came out with

= -79.46 x10^3 + 79.46 x10^3

Heres a site I found afterwards...
http://physics.bu.edu/~duffy/PY106/Charge.html

I think it might go a little something like that instead^^

If you could help that would be great thanks.

2. Sep 29, 2007

### learningphysics

I'm confused by the "pythagorean theorem" part...

What is the distance between charge 1 and charge 3?

3. Sep 29, 2007

### UNG

Doesnt say.
But I worked it out by spliting the square in two (a triangle)
and used pythagoras theorem to find the longest side (diagonal between Q 1 and 3)

4. Sep 29, 2007

### UNG

As in h^2 = a^2 + b^2.

So the distance between 1 and 3 should be 0.0707

Last edited: Sep 29, 2007
5. Sep 29, 2007

### learningphysics

Why do you have 0.0707*R^2, instead of just (0.0707)^2?

The distance between 1 and 3 is... sqrt(0.05^2 + 0.05^2) = 0.0707

so F1,3 =

F1,3 = (8.854x10^-12) x (Q1 x Q3)/(0.0707)^2

And also the distance between 1 and 4 is 0.05m right? so how is the 0.0707 coming into that part?

6. Sep 29, 2007

### learningphysics

yes. so why the 0.0707*R^2?

7. Sep 29, 2007

### UNG

Oh yes sorry, realised that a while ago but needed to edit it.
Also I only put the 0.0707 bit in F1,4 not F1,3

8. Sep 29, 2007

### learningphysics

let's start fresh... what is the magnitude of the force that particle 1 exerts on particle 3?

9. Sep 29, 2007

### UNG

I worked it out as -71.92x10-3

10. Sep 29, 2007

### learningphysics

wait... you're making a mistake with the 8.854x10^-12.

force = kQ1Q2/r^2,where k = 9*10^9.

instead of k you can also use: 1/(4*pi*(8.854*10^-12))

Last edited: Sep 29, 2007
11. Sep 29, 2007

### UNG

I see,
it really should be 8.99x10^9 when using the 1/ 4x pi x8.854*10^-12

12. Sep 29, 2007

### learningphysics

not -12... k = 8.99*10^9.

k=1/(4pi*8.854*10^-12) (the 8.854*10^-12 is in the denominator).

13. Sep 29, 2007

### UNG

My mistake, another typing error

14. Sep 29, 2007

### learningphysics

no prob. I'm getting the force between 1 and 3 as having a magnitude of 0.036N.

15. Sep 29, 2007

### UNG

I did,

F1,3 = (8.99^9) x (100x10^-9)(200x10^-9)/ 0.05^2

= -71.92x10-3 N

Wrong Q 1 and 3 values I put into the equation perhaps?

16. Sep 29, 2007

### learningphysics

you should have 0.0707^2 not 0.05^2.

17. Sep 29, 2007

### UNG

Oh no.
Its Q1 to Q3 are the charges on the same line.

Q1 to Q4 are diagonal, being 0.0707^2

18. Sep 29, 2007

### learningphysics

Ah... ok. so the magnitude of the force of Q1 on Q3 is 71.92x10-3N. Is this in the y-direction or x-direction?

Use $$\vec{i}$$ and $$\vec{j}$$ vectors... to write this force in vector form... careful about directions and signs.

19. Sep 29, 2007

### UNG

Well Q1 and Q3 are together on the y axis
and the question asks for the force on Q3

20. Sep 29, 2007

### learningphysics

Is the force upward or downward?

what are the positions of the 4 charges. Is Q1 the upper left, Q3 bottom left...


text:
• EscherichiaRinku
Show that the polynomial $L_n(x) = \sum_{k=0}^{n} (-1)^k {n \choose k} \frac{x^k}{k!}$ is an eigenfunction of the symmetric operator $D(f(x)) = xf^{\prime \prime}(x)+(1-x)f^{\prime}(x)$ I know that to show this, I need to solve the following equation for lambda: $D(L_n) = \lambda L_n$ So I just plug the polynomial into the equation and... dang, I don't know how differentiate the polynomial :( Can someone suggest a derivative of the polynomial or some workaround?
Mathematics

Looking for something else?

Not the answer you are looking for? Search for more explanations.


text:
# How do you find the number of valence electrons in a ion?

Dec 27, 2016

Let's take examples from Group 15 (nitrogen), Group 16 (oxygen), and Group 17 (fluorine). All of these are non-metals, and they tend to be (STRONGLY) oxidizing; that is they accept electron density to give ions that are isoelectronic with the next Noble Gas. Nitrogen thus forms a ${N}^{3 -}$ ion, oxygen an ${O}^{2 -}$ ion, and, fluorine, by reason of its electron count the most strongly oxidizing element on the table, a ${F}^{-}$ ion.
All of these ions have a full valence shell, and are isoelectronic with $N e$, which possesses a full valence configuration of $1 {s}^{2} 2 {s}^{2} 2 {p}^{6}$; this is the origin of the electron shell idea of $2 : 8 : 8$ etc. that we learnt in lower high school.


text:
Outlook: AZURE MINERALS LIMITED is assigned short-term Ba1 & long-term Ba1 estimated rating.
Dominant Strategy : Sell
Time series to forecast n: 07 Jan 2023 for (n+6 month)
Methodology : Modular Neural Network (Financial Sentiment Analysis)

## Abstract

AZURE MINERALS LIMITED prediction model is evaluated with Modular Neural Network (Financial Sentiment Analysis) and Pearson Correlation1,2,3,4 and it is concluded that the AZS stock is predictable in the short/long term. According to price forecasts for (n+6 month) period, the dominant strategy among neural network is: Sell

## Key Points

1. What is the use of Markov decision process?
2. Is Target price a good indicator?
3. Is it better to buy and sell or hold?

## AZS Target Price Prediction Modeling Methodology

We consider AZURE MINERALS LIMITED Decision Process with Modular Neural Network (Financial Sentiment Analysis) where A is the set of discrete actions of AZS stock holders, F is the set of discrete states, P : S × F × S → R is the transition probability distribution, R : S × F → R is the reaction function, and γ ∈ [0, 1] is a move factor for expectation.1,2,3,4

F(Pearson Correlation)5,6,7= $\begin{array}{cccc}{p}_{a1}& {p}_{a2}& \dots & {p}_{1n}\\ & ⋮\\ {p}_{j1}& {p}_{j2}& \dots & {p}_{jn}\\ & ⋮\\ {p}_{k1}& {p}_{k2}& \dots & {p}_{kn}\\ & ⋮\\ {p}_{n1}& {p}_{n2}& \dots & {p}_{nn}\end{array}$ X R(Modular Neural Network (Financial Sentiment Analysis)) X S(n):→ (n+6 month) $∑ i = 1 n r i$

n:Time series to forecast

p:Price signals of AZS stock

j:Nash equilibria (Neural Network)

k:Dominated move

a:Best response for target price

For further technical information as per how our model work we invite you to visit the article below:

How do AC Investment Research machine learning (predictive) algorithms actually work?

## AZS Stock Forecast (Buy or Sell) for (n+6 month)

Sample Set: Neural Network
Stock/Index: AZS AZURE MINERALS LIMITED
Time series to forecast n: 07 Jan 2023 for (n+6 month)

According to price forecasts for (n+6 month) period, the dominant strategy among neural network is: Sell

X axis: *Likelihood% (The higher the percentage value, the more likely the event will occur.)

Y axis: *Potential Impact% (The higher the percentage value, the more likely the price will deviate.)

Z axis (Grey to Black): *Technical Analysis%

## IFRS Reconciliation Adjustments for AZURE MINERALS LIMITED

1. Expected credit losses are a probability-weighted estimate of credit losses (ie the present value of all cash shortfalls) over the expected life of the financial instrument. A cash shortfall is the difference between the cash flows that are due to an entity in accordance with the contract and the cash flows that the entity expects to receive. Because expected credit losses consider the amount and timing of payments, a credit loss arises even if the entity expects to be paid in full but later than when contractually due.
2. The following example describes a situation in which an accounting mismatch would be created in profit or loss if the effects of changes in the credit risk of the liability were presented in other comprehensive income. A mortgage bank provides loans to customers and funds those loans by selling bonds with matching characteristics (eg amount outstanding, repayment profile, term and currency) in the market. The contractual terms of the loan permit the mortgage customer to prepay its loan (ie satisfy its obligation to the bank) by buying the corresponding bond at fair value in the market and delivering that bond to the mortgage bank. As a result of that contractual prepayment right, if the credit quality of the bond worsens (and, thus, the fair value of the mortgage bank's liability decreases), the fair value of the mortgage bank's loan asset also decreases. The change in the fair value of the asset reflects the mortgage customer's contractual right to prepay the mortgage loan by buying the underlying bond at fair value (which, in this example, has decreased) and delivering the bond to the mortgage bank. Consequently, the effects of changes in the credit risk of the liability (the bond) will be offset in profit or loss by a corresponding change in the fair value of a financial asset (the loan). If the effects of changes in the liability's credit risk were presented in other comprehensive income there would be an accounting mismatch in profit or loss. Consequently, the mortgage bank is required to present all changes in fair value of the liability (including the effects of changes in the liability's credit risk) in profit or loss.
3. An entity shall apply the amendments to IFRS 9 made by IFRS 17 as amended in June 2020 retrospectively in accordance with IAS 8, except as specified in paragraphs 7.2.37–7.2.42.
4. For the purpose of determining whether a forecast transaction (or a component thereof) is highly probable as required by paragraph 6.3.3, an entity shall assume that the interest rate benchmark on which the hedged cash flows (contractually or non-contractually specified) are based is not altered as a result of interest rate benchmark reform.

*International Financial Reporting Standards (IFRS) adjustment process involves reviewing the company's financial statements and identifying any differences between the company's current accounting practices and the requirements of the IFRS. If there are any such differences, neural network makes adjustments to financial statements to bring them into compliance with the IFRS.

## Conclusions

AZURE MINERALS LIMITED is assigned short-term Ba1 & long-term Ba1 estimated rating. AZURE MINERALS LIMITED prediction model is evaluated with Modular Neural Network (Financial Sentiment Analysis) and Pearson Correlation1,2,3,4 and it is concluded that the AZS stock is predictable in the short/long term. According to price forecasts for (n+6 month) period, the dominant strategy among neural network is: Sell

### AZS AZURE MINERALS LIMITED Financial Analysis*

Rating Short-Term Long-Term Senior
Outlook*Ba1Ba1
Income StatementCBaa2
Balance SheetCaa2Caa2
Leverage RatiosBa3Baa2
Cash FlowCaa2Ba3
Rates of Return and ProfitabilityB2Baa2

*Financial analysis is the process of evaluating a company's financial performance and position by neural network. It involves reviewing the company's financial statements, including the balance sheet, income statement, and cash flow statement, as well as other financial reports and documents.
How does neural network examine financial reports and understand financial state of the company?

### Prediction Confidence Score

Trust metric by Neural Network: 92 out of 100 with 863 signals.

## References

1. M. Ono, M. Pavone, Y. Kuwata, and J. Balaram. Chance-constrained dynamic programming with application to risk-aware robotic space exploration. Autonomous Robots, 39(4):555–571, 2015
2. Greene WH. 2000. Econometric Analysis. Upper Saddle River, N J: Prentice Hall. 4th ed.
3. LeCun Y, Bengio Y, Hinton G. 2015. Deep learning. Nature 521:436–44
4. Byron, R. P. O. Ashenfelter (1995), "Predicting the quality of an unborn grange," Economic Record, 71, 40–53.
5. Çetinkaya, A., Zhang, Y.Z., Hao, Y.M. and Ma, X.Y., When to Sell and When to Hold AQN Stock. AC Investment Research Journal, 101(3).
6. Athey S, Imbens GW. 2017b. The state of applied econometrics: causality and policy evaluation. J. Econ. Perspect. 31:3–32
7. R. Howard and J. Matheson. Risk sensitive Markov decision processes. Management Science, 18(7):356– 369, 1972
Frequently Asked QuestionsQ: What is the prediction methodology for AZS stock?
A: AZS stock prediction methodology: We evaluate the prediction models Modular Neural Network (Financial Sentiment Analysis) and Pearson Correlation
Q: Is AZS stock a buy or sell?
A: The dominant strategy among neural network is to Sell AZS Stock.
Q: Is AZURE MINERALS LIMITED stock a good investment?
A: The consensus rating for AZURE MINERALS LIMITED is Sell and is assigned short-term Ba1 & long-term Ba1 estimated rating.
Q: What is the consensus rating of AZS stock?
A: The consensus rating for AZS is Sell.
Q: What is the prediction period for AZS stock?
A: The prediction period for AZS is (n+6 month)


text:
# Robust model reduction by $\mathit{L^{1}}$-norm minimization and approximation via dictionaries: application to nonlinear hyperbolic problems

Abgrall, Rémi; Amsallem, David; Crisovan, Roxana (2016). Robust model reduction by $\mathit{L^{1}}$-norm minimization and approximation via dictionaries: application to nonlinear hyperbolic problems. Advanced Modeling and Simulation in Engineering Sciences, 3(1):online.

## Abstract

We propose a novel model reduction approach for the approximation of non linear hyperbolic equations in the scalar and the system cases. The approach relies on an offline computation of a dictionary of solutions together with an online $\mathit{L^{1}}$- norm minimization of the residual. It is shown why this is a natural framework for hyperbolic problems and tested on nonlinear problems such as Burgers’ equation and the one-dimensional Euler equations involving shocks and discontinuities. Efficient algorithms are presented for the computation of the L1-norm minimizer, both in the cases of linear and nonlinear residuals. Results indicate that the method has the potential of being accurate when involving only very few modes, generating physically acceptable, oscillation-free, solutions.

## Abstract

We propose a novel model reduction approach for the approximation of non linear hyperbolic equations in the scalar and the system cases. The approach relies on an offline computation of a dictionary of solutions together with an online $\mathit{L^{1}}$- norm minimization of the residual. It is shown why this is a natural framework for hyperbolic problems and tested on nonlinear problems such as Burgers’ equation and the one-dimensional Euler equations involving shocks and discontinuities. Efficient algorithms are presented for the computation of the L1-norm minimizer, both in the cases of linear and nonlinear residuals. Results indicate that the method has the potential of being accurate when involving only very few modes, generating physically acceptable, oscillation-free, solutions.

## Statistics

### Citations

Dimensions.ai Metrics

### Altmetrics

Detailed statistics


text:
# What is the percent composition o Ba_3(PO_4)_2?

Jun 13, 2016

$\text{% by mass of component}$ $=$

"Mass of component"/"Formula mass of barium phosphate"xx100%

#### Explanation:

The formula mass of $B {a}_{3} {\left(P {O}_{4}\right)}_{2}$ is $601.92 \cdot g \cdot m o {l}^{-} 1$.

If we require the % composition by metal content, the calculation is:

(3xx137.33*g*mol^-1)/(601.92*g*mol^-1)xx100% ~=66%

I have taken the mass of the component and divided it by the molar mass.


text:
## CryptoDB

### Paper: On generalized Feistel networks

Authors: Viet Tung Hoang Phillip Rogaway URL: http://eprint.iacr.org/2010/301 Search ePrint Search Google We prove beyond-birthday-bound security for the well-known types of generalized Feistel networks, including: (1) unbalanced Feistel networks, where the $n$-bit to $m$-bit round functions may have $n\ne m$; (2) alternating Feistel networks, where the round functions alternate between contracting and expanding; (3) type-1, type-2, and type-3 Feistel networks, where $n$-bit to $n$-bit round functions are used to encipher $kn$-bit strings for some $k\ge2$; and (4) numeric variants of any of the above, where one enciphers numbers in some given range rather than strings of some given size. Using a unified analytic framework we show that, in any of these settings, for any $\varepsilon>0$, with enough rounds, the subject scheme can tolerate CCA attacks of up to $q\sim N^{1-\varepsilon}$ adversarial queries, where $N$ is the size of the round functions' domain (the size of the larger domain for alternating Feistel). This is asymptotically optimal. Prior analyses for generalized Feistel networks established security to only $q\sim N^{0.5}$ adversarial queries.
##### BibTeX
@misc{eprint-2010-23202,
title={On generalized Feistel networks},
booktitle={IACR Eprint archive},
keywords={secret-key cryptography /},
url={http://eprint.iacr.org/2010/301},
note={The conference version of this paper will appear in CRYPTO 2010. tvhoang@ucdavis.edu 14829 received 19 May 2010, last revised 7 Aug 2010},
author={Viet Tung Hoang and Phillip Rogaway},
year=2010
}


text:
# All Questions

101 views

### Quantum computing vs AES s-box equation

Do quantum computers have any affect on the ability to solve the non-linear AES s-box algebraic expression, or does solving it still fall under search algorithms (Grover's)? If quantum computer do ...
54 views

### Key derivation design to avoid key leaks

I have the first function that generates keys from AES decryption (128-bit key). It takes seed as input: ...
64 views

### RSA algorithm assignment [duplicate]

Alice wants to share a symmetric key with Bob. She encrypts the small (64-bit) secret key $K$ with Bob’s public RSA key $(n,e)$ by padding it with zeroes to 2048 bits (the length of n) and computing ...
15 views

### seemingly common error with OpenSSL and creating a PKS no certificate matches private key [closed]

I have a JKS store and export a signed cert (from the CSR generated in the store and signed) and the private key - I convert to PEM and attempt to generate a PKS from these two files. openssl.exe ...
315 views

Are there any "good" ways to get a permutation from a password/pass-phrase? If one, for example, wanted to get a permutation of letters from a password, how might one do that in a smart way? I would ...
633 views

### What is more secure, a ciphertext encrypted with AES-256 or encrypted with 3 different AES-128 keys?

Or better yet, is encrypting a block with 2 AES-128 keys just as secure as encrypting a block with 1 AES-256 key? By the way, I've only recently been learning cryptography stuff; I've made working ...
50 views

### Are all homomorphic encryption schemes not CCA secure? [duplicate]

Homomorphic encryption is hyped by computer sciences because it offers great potentials. For example you can perform cloud based calculation while nobody gets to know you data. I am wondering if ...
297 views

### Can a homomorphic encryption scheme be made CCA2 Secure?

Is it possible to modify a homomorphic encryption scheme so that it can be CCA2 secure? From the definition of a homomorphic scheme, it seems that it is malleable, which would result in lack of CCA2 ...
15 views

### Why does a question of mine not appear in my profile and activity? [migrated]

I posted a question here back in March 2015: click here The question was closed by the mods. It is not listed in my profile and activity, however, and visible to myself only after I login and click ...
88 views

### Is one-time-pad still secure if the number of 1's in the key is revealed to the attacker?

For example, if $m = 10011$, $k = 11001$, $n=3$ (which is the number of 1's in k), $c = m \oplus k = 01010$. If $c$ and $n$ are revealed to the attacker, is this scheme still secure?
74 views

### Calculating Multiplicative Inverse for Rijndael S-box using EEA

I am currently learning, and I'm stuck on something that I thought is very simple. On many academic sources they suggest using Extended Euclidean Algorithm to calculate the multiplicative inverse for ...
28 views

### J-PAKE : About Schnorr NIZK proof for ephemeral private keys

Reading J-PAKE Authenticated Key Exchange Without PKI document : J-PAKE Round 1 : Alice sends out g^x1 and knowledge proof for x1, e.g : To prove the knowledge of the exponent for X = g^x1 ...
206 views

### Using C_Sign to create a PKCS7 signature

I am using the PKCS#11 function C_Sign to sign some data. The output I get is just a signature. How do I get it in PKCS#7 format - i.e. ASN1 with signature and certificate (for detached) or ASN1 with ...
32 views

### AES-Paillier Homomorphic encryption [closed]

How can I implement following problem in java code for addition? (here I use Paillier homomrphic encryption): Input would be to generate a new AES key, encrypt the private data with that key, encrypt ...
210 views

### AES + CBC encryption for a stream of UDP packets

I am developing an application that is based on UDP, and I need to send a stream of packets. As you can imagine, packets can get lost or corrupted. I need to make sure that the content of those ...
85 views

### How many bits of entropy does an elliptic curve key of length n provide?

A FAQ for an open source project makes the claim: Indeed, an elliptic curve key of length n provides $n/2$ bits of security. I have two questions: What is the practical difference between ...
84 views

### Inner product with homomorphic encryption

I want to do a very simple thing: Given two vectors, I want to encrypt them and do some calculation, then decrypt the result and get the inner product between both vectors. I want to do this as fast ...
66 views

### How bad it is using the same IV twice with AES/GCM?

I understand that initialization vectors should not be used twice when using AES/GCM. I am using a counter as initialization vector. Every time I send out a new packet (I am developing an UDP based ...
79 views

### Is this a secure method of encrypting with authentication?

My goal is to allow two clients to send files securely over an untrusted network without the need for more than one block of information to be sent. Both clients have ECDSA keys of size 256 bits. I'd ...
48 views

### RSA: Range of public modulus

I know the public modulus is the product of two primes. For key with length L, the public modulus N should be such ...
398 views

### 1 Billion Bit Encryption?

So, browsing through YouTube, I stumbled on this video interview of John Draper (Captain Crunch), one of the first "hackers". He talks for about 3 minutes (until 27:48) about his home rolled ...
32 views

### Ciphertext and tag size and IV transmission with AES in GCM mode

I am completely new to using AES in GCM mode of operation, and I have not a very large background in cryptography as well. I have been playing with OpenSSL trying to encrypt and decrypt some messages. ...
724 views

### If RSA is only used to encrypt symmetric keys which are random, what's wrong with textbook RSA?

IND-CPA is used to protect against frequency analysis AFAICT. But if RSA is only used to encrypt symmetric keys (AFAICT) then what's wrong with using only textbook RSA because random keys are very ...
60 views

### Can there be a need for 1024-bit (symmetric) encryption?

I think we are all aware of the CAESAR-competition. Now the aim of this competition is to select a (portfolio of) winner(s) which provide authenticated encryption. I'll now assume that the results ...
43 views

### How does DPA work on AES?

I am really not much of a crypto guy so I don't really get how a differential power analysis on AES works. Can somebody explain it to me how it basically works?
75 views

29 views

### What is the difference between a PRF and a PRF+?

What is the difference between a PRF and a PRF+? I am understanding them to mean the same thing, but I imagine that is because I don't understand their differences. The IKE RFC defines a PRF as: ...
74 views

### computational complexity class of decryption of AES [closed]

I haven't really seen what computational complexity class of decryption of AES is. Can anyone provide reference papers or answers here?
53 views

### How much pre-hashing a password increase security against brute force attack?

I am wondering how much hashing a password used as key for a symmetric key algorithm helps preventing brute force attack on crypted text. Let's assume I want to crypt text A using key B using ...
73 views

### Which is the most secure steganography technique? [closed]

Just like we have AES in crypotography, which is the most secure technique in Steganography? I am looking for a technique in which the standard image characteristic modifications it does go ...
76 views

### What are the advantages of using OFB (Output Feedback Mode)? [closed]

I have a problem with OFB mode, because I have heard that it is stronger than CFB.
24 views

### Could a crypto system that uses non-FIPS crypto but then upgrades complete to FIPS be FIPS certified?

I know most people around here (including myself) are anti-FIPS, but I have a FIPS related question. Could a crypto system that is not FIPS, e.g. one based on primitives like Curve25519, achieve FIPS ...
97 views

### Secure symmetric encryption algorithm for any-size base62 data

I am searching for a secure algorithm to encrypt base62 (or any other base) data for ids in urls. It should feature: No blocksize etc, limiting the length of the message to a factor of n If you ...
52 views

### What is the complexity for attacking 3DES in linear or differential cryptanalysis?

I know that 3DES is NOT vulnerable to DC , LC . But is it because the attacks requires too many input\output pairs ? Or because it's impossible ? (i.e requires more than 2^64 pair )


text:
# Different definitions of Weyl Tensor

I'm trying to prove identity $$\nabla^{\rho}C_{\rho\sigma\mu\nu}=\nabla_{[\mu}R_{\nu]\sigma}+\frac{1}{6}g_{\sigma[\mu}\nabla_{\nu]}R$$ for $4D$ spacetime.

The task seems simple, requiring second Bianchi identity for tensor of curvature, but I seem to be missing out something obvious. Carroll (Spacetime and Geometry pg. 147) defines Weyl tensor in $n$ dimensions as $$C_{\rho\sigma\mu\nu}=R_{\rho\sigma\mu\nu}-\frac{2}{n-2}(g_{\rho[\mu}R_{\nu]\sigma}-g_{\sigma[\mu}R_{\nu]\rho})+\frac{2}{(n-1)(n-2)}g_{\rho[\mu}g_{\nu]\sigma}R.$$

The first term cancels out the part of the second term after I act with covariant derivative. The consequence of Bianchi identity that I use is: $$\nabla^{\rho}R_{\rho\sigma\mu\nu}=\nabla_{[\mu}R_{\nu]\sigma}.$$

I have also found different definition of Weyl tensor(1):

$$C_{\rho\sigma\mu\nu}=R_{\rho\sigma\mu\nu}-\frac{1}{n-2}(g_{\rho[\mu}R_{\nu]\sigma}-g_{\sigma[\mu}R_{\nu]\rho})+\frac{1}{(n-1)(n-2)}g_{\rho[\mu}g_{\nu]\sigma}R$$

and in that case I get the right-hand of the first equation multiplied by $\frac{1}{2}$.

My guess is that I'm missing out something in the definitions/notation or my derivation of second Bianchi identity is wrong.

• Please, post the source for the second definition, the one without the 2s – DanielC Jan 22 '18 at 18:05
• I have edited the post. – Caneholder123 Jan 22 '18 at 18:12

Some texts define $$A_{[\mu\nu]} = A_{\mu\nu} - A_{\nu\mu}\,,$$ whereas others define $$A_{[\mu\nu]} = \frac{1}{2} \left( A_{\mu\nu} - A_{\nu\mu} \right)\,.$$ I personally like the second convention much more!
The way you can check which convention is being used is to note that the Weyl tensor is defined as the tracefree part of the Riemann tensor. In other words, it is required to satisfy $$C^\mu{}_{\rho\mu\sigma} = 0 \, .$$


text:
Velocity Reviews > Ruby > Separator in $PATH # Separator in$PATH

Stefano Mioli
Guest
Posts: n/a

 10-19-2010
Hello everyone,
Unix-like operating systems use a colon to separate each directory in
the PATH, while Windows uses a semicolon.

The question is: is there some class in the Ruby library that knows
Or do I have to resort to something like the following?

if RUBY_PLATFORM =~ /(win|w)32\$/
# ...
end

I'm asking this question because I need to figure out if a given
executable is in the path and, if it does, retrieve its full path.
So I whipped up this one-liner which seems to work as expected (except
on Windows, of course):

ENV["PATH"].split(":").collect {|p| File.join(p, "foo")}.keep_if{|p|
File.exist? p}.first

where "foo" is the name of the executable.
While we're at it, can someone think of a better / more idiomatic way to
do it?

Obviously, simply trying to run the executable is not an option.

--
Stefano

Daniel Berger
Guest
Posts: n/a

 10-19-2010

On Oct 19, 2:02=A0pm, Stefano Mioli <(E-Mail Removed)> wrote:
> Hello everyone,
> =A0 =A0 =A0 =A0 Unix-like operating systems use a colon to separate each =

directory in
> the PATH, while Windows uses a semicolon.
>
> The question is: is there some class in the Ruby library that knows

File:ATH_SEPARATOR

> I'm asking this question because I need to figure out if a given
> executable is in the path and, if it does, retrieve its full path.

require 'ptools'

File.which('ls') # =3D> '/bin/ls'

Works on Windows, too, with or without an extension:

File.which('notepad.exe') # Also works

Regards,

Dan

Stefano Mioli
Guest
Posts: n/a

 10-19-2010
On Tue, Oct 19, 2010 at 10:08 PM, Daniel Berger <(E-Mail Removed)> wrote:
>
> On Oct 19, 2:02=A0pm, Stefano Mioli <(E-Mail Removed)> wrote:

>> The question is: is there some class in the Ruby library that knows

>
> File:ATH_SEPARATOR
>
>> I'm asking this question because I need to figure out if a given
>> executable is in the path and, if it does, retrieve its full path.

>
> require 'ptools'
>
> File.which('ls') # =3D> '/bin/ls'
>
> Works on Windows, too, with or without an extension:
>
> File.which('notepad') =A0 =A0 # Works
> File.which('notepad.exe') # Also works

Many thanks, Dan.
I didn't know about ptools, and somehow I just saw File::SEPARATOR,
but not File:ATH_SEPARATOR.

--=20
Stefano

Robert Klemme
Guest
Posts: n/a

 10-20-2010
On Wed, Oct 20, 2010 at 9:20 AM, GianFranco Bozzetti
<(E-Mail Removed)> wrote:
> string#split accept a regular expression
>
> path_list = ENV['PATH'].split(/[:;]/) # work s on Linus and Windows
>
> HTH gfb

Well, it works. But it isn't helpful.

irb(main):002:0> 'C:\\foo;W::\\bar'.split(/[:;]/)
=> ["C", "\\foo", "W", "", "\\bar"]

Cheers

robert

--
remember.guy do |as, often| as.you_can - without end
http://blog.rubybestpractices.com/


text:
## Precalculus (6th Edition) Blitzer

About $4$ grams
Model: $A=A_{0}e^{kt}$ $t=0$ for the year $2010.$ Unknown: $A$, when $A_{0}=16, t=11430,k=-0.000121t$ $A=A_{0}e^{kt}=16e^{-0.000121\cdot 11430}\approx 4.013$


text:
Contents

group theory

Contents

Definition

Discrete case

Given an action $G\times X\to X$ of a (discrete) group $G$ on a set $X$, any set of the form $G x = \{g x|g\in G\}$ for a fixed $x\in X$ is called an orbit of the action, or the $G$-orbit through the point $x$. The set $X$ is a disjoint union of its orbits.

Category of orbits

The category of orbits of a group $G$ is the full subcategory of the category of sets with an action of $G$.

Since any orbit of $G$ is isomorphic to the orbit $G/H$ for some group $H$, the category of $G$-orbits admits the following alternative description: its objects are subgroups $H$ of $G$ and morphisms $H_1\to H_2$ are elements $[g]\in G/H_2$ such that $H_1\subset g H_2g^{-1}$.

In particular, the group of automorphisms of a $G$-orbit $G/H$ is $N_G(H)/H$, where $N_G(H)$ is the normalizer of $H$ in $G$.

Topological case

If $G$ is a topological group, $X$ a topological space and the action continuous, then one can distinguish closed orbits from those which are not. Even when one starts with $G,X$ Hausdorff, the space of orbits is typically non-Hausdorff. (This problem is one of the motivations of the noncommutative geometry of Connes’ school.)

If the original space is paracompact Hausdorff, then every orbit $G x$ as a topological $G$-space is isomorphic to $G/H$, where $H$ is the stabilizer subgroup of $x$.

References

Textbook accounts:

Last revised on April 18, 2021 at 12:22:18. See the history of this page for a list of all contributions to it.


text:
show · st_group.probabilities all knowls · up · search:

If $a_i:=a_i(g)$ denotes the $i$th coefficient of the characteristic polynomial $\sum a_ix^i$ of a random matrix $g$ in a Sato-Tate group $G$ with Haar measure $\mu$, then $\mathrm{Pr}[a_i=n] := \mu(\{g\in G|a_i(g)=n\})$ can be viewed as the probability that a random $g\in G$ satisfies $a_i(g)=n$. This is a rational number equal to the proportion of connected components of G on which $a_i$ is identically equal to $n$, by Proposition 8.4.3.3 of Serre's Lecture's on $N_X(p)$ [10.1201/b11315 ]. This probability is necessarily zero unless $n$ is one of a finite set of integers.

Note that while $\mathrm{Pr}[a_i=n]=0$ implies that $\{g\in G:a_i(g) = n\}$ has measure zero, this set need not be empty (unless $G$ is finite).

Authors:
Knowl status:
• Review status: reviewed
• Last edited by Kiran S. Kedlaya on 2021-05-11 23:41:54
Referred to by:
History: Differences


text:
## VRNet: Learning the Rectified Virtual Corresponding Points for 3D Point Cloud Registration

#### IEEE Transactions on Circuits and Systems for Video Technology

###### Zhiyuan Zhang1, Jiadai Sun1, Yuchao Dai1, Bin Fan1, Mingyi He1

1School of Electronics and Information, Northwestern Polytechnical University, Xi'an, China

### Abstract

3D point cloud registration is fragile to outliers, which are labeled as the points without corresponding points. To handle this problem, a widely adopted strategy is to estimate the relative pose based only on some accurate correspondences, which is achieved by building correspondences on the identified inliers or by selecting reliable ones. However, these approaches are usually complicated and time-consuming. By contrast, the virtual point-based methods learn the virtual corresponding points (VCPs) for all source points uniformly without distinguishing the outliers and the inliers. Although this strategy is time-efficient, the learned VCPs usually exhibit serious collapse degeneration due to insufficient supervision and the inherent distribution limitation. In this paper, we propose to exploit the best of both worlds and present a novel robust 3D point cloud registration framework. We follow the idea of the virtual point-based methods but learn a new type of virtual points called rectified virtual corresponding points (RCPs), which are defined as the point set with the same shape as the source and with the same pose as the target . Hence, a pair of consistent point clouds, i.e . source and RCPs, is formed by rectifying VCPs to RCPs (VRNet), through which reliable correspondences between source and RCPs can be accurately obtained. Since the relative pose between source and RCPs is the same as the relative pose between source and target , the input point clouds can be registered naturally. Specifically, we first construct the initial VCPs by using an estimated soft matching matrix to perform a weighted average on the target points. Then, we design a correction-walk module to learn an offset to rectify VCPs to RCPs, which effectively breaks the distribution limitation of VCPs. Finally, we develop a hybrid loss function to enforce the shape and geometry structure consistency of the learned RCPs and the source to provide sufficient supervision. Extensive experiments on several benchmark datasets demonstrate that our method achieves advanced registration performance and time-efficiency simultaneously.

### Contribution

• We propose a point cloud registration method named VRNet to guarantee high accuracy and high timeefficiency. We present a new type of virtual points called RCPs, which maintain the same shape as the source and the same pose as the target, to help build reliable correspondences.
• We design a novel correction-walk module in our VRNet to learn an offset to break the distribution limitation of the initial VCPs. Besides, a hybrid loss function is proposed to enhance the rigidity and geometric structure consistency between the learned RCPs and the source.
• Remarkable results on benchmark datasets validate the superiority and effectiveness of our proposed method for robust 3D point cloud registration.

### Motivation

1) The degeneration of the learned corresponding points. Red and blue represent the source and the target respectively. Pink indicates the learned corresponding points. The matching lines connect the source points and the corresponding points. Due to insufficient supervision, the learned corresponding points of DCP and RPMNet degenerate seriously. 2) Illustration of the distribution limitation of VCPs. The red and green represent the source and the target respectively. In this case, only a part of corresponding points can be fitted by the VCPs, which are generated by performing the weighted average on the target. And the corresponding points of the source points marked by the box can never be fitted since the distribution of the VCPs is limited in the convex set of the target. 3) Illustration of our VRNet. ① source and ④ target have different poses and different shapes (broken tail and wing in source and target respectively). The existing methods will learn degenerated VCPs indicated by the pink in ②. Conversely, our VRNet devotes to learning the RCPs indicated by ③, which maintain the same shape as the source and the same pose as the target, by unfolding VCPs and rectifying the partiality of the wing. Hence, the reliable correspondences of these consistent point clouds, i.e. source and RCPs, can be obtained easily since the influence of outliers has been eliminated. Further, the relative pose between source and RCPs can be solved accurately, which is same as the relative pose between source and target.

### Network Architecture

The network architecture of our proposed VRNet. Given the source and target, DGCNN and Transformer are applied to extract point features. Then, a soft matching matrix is achieved based on the constructed similarity matrix. Virtual corresponding points and corresponding point features are obtained by using the matching matrix to perform the weighted average on the target point cloud and the target point features respectively. To break the distribution limitation, a correction-walk module is proposed to learn the offset to amend the VCPs to the desired RCPs. Finally, the rigid transformation is solved by the Procrustes algorithm. The network is supervised by the proposed hybrid loss function, which enforces the rigidity and geometry structure consistency between the learned RCPs and the source point cloud.

### Method Analyze

Visualization of the source point (purple), the target point cloud (green), the learned VCPs (gray), RCPs (blue), and the learned offset (red line). All points clouds are calibrated to the same pose for clear comparison. Obviously, the VCPs approximate the source as much as possible but it is limited in the target distribution. Then, the correction-walk module amends the VCPs to the RCPs, which present a more consistent distribution with the source than the VCPs and the origianl target.

### Citation

@ARTICLE{zhang_vrnet_tcsvt_2022,
title={VRNet: Learning the Rectified Virtual Corresponding Points for 3D Point Cloud Registration},
author={Zhang, Zhiyuan and Sun, Jiadai and Dai, Yuchao and Fan, Bin and He, Mingyi},
journal={IEEE Transactions on Circuits and Systems for Video Technology},
year={2022},
volume={32},
number={8},
pages={4997-5010}}


text:
# Circle A has a center at (2 ,2 ) and a radius of 5 . Circle B has a center at (12 ,8 ) and a radius of 1 . Do the circles overlap? If not what is the smallest distance between them?

Feb 3, 2016

The circles do not overlap.
There is a minimum distance of $2 \sqrt{34} - 6 \approx 5.66$ units between them.

#### Explanation:

The length of a line segment joining the centers of the two circles is
$\textcolor{w h i t e}{\text{XXX}} \sqrt{{\left(12 - 2\right)}^{2} + {\left(8 - 2\right)}^{2}} = \sqrt{{10}^{2} + {6}^{2}} = 2 \sqrt{34}$

The distance from the center of Circle A to the edge of Circle A along the line segment joining the two circles is $5$ (the radius of A).

The distance from the edge of A to the center of Circle B along the line segment joining the centers is $2 \sqrt{34} - 5$

The distance from the center of Circle B to the edge of Circle B along the line segment joining the centers is $1$ (the radius of B).

The distance between the edges of the two circles is
$\textcolor{w h i t e}{\text{XXX}} \left(2 \sqrt{34} - 5\right) - 1$

$\textcolor{w h i t e}{\text{XXX}} = 2 \sqrt{34} - 6$

$\textcolor{w h i t e}{\text{XXX}} \approx 5.66$ (in whatever nits are being used)


text:
# Tag Info

0

The CWT is not, per se, superior to STFT. Due to its variations in scale, it can be better, for instance, when: you address natural signals where transients are shorter than more stationary parts, you do not know the appropriate scale of observation. which is neither the case from your signal: precise frequency on the same support. On the one hand, you ...

1

[Beginning of the story] Remember the discrete wavelet curse: in 1D, with 2-scale or dyadic wavelets, you cannot have finite support, realness, orthogonality and linear phase (symmetry/antisymmetry) at the same time, except for the Haar wavelet, which lacks of regularity and overlap. You have to lift one constraint to have the other fulfilled. For instance : ...

0

Depends on what kind of “sense” you want. A 1 cycle sine wavelet might give you good time resolution for locating a mostly positive to negative zero-crossing waveform slice, but almost no frequency resolution, as the nearest orthogonal sinewave is a whole octave higher. Add more cycles and you get more frequency resolution, but less time resolution. A ...

4

With all due caution, no in both cases (title and body question). I'll start with the second one. Continuous wavelets use all dilations of the mother wavelet, which are not accessed with the STFT The STFT is complex in general, and the windowed sine is not. For the first one: I never tried it, and do not remember having seen it in use, and one should ...

2

No, since the STFT gives you complex values by not only correlating to sines of different periods, but also cosines.

1

Not really. Unless you fully understand the math behind the DFT, you are likely to run into problems like circular vs linear convolution, time domain aliasing, excessive time domain ringing, etc. For "light weight" frequency selectivity application, time domain filter is typically a lot easier.

0

They are equivalent, as long as $j_1$ (first formula) and $-j_2$ (second formula) span the same integer set. They are, if $j_1\in\mathbb{Z}$ and $j_2\in\mathbb{Z}$, or if $j_1\in\mathbb{N}^+$ (positive integers) and $j_2\in\mathbb{N}^-$ (negative integers). They are, under the change of variable: $t\to 2^{2j}x$. Let us remind that if $\psi(u)$ is of unit ...

0

They’re equivalent, but the distinction seems to usually come from which definition of multiresolution analysis one uses - ascending or descending chains of detail/approximation spaces.

0

I don't think there is any single best number for normalisation because it depends on the structure of the values in your lattice. In the simplest case where all values are equal, the predict operation zeros the black points and the update does not change the white points. Because each predict-update pair halves the number of nonzero points, multiplying ...

Top 50 recent answers are included


text:
Perfect before 2016 ends

Find the number of perfect squares less than or equal to 2016 that can be expressed as $$a^4 + 5bc(a^2 + b) + 2$$ for some nonnegative integers $$a$$, $$b$$, and $$c$$.

This problem is part of the set "Symphony"

×


text:
# Can anyone help me proving this with Mathematical induction?

Prove that the product of $n$ consecutive numbers is divisible by $n!$

E.g. for $n=5$, we have that $5! | (10\cdot11\cdot12\cdot13\cdot14)$

#### Solutions Collecting From Web of "Can anyone help me proving this with Mathematical induction?"

Hint:

It is obvious that $n!\mid n!$ for any $n$.

It is also obvious that $1\mid k$ for any $k$.

Notice also that $(k+1)(k+2)\cdots(k+n)=k(k+1)\cdots(k+n-1) + n\cdot \underbrace{(k+1)(k+2)\cdots(k+n-1)}_{(n-1)~\text{consecutive numbers}}$

To prove: $n!$ divides the product of n consecutive integers. Proof: Consider n consecutive integers: $k$, $k+1$, $k+2$…, $k+n-1$. Since $1$ divides $k$, and $2$ divides either $k$ or $k+1$, and $3$ divides either $k$ or $k+1$ or $k+2$…, and $n$ divides either $k$ or $k+1$ or $k+2$… or $k+n-1$, therefore $1$ x $2$ x $3$… x $n$, = $n!$, divides k(k+1)(k+2)…(k+n-1).


text:
Differentiate without using natural logs

1. Mar 10, 2013

Feodalherren

1. The problem statement, all variables and given/known data

$2^{Sin(PiX)}$

2. Relevant equations

3. The attempt at a solution

= $e^{(Sin(\PiX})ln2$

y'= $e^{(Sin(\PiX})ln2$ d/dx [Sin $\Pi$X] ln 2

and I'm stuck.... The product rule will automatically lead to to differentiating ln 2.

2. Mar 10, 2013

LCKurtz

$\ln 2$ is just a constant. Just leave it there and differentiate the sine. You can simplify that exponential back to its other form in the answer.

3. Mar 11, 2013

Feodalherren

I'm an idiot.... Thanks that solved my problem :).


text:
# Integral Limits Placement in LaTeX

I'm using a converter to generate LaTeX codes. The converter gives me the results below for integral and sum. limits are above and below. I want sum and other symbol limits as given in (1) but integral limits as given (2). I don't want to change the code for integrals manually every time. What command should I use?

\documentclass[11pt,a4paper]{exam}
\usepackage[utf8x]{inputenc}
\usepackage{ucs}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{graphicx}
\usepackage[left=2.00cm, right=2.00cm, top=2.00cm, bottom=2.00cm]{geometry}
\begin{document}
$$\underset{1}{\overset{2}{\mathop \int }}\,{{x}^{2}}dx,\underset{i=1}{\overset{n}{\mathop \sum }}\,i,~\underset{i=1}{\overset{\infty }{\mathop \bigcup }}\,{{B}_{i}}$$

$$\int_{1}^{2} x^2~dx$$
\end{document}

• Why are you using underset? – Sigur Nov 20 '13 at 16:51
• The converter does a very bad work. – egreg Nov 20 '13 at 16:51
• egreg. you are right. if it can't be changed by a command, can you suggest a different converter? Sigur. converter gives that. – mert Nov 20 '13 at 16:54
• What is this converter? – Sigur Nov 20 '13 at 17:02
• mathtype toggletex – mert Nov 20 '13 at 17:29

The converter shouldn't use \overset and \underset: it's just wrong!

Correct code for the examples is

\documentclass[11pt,a4paper]{exam}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage[left=2.00cm, right=2.00cm, top=2.00cm, bottom=2.00cm]{geometry}

\begin{document}

$$\int_{1}^{2}x^{2}\,dx,\quad \sum_{i=1}^{n}i,\quad \bigcup_{i=1}^{\infty}B_{i}$$

\end{document}

The converter is doing bad work: it adds really useless constructions (which are wrong in some cases).

• An alternate usage for integral is $\int\limits_{1}^{2}x^{2}\,dx$ – ferahfeza Nov 20 '13 at 17:27
• @ferahfeza I don't think that \limits is what the OP wants. – egreg Nov 20 '13 at 17:41
• you might want to mention that \overset and \underset don't even put the limits in the right position; compare with \int\limits. – barbara beeton Nov 20 '13 at 19:11


text:
### Sample Papers

Download the PDF Sample Papers Free for off line practice and view the Solutions online.

### Book Store

Currently only available for.
CBSE

### Test Series

Pre-Board Question Papers are now available online for students to practice and excel the exams based on the latest syllabus and marking scheme given by respective boards.

# CBSE Physics 2011 Exam Questions

11.

What happens to the width of depletion layer of a p-n junction when it is (i) forward biased, (ii) reverse biased?

(i) When forward biased, the width of depletion layer decreases.

(ii) When reverse biased, the width of depletion layer increases.

761 Views

12.

Using the curve for the binding energy per nucleon as a function of mass number A, state clearly how the release in energy in the processes of nuclear fission and nuclear fusion can be explained.

The binding energy per nucleon increases when a heavy nucleus breaks into two lighter nuclei. That is, energy would be released during the process of nuclear fusion.

When light nuclei join to form a heavy nucleus, the binding energy per nucleon of fused heavier nucleus is more than the binding energy per nucleon of lighter nuclei. Again, there is release of energy in this process
1532 Views

13.

What is sky wave communication? Why is this mode of propagation restricted to the frequencies only up to few MHz?

Sky wave propagation is a mode of propagation in which communication of radio waves in frequency range 30 MHz–40 MHz takes place due to reflection from the ionosphere.

For frequencies higher than few MHz, the sky waves penetrate the ionosphere and are not reflected back.

1775 Views

14.

Draw a labelled diagram of a full wave rectifier circuit. State its working principle. Show the input-output waveforms.

The circuit of Full wave rectifier is as shown below:

Working principle: The underlying working principle of full wave rectifier is that the p-n junction conducts when it is forward biased and does not conduct when it is reverse biased.

The input and output waveform is shown below:

1663 Views

15.

In the meter bridge experiment, balance point was observed at J with AJ = l.

(i) The values of R and X were doubled and then interchanged. What would be the new position of balance point?

(ii) If the galvanometer and battery are interchanged at the balance position, how will the balance point get affected?

i) Balance point is obtained by,

When both R and X are doubled and then interchanged, new balance length becomes l’ which is given by,

Now, from the above two equations, we have

ii) The balance point will not get affected if galvanometer and balance point are interchanged at this position.

1272 Views

16.

Write any two characteristic properties of nuclear force.

(i) Nuclear forces are short range attractive forces.

(ii) Nuclear forces are charge – independent.

734 Views

17.

Two heating elements of resistance R1 and R2 when operated at a constant supply of voltage, V, consume powers P1 and P2 respectively. Deduce the expressions for the power of their combination when they are, in turn, connected in (i) series and (ii) parallel across the same voltage supply.

i) When they are in series combination,

Net resistance, R = R1 + R2                                                 … (1)

Heating elements are operated at same voltage V, we have

So, from equation (1), we have

ii) When the resistors are connected in parallel combination,

Net resistance is given by,

2201 Views

18.

Define the term ‘stopping potential’ in relation to photoelectric effect.

Stopping potential is the minimum retarding or negative potential of anode of a photoelectric tube for which photoelectric current stops or becomes zero.

1384 Views

19.

A parallel plate capacitor is being charged by a time varying current. Explain briefly how Ampere’s circuital law is generalized to incorporate the effect due to the displacement current.

When AC current is passed through capacitor, current moves from one plate to another. According to Ampere’s circuital law, a magnetic field has to exist between the plates of the capacitor for the current transfer to happen. So, Maxwell modified Ampere’s circuital law with the help of continuity equation.

The modified Ampere’s law by Maxwell is given by,

where, iD, is called the Displacement current.

2219 Views

20.

Net capacitance of three identical capacitors in series is 1 F. What will be their net capacitance if connected in parallel?

Find the ratio of energy stored in the two configurations if they are both connected to the same source.

Let,C be the capacitance of each capacitor,

In a series combination,

When these capacitors are connected in parallel, net capacitance, CP = 3 C = 33 = 9F

Ration of energy stored is given by,

2768 Views


text:
×

# #25

Let ABCD be a rectangle and let E and F be points on CD and BC respectively such that area of $$\triangle ABC = 16$$ , area of $$\triangle CEF = 9$$ and area of $$\triangle ABE = 25$$, What is the area of $$\triangle AEF$$?

Note by Vilakshan Gupta
2 months ago

Sort by:

30

- 1 month, 1 week ago

I've done this one earlier. The answer is 30..

- 2 months ago


text:
• Create Account

### #Actualfrob

Posted 22 November 2012 - 03:00 AM

I just want to know the % amount spent on advertisement and if that is typically the 'primary' expense, it doesnt have to be actual amounts either.

Software development costs are usually less than 1/3 of the total costs.

As you pointed out, advertising is probably the biggest single expense. In one game we had a $2M development fund, and I learned they spent$3.5M on advertising.

I've seen similar ratios on expensive games, with development costs in the tens of millions and non-development costs about 2x more than that. A global advertising blitz in game magazines, web banners, in-store displays, promotions, and so on gets expensive very quickly. Just getting in-store product placement can cost millions by itself.

In the grand scheme of business, writing software is the easy part. Making it profitable is difficult.

### #1frob

Posted 22 November 2012 - 02:57 AM

I just want to know the % amount spent on advertisement and if that is typically the 'primary' expense, it doesnt have to be actual amounts either.

Software development costs are usually less than 1/3 of the total costs.

As you pointed out, advertising is probably the biggest single expense. In one game we had a $2M development fund, and I learned they spent$3.5M on advertising.

I've seen similar ratios on expensive games, with development costs in the tens of millions and non-development costs about 2x more than that.

In the grand scheme of business, writing software is the easy part. Making it profitable is difficult.

PARTNERS


text:
# Complexity and subcomplexities, Part 3

## Logarithm   $\mathit {lt}$   and subcomplexity   $\mathit{C0}$

Let, as always,   $\log$   be the natural logarithmic function. For the given complexity theme we will need the base   $T:=3^\frac 13$   logarithmic function   $\mathit {lt}$,   i.e.

$$\forall_{x\in(0;\infty)}\quad \mathit{lt}(x)\ :=\ \frac {3\cdot \log(x)}{\log(3)}$$

For instance,   $\mathit {lt}(3^t)\ =\ 3\cdot t$. Now we can define a (pretty ambitious) candidate   $\mathit{C0}$   for a subcomplexity in terms of   $\mathit{lt}\,$:

• $\mathit{C0}(1)\ :=\ 1$
• $\forall_{n=2\ 3\ \ldots}\quad \mathit{C0}(n)\ :=\ \lceil\mathit{lt}(n)\rceil$.

The inequalities:

• $T^3 = 3 < 2^3 < 9 = T^6$
• $T^3 = 3$
• $T^9 = 27 < 4^3 < 81 = T^12$
• $T^{12} = 81 < 5^3 < 243 = T^{15}$
• $T^{12} = 81 < 6^3 < 243 = T^{15}$
• $T^{15} = 243 < 7^3 < 729 = T^{18}$
• $T^{15} = 243 < 8^3 < 729 = T^{18}$

(and equality   $\mathit{C0}(1)=1$)   imply

• $\mathit{C0}(1)=1$
• $\mathit{C0}(2)=2$
• $\mathit{C0}(3)=3$
• $\mathit{C0}(4)=4$
• $\mathit{C0}(5)=5$
• $\mathit{C0}(6)=5$
• $\mathit{C0}(7)=6$
• $\mathit{C0}(8)=6$

We see that   $\mathit{C0}$   has the first subcomplexity property   ($\mathit{C0}(1)\le 1$)   by definition. Next,

• $\mathit{C0}(1\ 1\ +)\ =\ 2 =\ \mathit{C0}(1)\ \mathit{C0}(1)\ +$
• $\mathit{C0}(2\ 1\ +)\ = \lceil\mathit{lt}(3)\rceil\ =\ 3\ =\ \mathit{C0}(2)\ \mathit{C0}(1)\ +$
• $\mathit{C0}(2\ 2\ +)\ = \lceil\mathit{lt}(4)\rceil\ =\ 4\ =\ \mathit{C0}(2)\ \mathit{C0}(2)\ +$
• Let   $a\ge 3$   and   $b\in\{1\ 2\}$.   Then

$$\mathit{C0}(a\ b\ +)\ = \lceil\mathit{lt}(a\ b\ +)\rceil\ \ =\ \ \left\lceil\mathit{lt}(a)\ \ \mathit{lt}(1\ \frac ba\ +)\ \ +\right\rceil\ \ \le\ \ \mathit{rn}(a)\ \ \left\lceil\frac b{a\cdot\log(T)}\right\rceil\ +$$
But    $a\cdot\log(T)\ \ge\ \log(3)\ > 1$    hence

$$\mathit{C0}(a\ b\ +)\ \le\ \mathit{C0}(a)\ b\ +\ \ =\ \ \mathit{C0}(a)\ \mathit{C0}(b)\ +$$

• Let   $\min(a\ b)\ge 3$.   Then    $a\ b\ \bullet\ >\ a\ b\ +$    hence    $\mathit{lt}(a\ b\ +)\ \le\ \mathit{lt}(a)\ \mathit{lt}(b)\ +$.

Thus we have shown the second subcomplexity property:
$$\forall_{a\ b\in\mathbb N}\quad \mathit{C0}(a\ b\ +)\ \le\ \mathit{C0}(a)\ \mathit{C0}(b)\ +$$

The third property is easier. Let   $a\ b\in\mathbb N$.   Then:

• if   $\min(a\ b)=1$   then $\mathit{C0}(a\ b\ \bullet)\ <\ \mathit{C0}(a)\ \mathit{C0}(b)\ +$;
• $\mathit{C0}(2\ 2\ \bullet)\ =\ 4\ =\ \mathit{C0}(2)\ \mathit{C0}(2)\ +$;
• if   $a\ge 3$   then

$$\mathit{C0}(a\ 2\ \bullet)\ =\ \lceil\mathit{lt}(a\ 2\ \bullet)\rceil\ =\ \lceil\mathit{lt}(a)\ \mathit{lt}(2)\ +\ \le\ \mathit{C0}(a)\ \lceil\mathit{lt}(2)\rceil\ +\ =\ \mathit{C0}(a)\ 2\ +$$
i.e.
$$\mathit{C0}(a\ 2\ \bullet)\ \le\ \mathit{C0}(a)\ \mathit{C0}(2)\ +$$

• if   $\min(a\ b)\ge 3$   then
$$\mathit{C0}(a\ b\ \bullet)\ =\ \lceil\mathit{lt}(a\ b\ \bullet)\rceil\ =\ \lceil\mathit{lt}(a)\ \mathit{lt}(b)\ +\ \rceil\ \le\ \lceil\mathit{lt}(a)\rceil\ \lceil\mathit{lt}(b)\rceil\ +\ =\ \mathit{C0}(a)\ \mathit{C0}(b)\ +$$
i.e.
$$\mathit{C0}(a\ b\ \bullet)\ \ \le\ \ \mathit{C0}(a)\ \mathit{C0}(b)\ +$$

We have shown that function   $\mathit{C0}$   is a subcomplexity.

## Complexity computations with   $\mathit{C0}$

By definition of   $\mathit{C0},$:

• $\mathit{C0}(1) := 1$
• $\mathit{C0}(2) := 2$
• $\mathit{C0}(3) := \lceil\mathit{lt}(3)\rceil = 3$
• $\mathit{C0}(4) := \lceil\mathit{lt}(4)\rceil = 4$
• $\mathit{C0}(5) := \lceil\mathit{lt}(5)\rceil = 5$
• We had all the above equalities but the last one. Since:
$$T^{12} = 81 < 125 = 5^3 < 243 = T^{15}$$ so that $$12\ \ <\ \ 3\ \mathit{lt}(5)\ \bullet\ \ <\ \ 15$$ i.e. $$4\ \ <\ \ \mathit{lt}(5)\ \ < 5$$ it follows that indeed   $\lceil\mathit{C0}(5)\rceil\ =\ 5$. We already know that: $$\forall_{k\in\mathbb N}\quad \mathit{rn}(k)\ \le\ k$$ Thus $$\forall_{k=1\ldots 5}\quad k\ =\ \mathit{C0}(k)\ \le\ \mathit{rn}(k)\ =\ k$$ Thus, applying nothing but subcomplexity   $\mathit{C0}$   we have obtained an independent demonstration of the proposition: $$\forall_{k=1\ldots 5}\quad \mathit{C0}(k)\ =\ k$$ (earlier the same was shown by subcomplexity   $m_5$). Actually, $$T^{12} = 81 < 216 = 6^3 < 243 = T^{15}$$ $$T^{15} = 243 < 343 = 7^3 < 729 = T^{18}$$ $$T^{15} = 243 < 512 = 8^3 < 729 = T^{18}$$ i.e. $$4 < \mathit{lt}(6) < 5$$ $$5 < \mathit{lt}(7) < 6$$ $$5 < \mathit{lt}(8) < 6$$ or $$\mathit{C0}(6) = 5$$ $$\mathit{C0}(7) = 6$$ $$\mathit{C0}(8) = 6$$ while we already know, due to the representations: $$6 = 1\ 1\ 1 + 1\ 1\ +\ \bullet$$ etc. that $$\mathit{rt}(6)\le 5\qquad\mathit{rt}(7)\le 6\qquad \mathit{rt}(8)\le 6$$ Thus $$\mathit{rn}(6) = 5$$ $$\mathit{rn}(7) = 6$$ $$\mathit{rn}(8) = 6$$. We also know that    $\mathit{rn}(3^n)\ \le\ 3\ n\ \bullet$,    and on the other hand    $\mathit{C0}(3^n)\ =\ 3\ n\ \bullet$.    It follows that THEOREM 0   (in infix notation!–not Łukasiewicz)

• $\mathit{rn}(1)=1\qquad\qquad\mathit{rn}(2)=2$
• $\forall_{n\in\mathbb N}\quad \mathit{rn}(n)\ \ge\ \mathit{lt}(n)$
• $\forall_{n\in\mathbb N}\quad \mathit{rn}(3^n)\ =\ 3\cdot n$
• $\forall_{K\ n\in\mathbb N}\quad \left(\ K > 3^n\quad\Rightarrow\quad \mathit{rn}\left(K\right) \ge 3\cdot n + 1\ \right)$
• $\forall_{n\in\mathbb N}\quad\mathit{rn}(3^n+1)\ =\ 3\cdot n + 1$


text:
# Proportional Relationships

## Objective

Make connections between the four representations of proportional relationships (Part 1).

## Common Core Standards

### Core Standards

?

• 7.RP.A.2 — Recognize and represent proportional relationships between quantities.

• 7.RP.A.2.A — Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

• 7.RP.A.2.B — Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

• 7.RP.A.2.C — Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

• 7.RP.A.2.D — Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

?

• 6.RP.A.3

## Criteria for Success

?

1. Identify the constant of proportionality in graphs, equations, and tables.
2. Represent and analyze proportional relationships in graphs, equations, and tables.

## Tips for Teachers

?

Lessons 10 and 11 pull together all the representations of proportional relationships – written description, table, graph, and equation – that students have been studying since the beginning of the unit. As needed, review any one representation that students may be stuck on, but continue to engage them in looking at multiple representations at a time in order to strengthen the connections between them.

#### Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Problems 1 and 3 (can be done independently). Find more guidance on adapting our math curriculum for remote learning here.

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

## Anchor Problems

?

### Problem 1

A scientist plants a seed in a laboratory and tracks the growth of the plant. The height of the plant in centimeters is proportional to the number of days since it was planted.

1. Explain what point B represents in context of the situation.
2. At what rate is the plant growing? Indicate this as a point on the graph.
3. Write an equation that represents the relationship between days and height.
4. If the plant continues to grow at this rate, how tall will it be after 12 days?
5. If the plant continues to grow at this rate, when will it be 6 cm tall?

### Problem 2

Match each table to its equation.

1.   ${y = {1 \over 2}x}$
2.   ${y = {2 \over 3}x}$
3.   ${y = 2x}$
4.   ${y=3x}$

### Problem 3

The cost you pay for limes is proportional to the number of limes you buy. Four different stores sell limes for different amounts, as shown in the graphs, table, and equation below. Which store should you go to if you want to pay the least amount for limes? Explain your answer.

## Problem Set

?

The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

Let $y$ represent the number of centimeters and $x$ represent the number of inches. Represent the relationship in the coordinate plane below, and then write an equation that approximates the relationship between inches and centimeters.