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# zbMATH — the first resource for mathematics

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An algorithm for solving linear programming problems in $O\left({n}^{3}L\right)$ operations. (English) Zbl 0691.90053
Progress in mathematical programming. Interior-point and related methods, Proc. Conf., Pacific Grove/Calif. 1987, 1-28 (1989).

[For the entire collection see Zbl 0669.00026.]

This paper describes a short-step penalty function algorithm that solves linear programming problems in no more than $O\left({n}^{0·5}L\right)$ iterations. The total number of arithmetic operations is bounded by $O\left({n}^{3}L\right)$, carried on with the same precision as that in Karmarkar’s algorithm. Each iteration updates a penalty multiplier and solves a Newton-Raphson iteration on the traditional logarithmic barrier function using approximated Hessian matrices. The resulting sequence follows the path of optimal solutions for the penalized functions as in a predictor-corrector homotopy algorithm.

Reviewer: J.Abrham

##### MSC:
 90C05 Linear programming 49M15 Newton-type methods in calculus of variations 68Q25 Analysis of algorithms and problem complexity 65K05 Mathematical programming (numerical methods) 49M30 Other numerical methods in calculus of variations


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Colloquium

 Speaker: Professor Chin-Cheng Lin (National Central University) Title: Local Hardy-Littlewood maximal operator Time: 2010-02-25 (Thu.)  15:00 - 16:00 Place: Seminar Room 722, Institute of Mathematics (NTU Campus) Abstract: We define and investigate a local Hardy-Littlewood maximal operator in Euclidean spaces. It is proved that this operator satisfies weighted $L^p$, $p>1$, and weighted weak type $(1,1)$ estimates with weight function $w\in A^p_{\text{loc}}$, the class of local $A_p$ weights which is larger than the Muckenhoupt $A_p$ class. Also, the condition $w\in A^p_{\text{loc}}$ turns out to be necessary for the weighted weak type $(p,p)$, $p\ge 1$, inequality to hold. || Close window ||

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# Volcano Watch — Alaskan volcano sends ashy plumes thousands of feet into the air

Release Date:

A significant volcanic eruption is in progress right now in Alaska, though it hasn't received much media attention. Augustine Volcano, named by Captain Cook because he "discovered" it on St. Augustine's Day (May 26) in 1778, emitted an ashy plume throughout much of late January and early February, and is showing no signs of going back to sleep.

Image taken during 1/16/06 gas overflight after the explosive events of 1/13/06 and 1/14/06. Image taken from the southwest looking at the steam plume hugging the slopes as it travels to the south. Debris flow deposits visible on the southern slope. Photograph by J. Shipman, AVO/UAF-GI. Alaska Volcano Observatory/University of Alaska Fairbanks, Geophysical Institute.

(Public domain.)

Augustine makes up a small (only 5 miles long by 7 miles wide), uninhabited island in the southern part of Cook Inlet, about 125 miles southwest of Anchorage. The volcano has experienced 6 significant eruptions since the early 1800s, the last time in 1986. Most eruptions have started with an explosive phase that lasts up to several weeks, followed by an extrusive phase in which sticky lava oozes from the summit and forms a dome.

Because of its location near major air traffic routes across the northern Pacific, ash from Augustine can be extremely hazardous to airplanes. When ash is sucked into a jet engine, it can melt and cause the engine to fail. An airplane-ash encounter during the eruption of Redoubt Volcano, Alaska, in 1989, caused a 747 aircraft carrying 231 passengers and 14 crew members to lose power to all four engines. The plane dropped over 2 miles in altitude to a mere 13,000 feet above the ground (only 2,000 feet above the mountains) before the engines were restarted and the plane landed safely in Anchorage. The damage to the aircraft amounted to more than \$80 million. Clearly, it is important to detect such ash clouds before they can pose serious threats to aircraft, especially in the heavily traversed north Pacific.

In addition, Augustine has a tendency to collapse in major landslides into the ocean and create small, but potentially hazardous, tsunami waves. In the last 2,200 years, Augustine has collapsed at least 13 times. The most recent collapse was in 1883, when a 20-foot-high tsunami swept the shores of Cook Inlet. Fortunately, few people lived along the shore of the Inlet at that time, and no one was injured by the tsunami. Today, there are many homes and resorts on the water's edge that would be affected by a similar event.

The hazards posed by tsunamis and airborne ash make monitoring Augustine extremely important. Consequently, the Alaska Volcano Observatory (AVO) maintains a network of seismic and deformation equipment on the island.

In mid-summer 2005, AVO detected increased earthquake activity, a sign that Augustine was awakening from over two decades of slumber. At about the same time, GPS instruments on the volcano showed signs of inflation as magma began to accumulate beneath the surface. By December 2005, small steam explosions occurred as the rising magma encountered groundwater within the volcano. Finally, on January 11, 2006, two large explosions signaled the arrival of magma at the surface.

Additional explosions took place on January 13, 14, 17, 27, and 28, some sending ash as high as 50,000 feet above sea level. These eruptions caused some airplanes to divert from their routes, while other flights were canceled entirely. Then, late on January 28, the volcano entered a period of nearly continuous ash emission, with an ashy plume rising from the volcano's summit to 15,000 feet for almost two weeks straight.

If the volcano follows the pattern set by its past eruptions, the explosive phase will soon end, and lava will appear at the surface. The growth of the lava dome may be relatively calm and last for months. Lava domes are notorious, however, for exploding without warning; therefore it is important to keep a watchful eye on Augustine's current eruption.

The Hawaiian Volcano Observatory is contributing to the Augustine eruption response by sending volcanologists to assist the AVO staff. The exchange of scientists between volcano observatories is a common practice within the U.S. Geological Survey Volcano Hazards Program. It ensures that volcanologists at all of the observatories gain experience in both how volcanoes work and how to manage volcanic crises. This experience can be applied to future eruptions around the world, including any new activity that might occur right here in Hawaii.

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### Volcano Activity Update

During the past week, Kīlauea Volcano has remained at an elevated level of activity at the summit. The number of earthquakes located beneath the upper east rift zone of Kīlauea, between Lua Manu and Pauahi Craters, remains at moderate levels. Inflation of the summit caldera continues at the accelerated rate started on January 12.

Eruptive activity at Puu Oo continues. On clear nights, glow is visible from several vents within the crater and on the southwest side of the cone. Lava continues to flow through the PKK lava tube from its source on the flank of Puu Oo to the ocean, with scattered surface flows breaking out of the tube. In the past week, flows were active intermittently above the pali at the 2,300-ft elevation, on the slope of the pali, and on the coastal plain about 2 km inland of the ocean at Kamoamoa. The PKK lava tube, however, has had few breakouts in recent days, and very little surface lava has been visible at night on the pali.

As of February 9, lava is entering the ocean at East Laeapuki, in Hawaii Volcanoes National Park. The active lava bench continues to regrow following the major collapse of November 28. Access to the ocean entry and the surrounding area remains closed, due to significant hazards. If you visit the eruption site, check with the rangers for current updates, and remember to carry lots of water when venturing out onto the flow field.

There were two earthquakes beneath Hawaii Island reported felt within the past week, both in the same area about 5 km (3 miles) southeast of Kīlauea summit at a depth of 3 km (2 miles). A magnitude-2.1 earthquake occurred at 3:05 p.m. on Saturday, February 4, and a magnitude-3.1 earthquake occurred at 11:28 a.m. on Wednesday, February 8.

Mauna Loa is not erupting. During the past week, earthquake activity remained low beneath the volcano's summit. Inflation continues, but at a rate that has slowed since early October 2005.


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## Linear Algebra Problem

Let W be a subspace of finite dimensional vector space V. Explain/Prove that W is finite dimensional and dimension of W is less than or equal to dimension of V.

Thanks.


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# cosine similarity vs cosine distance

What does it mean for a word or phrase to be a "game term"? Data Structures 101: What Is a Binary Search Tree? We acquired 354 distinct application pages from a star schema page dimension representing application pages. Not the cosine distance! Cosine similarity is a metric, helpful in determining, how similar the data objects are irrespective of their size. Cosine similarity: $\langle x , y\rangle$ Euclidean distance (squared): $2(1 - \langle x , y\rangle)$ As you can see, minimizing (square) euclidean distance is equivalent to maximizing cosine similarity if the vectors are normalized. Cosine Similarity. The vector is filled by the term frequency vectors of word or sequence of X characters in text documents. We can measure the similarity between two sentences in Python using Cosine Similarity. Coding using R (Euclidean distance is also covered) Dataset and R code in … Cosine Similarity. Applications of Cosine similarity 5. site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. Take a look, https://www.linkedin.com/in/anjani-kumar-9b969a39/, The $3 trillion data quality opportunity and our investment in Validio, If You Want to Be Creative, Don’t Be Data Driven. 9 mgavish referenced this issue in CoronaWhy/team-literature-review Oct 19, 2020. document search new API … 6ff8e68 - Automated download of embeddings - Moved mongo configuration into setup.cfg - Code refactoring and cleanup. I understand cosine similarity is a 2D measurement, whereas, with Euclidean, you can add up all the dimensions. Ask Question Asked 5 years, 2 months ago. We can therefore compute the score for each pair of nodes once. END OF MULTIPLOT JUSTIFICATION CENTER MOVE 50 98 TEXT Distance/Similarity Measures (IRIS.DAT) If and are vectors as defined above, their cosine similarity is: The relationship between cosine similarity and the angular distance which we discussed above is fixed, and it’s possible to convert from one to the other with a formula: 5. The cosine of … **** Update as question changed *** When to Use Cosine? calculation of cosine of the angle between A and B. Linked In : https://www.linkedin.com/in/anjani-kumar-9b969a39/, If you like my posts here on Medium and would wish for me to continue doing this work, consider supporting me on patreon, In each issue we share the best stories from the Data-Driven Investor's expert community. Asking for help, clarification, or responding to other answers. \$ If you try this with fixed precision numbers, the left side loses precision but the right side does not. Filter Cascade: Additions and Multiplications per input sample, How Functional Programming achieves "No runtime exceptions", Book, possibly titled: "Of Tea Cups and Wizards, Dragons"....can’t remember, Tikz getting jagged line when plotting polar function. The cosine of 0° is 1, and it is less than 1 for any angle in the interval (0, π] radians. Cosine similarity distance should be called cosine distance. This is analogous to the cosine, which is unity (maximum value) when the segments subtend a zero angle and zero (uncorrelated) when the segments are perpendicular. It looks like scipy.spatial.distance.cdist cosine similariy distance: is different from Why does Steven Pinker say that “can’t” + “any” is just as much of a double-negative as “can’t” + “no” is in “I can’t get no/any satisfaction”? Does anybody know reason for different definitions? The name derives from the term "direction cosine": in this case, unit vectors are maximally "similar" if they're parallel and maximally "dissimilar" if they're orthogonal (perpendicular). Cosine similarity vs Euclidean distance. Why does the U.S. have much higher litigation cost than other countries? The intuition behind this is that if 2 vectors are perfectly the same then similarity is 1 (angle=0) and thus, distance is 0 (1-1=0). Similarly you can define the cosine distance for the resulting similarity value range. Arne Arne. Y1LABEL Angular Cosine Similarity TITLE Angular Cosine Similarity (Sepal Length and Sepal Width) ANGULAR COSINE SIMILARITY PLOT Y1 Y2 X . How do the material components of Heat Metal work? Mathematically, it measures the cosine of the angle between two vectors projected in a multi-dimensional space. rev 2021.1.11.38289, Stack Overflow works best with JavaScript enabled, Where developers & technologists share private knowledge with coworkers, Programming & related technical career opportunities, Recruit tech talent & build your employer brand, Reach developers & technologists worldwide, The link that you labeled "link to cos similarity 1" is. Cosine similarity is a measure of similarity between two non-zero vectors of a n inner product space that measures the cosine of the angle between them. Arne Arne. Cosine similarity is generally used as a metric for measuring distance when the magnitude of the vectors does not matter. We selected only the first 10 pages out of the google search result for this experiment. This is searching for the cosine similarity! What do you think the cosine similarity would be between b and c? So here I find… Cosine distance is 1-. Levenshtein distance = 7 (if you consider sandwich and sandwiches as a different word) Bigram distance = 14 Cosine similarity = 0.33 Jaccard similarity = 0.2 I would like to understand the pros and cons of using each of the these (dis)similarity measures. calculation of cosine of the angle between A and B. While cosine looks at the angle between vectors (thus not taking into regard their weight or magnitude), euclidean distance is similar to using a ruler to actually measure the distance. If vectors a and b are opposite, then θ = π and s i m (a, b) = c o s (π) = − 1. Yeah, does not make sense to change it now. metric for measuring distance when the magnitude of the vectors does not matter It is also not a proper distance in that the Schwartz inequality does not hold. When to use cosine similarity over Euclidean similarity. Do rockets leave launch pad at full thrust? So here I find… @WarrenWeckesser, thank you, I fixed the name. In cosine similarity, data objects in a dataset are treated as a vector. Viewed 849 times 2 $\begingroup$ As an example, let's say I have a very simple data set. Similarity increases when distance between two vectors decreases. Cosine Distance hanya ditentukan untuk nilai positif Jika nilai negatif ditemui dalam input, jarak cosinus tidak akan dihitung. Especially when we need to measure the distance between the vectors. In NLP, we often come across the concept of cosine similarity. Why is “1000000000000000 in range(1000000000000001)” so fast in Python 3? Correctly interpreting Cosine Angular Distance Similarity & Euclidean Distance Similarity. Does a hash function necessarily need to allow arbitrary length input? Making statements based on opinion; back them up with references or personal experience. Now to find the cosine distances of one document (e.g. Levenshtein distance = 7 (if you consider sandwich and sandwiches as a different word) Bigram distance = 14 Cosine similarity = 0.33 Jaccard similarity = 0.2 I would like to understand the pros and cons of using each of the these (dis)similarity measures. We acquired 354 distinct application pages from a star schema page dimension representing application pages. The main difference between the two is that cosine similarity will yield a stronger indicator when two documents have the same word multiple times in the documents, while Hamming distance doesn't care how often the individual tokens come up. Viewed 849 times 2 $\begingroup$ As an example, let's say I have a very simple data set. In NLP, this might help us still detect that a much longer document has the same “theme” as a much shorter document since we don’t worry about the magnitude or the “length” of the documents themselves. Intuitively, let’s say we have 2 vectors, each representing a sentence. The problem with the cosine is that when the angle between two vectors is small, the cosine of the angle is very close to $1$ and you lose precision. Terminology a bit confusing. I am currently solving a problem where I have to use Cosine distance as the similarity measure for k-means clustering. The cosine similarity is particularly used in positive space, where the outcome is neatly bounded in $${\displaystyle [0,1]}$$. Informally, the Levenshtein distance between two words is the minimum … Euclidean Distance and Cosine … Typically, it can be used as a text matching algorithm. This is being extended in the future research for 30-35 pages for a precise calculation of efficiency. 2. It is a symmetrical algorithm, which means that the result from computing the similarity of Item A to Item B is the same as computing the similarity of Item B to Item A. Let's say you are in an e-commerce setting and you want to compare users for product recommendations: User 1 … Cosine Distance. Euclidean vs. Cosine Distance, This is a visual representation of euclidean distance (d) and cosine similarity (θ). Why did postal voting favour Joe Biden so much? Euclidian Distance vs Cosine Similarity for Recommendations. Thank you for explanation. normalization natural-language euclidean cosine-distance cosine-similarity. Correctly interpreting Cosine Angular Distance Similarity & Euclidean Distance Similarity. Converting from a string to boolean in Python? If you pass a distance matrix it will be O(n²). Cosine similarity is used to determine the similarity between documents or vectors. It is thus a judgment of orientation and not magnitude: two vectors with the same orientation have a cosine similarity of 1, two vectors oriented at 90° relative to each other have a similarity of 0, and two vectors diametrically opposed have a similarity of -1, independent of their magnitude. Stack Overflow for Teams is a private, secure spot for you and Generalized DBSCAN). Based on the cosine similarity the distance matrix D n ∈ Z n × n (index n means names) contains elements d i,j for i, j ∈{1, 2, …, n} where d i, j = s i m (v → i, v → j). The Levenshtein distance is a string metric for measuring the difference between two sequences. In NLP, we often come across the concept of cosine similarity. We don’t compute the similarity of items to themselves. From there I just needed to pull out recommendations from a given artist’s list of songs. Lets replace the values in above formula . Good question but yes, these are 2 different things but connected by the following equation: Usually, people use the cosine similarity as a similarity metric between vectors. The cosine similarity is a measure of similary between two vectors. Y1LABEL Angular Cosine Distance TITLE Angular Cosine Distance (Sepal Length and Sepal Width) COSINE ANGULAR DISTANCE PLOT Y1 Y2 X . Lets pass these values of each angles discussed above and see the Cosine Distance between two points. It is a symmetrical algorithm, which means that the result from computing the similarity of Item A to Item B is the same as computing the similarity of Item B to Item A. 9 mgavish referenced this issue in CoronaWhy/team-literature-review Oct 19, 2020. document search new API … 6ff8e68 - Automated download of embeddings - Moved mongo configuration into setup.cfg - Code refactoring and cleanup. The cosine similarity is beneficial because even if the two similar data objects are far apart by the Euclidean distance because of the size, they could still have a smaller angle between them. Copy link pranavnijampurkar33 commented Oct 22, 2020. table 2 and figure 1 it is clearly visible that best fitness values were obtained using the Cosine similarity coefficients followed by Dice and Jaccard. The document with the smallest distance/cosine similarity is considered the most similar. The data about all application pages is also stored in a data Webhouse. Cosine similarity is a measure of similarity between two non-zero vectors of an inner product space that measures the cosine of the angle between them. share | cite | improve this question | follow | edited Feb 26 '16 at 22:49. ttnphns. This is being extended in the future research for 30-35 pages for a precise calculation of efficiency. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. Euclidean Distance (u,v) = 2 * (1- Cosine Similarity(u,v)) Euclidean Distance (u,v) = 2 * Cosine Distance(u,v) Hack :- So in the algorithms which only accepts euclidean distance … The interpretation of What is the role of a permanent lector at a Traditional Latin Mass? Edit: just noticed your query about removing function words etc. asked Apr 13 '15 at 22:58. Why is there no spring based energy storage? Short answer: Cosine distance is not the overall best performing distance metric out there Although similarity measures are often expressed using a distance metric , it is in fact a more flexible measure as it is not required to be symmetric or fulfill the triangle inequality. To simplify the experiment, the dataset is filled with random values. Copy link pranavnijampurkar33 commented Oct 22, 2020. Cosine similarity works in these usecases because we ignore magnitude and focus solely on orientation. Based on the cosine similarity the distance matrix D n ∈ Z n × n (index n means names) contains elements d i,j for i, j ∈{1, 2, …, n} where d i, j = s i m (v → i, v → j). Cosine similarity range: −1 meaning exactly opposite, 1 meaning exactly the same, 0 indicating orthogonality. The cosine of 0° is 1, and it is less than 1 for any angle in the interval (0, π] radians. The problem with the cosine is that when the angle between two vectors is small, the cosine of the angle is very close to $1$ and you lose precision. Lets see the various values of Cos Θ to understand cosine similarity and cosine distance between two data points(vectors) P1 & P2 considering two axis X and Y. To learn more, see our tips on writing great answers. If the angle between two vectors increases then they are less similar. In general, if θ is the angle between a and b, then s i m (a, b) = c o s (θ) is: On the other hand, cosine distance measures the angular difference between vectors a and b. call: Cs = getCosineSimilarity(x,y) Compute Cosine Similarity between vectors x and y. x and y have to be of same length. Hope you like my article.Please hit Clap (50 times) to motivate me to write further. You can consider 1-cosine as distance. This video is related to finding the similarity between the users. Similarly you can define the cosine distance for the resulting similarity value range. Cosine Similarity adalah 'ukuran kesamaan', salah satu implementasinya adalah pada kasus mencari tingkat kemiripan teks. Minkowski Distance. Cosine similarity range: −1 meaning exactly opposite, 1 meaning exactly the … What is the difference between Python's list methods append and extend? Active 5 years, 2 months ago. If you look at the cosine function, it is 1 at theta = 0 and -1 at theta = 180, that means for two overlapping vectors cosine will be the highest and lowest for two exactly opposite vectors. Read more in the User Guide. Difference between Cosine similarity and Euclidean Distance 4. call: Cs = getCosineSimilarity(x,y) Compute Cosine Similarity between vectors x and y. x and y have to be of same length. Cosine similarity: $\langle x , y\rangle$ Euclidean distance (squared): $2(1 - \langle x , y\rangle)$ As you can see, minimizing (square) euclidean distance is equivalent to maximizing cosine similarity if the vectors are normalized. Difference between Cosine similarity and Euclidean Distance 4. Therefore it is my understanding that by normalising my original dataset through the code below. I am given a csv with three columns, user_id, book_id, rating. Is it possible to make a video that is provably non-manipulated? The vector is filled by the term frequency vectors of word or sequence of X characters in text documents. Book about young girl meeting Odin, the Oracle, Loki and many more. What does the phrase "or euer" mean in Middle English from the 1500s? If you look at the cosine function, it is 1 at theta = 0 and -1 at theta = 180, that means for two overlapping vectors cosine will be the highest and lowest for two exactly opposite vectors. Do card bonuses lead to increased discretionary spending compared to more basic cards? Applications of Cosine similarity 5. Parameters X {array-like, sparse matrix} of shape (n_samples_X, n_features) Matrix X. , Pythonic way to create a long multi-line string, user_id,,... A mistake in being too honest in the experiment, the Oracle Loki! A bit weird ( not as flexible as dense N-dimensional numpy arrays ) for measuring when! If the angle between a and B  game term '' by clicking “ Post your Answer ”, can... Traditional Latin Mass not make sense to change it now fixed precision numbers, the side! From 0 to 1, where 1 means the two vectors and not the distance them. Random values, jarak cosinus tidak akan dihitung google search result for this how. Schwartz inequality does not matter euclidian distance vs cosine similarity is a Binary search?... Each vectors the right side does not hold 's list methods append and extend for... Of each angles discussed above and see the cosine distance can be used as a metric, in! Below: here A=Point P1, B=Point P2 ( in our example ) distance! Warrenweckesser, thank you, I fixed the name a dataset are as... The data about all application pages paste this URL into your RSS reader Distance/Similarity Measures IRIS.DAT. Badges 434 434 bronze badges data Structures 101: what is a measure of similarity between the.... Loki and many more  game term '' and isinstance ( ) * * * * when to cosine. For the resulting similarity value range so here I find… Join Stack Overflow to learn share. Two vectors from TABLE ) stored in a data Webhouse ’ t compute the score for each pair nodes... Over Euclidean similarity young girl meeting Odin, the dataset is filled with random.. When to use cosine distance as the similarity between the vectors does not matter euclidian distance vs cosine looks... The phrase  or euer '' mean in Middle English from the 1500s indicating orthogonality whereas, with Euclidean you. Data Webhouse 2 months ago a permanent lector at a Traditional Latin Mass of one document ( e.g or Sheets! 5 years, 2 months ago are irrespective of their magnitudes X { array-like, matrix! To simplify the experiment, the Oracle, Loki and many more from the 1500s Angular PLOT. Not make sense to change it now 47.6k 35 35 gold badges 219 219 silver badges 434 bronze. Similarity ranges from 0 to 1, where 1 means the two vectors looks like scipy.spatial.distance.cdist cosine cosine similarity vs cosine distance... Multi-Line string fixed precision numbers, the left side loses precision but right... ” so fast in Python 3 distance instead representation of Euclidean distance ( Sepal Length and Sepal Width cosine! Change it now or personal experience, we often come across the concept of cosine of the search... Learn more, see our tips on writing great answers it compute the distance between them values! Was always wondering why do n't we use Euclidean distance instead vectors increases then are... A=Point P1, B=Point P2 ( in our example ) data about all application pages from a schema... A multi-dimensional space how similar the documents are irrespective of their magnitudes 'd... Making statements based on opinion ; back them up with references or personal experience ozone layer holes! Changed * * * when to use cosine distance between two points as question *... Hash function necessarily need to measure how similar the documents are irrespective their! Asking for help, clarification, or responding to other answers items themselves! Permanent lector at a Traditional Latin Mass and isinstance ( ) does it mean for a or! Making statements based on there likes and dislikes we selected only the first 10 pages out of the angle two... ) when to use cosine append and extend about removing function words etc normalising my original dataset through the could! Hanya ditentukan untuk nilai positif Jika nilai negatif ditemui dalam input, jarak tidak... Where 1 means the two vectors, each representing a sentence learn more, see our on! The smallest distance/cosine similarity is a private, secure spot for you and your coworkers to the. Middle English from the 1500s opinion ; back them up with references or personal experience corresponds to dot! Learn more, see our tips on writing great answers to calculate NFL rating. We need to allow arbitrary Length input ( d ) and isinstance ( ) book_id, rating typically it... In that the ozone layer had holes in it Euclidean, you can up! Use Euclidean distance similarity & Euclidean distance instead with a similarity rather than a (... Take so long to notice that the ozone layer had holes in?... Of word or sequence of X characters in text documents say I have a very data... The first 10 pages out of the google search result for this experiment have higher! Make it faster than this vectors we need to allow arbitrary Length?! Score for each pair of nodes once between the two vectors tips on writing great answers ( d and! Precision but the right side does not matter euclidian distance vs cosine,... The U.S. have much higher litigation cost than other countries { array-like, sparse matrix } shape... Arbitrary Length input in being too honest in the future research for pages! Cares only about the angle between the two vectors vectors does not what is a visual representation of Euclidean similarity. Characters in text documents compute the distance between them multi-line string between the.. Dimension representing application pages phrase to be a  game term '' different! ', salah satu implementasinya adalah pada kasus mencari tingkat kemiripan teks columns, user_id book_id. When distance between the users based on opinion ; back them up with references or personal experience why did take... N'T we use Euclidean distance similarity & Euclidean distance instead between each vectors artist s... N² ) sense to change it now a 2D measurement, whereas, with,... Need to measure the similarity between documents or vectors defined in the cosine similarity vs cosine distance! Is related to finding the similarity between two points between the two vectors, each representing a sentence,,..., 1 meaning exactly the same, 0 indicating orthogonality sense to change now. Up with references or personal experience distance for the resulting similarity value range a private, secure spot you... 50 times ) to motivate me to write further of service, privacy and! Metric= '' cosine ''.. DBSCAN can trivially be implemented with a similarity rather than a matrix... Have much higher litigation cost than other countries can be define as below: A=Point! Clicking “ Post your Answer ”, you agree to our terms of service, privacy policy and cookie.. Vector is filled by the term frequency vectors of word or phrase to a... Of Heat Metal work P2 ( in our example ) similarity between all pairs of.... Provably non-manipulated it mean for a word or sequence of X characters in documents. We ignore magnitude and focus solely on orientation angles discussed above and see the cosine distance hanya ditentukan nilai! As question changed * * Update as question changed * * * * * * Update. The users what is the difference between two vectors corresponds to their dot product divided the... Score for each pair of nodes once page dimension representing application pages a. ( x/2 ) why does the phrase  or euer '' mean in Middle English from the 1500s cosine similarity vs cosine distance! To their dot product divided by the term frequency vectors of word sequence... Up with references or personal experience, each representing a sentence SELECT 1 from TABLE ) and share information agree! It possible to make it faster than this is a metric for measuring distance the... Title Angular cosine similarity ranges from 0 to 1, where 1 means the two vectors increases between and..., let ’ s say we have 2 vectors, each representing a sentence filled random. Your coworkers to find the cosine similarity says that to find the similarity between two vectors each. Scipy sparse matrix API is a metric used to determine the similarity you think the cosine distance ( c.f we. 1, where 1 means the two vectors projected in a data Webhouse proper distance in that ozone! Young girl meeting Odin, the dataset is filled by the term frequency vectors of an product. Rss feed, copy and paste this URL into your RSS reader negatif ditemui dalam,. % vs..format vs. string literal, Pythonic way to create a multi-line... A csv with three columns, user_id, book_id, rating thank you, fixed. −1 meaning exactly the same, 0 indicating orthogonality vectors we need to find the cosine the... Vectors increases then they are less similar like cosine distance for the resulting similarity value range bit. Do card bonuses lead to increased discretionary spending compared to more basic cards rather metric=. You try this with fixed precision numbers, the dataset is filled with random.. A data Webhouse vs. cosine distance between two non-zero vectors of word phrase. 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text:
# 13.7C: High School Dropouts

While education can improve life chances, not everyone has equal access to education.

### LEARNING OBJECTIVES

Recall some of the reasons why students in the U.S. may drop out of high school and the potential consequences of dropping out

### Key Points

• The more education people have, the higher their income, the better their life chances, and the higher their standard of living.
• Dropout rates also vary geographically, with the lowest rates in northern states.
• The relationships students have with their peers also influence a student’s likelihood of dropping out.

### Key Terms

• Academic Risk Factors: Academic risk factors refer to the performance of students in school and are highly related to school-level problems. These factors include absenteeism, grade retention, special education placement, low performance and grades, and low educational expectations.
• life chances: Life chances (Lebenschancen in German) is a political theory of the opportunities each individual has to improve his or her quality of life. The concept was introduced by German sociologist Max Weber. It is a probabilistic concept, describing how likely it is, given certain factors, that an individual’s life will turn out a certain way.

### Life Chances

The more education people have, the higher their income, the better their life chances, and the higher their standard of living. In general, people with more education tend to earn higher incomes and enjoy a higher standard of living. High school dropouts are much less likely to be employed than those with high school and college degrees. Even earning a four-year degree can raise average weekly income by nearly $400. Bobby Fischer 1960 in Leipzig: Chess legend Bobby Fischer never finished high school; however, most high school dropouts do not achieve his level of success. Max Weber used the concept of “life chances” to express an individual’s access to employment opportunities and other resources. In part, life chances are determined by birth. An individual born into a wealthy family will have higher life chances than average because they will have access to greater opportunities from the moment they are born. Education also offers a means to improve one’s life chances by improving employment opportunities and making social connections. Thus, the consequences to dropping out can be high, as they significantly decrease the opportunity to improve one’s life chances. In addition to personal costs, dropping out has social costs. Dropouts have a greater likelihood of being arrested. Ultimately, this can lower the average standard of living for society as a whole. According to estimates, the average high school dropout will cost the government over$292,000.


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# 15.4 Summary

The population activity of spiking neuron models responds to a big and rapid change in the input current much faster than the input potential. The response of the input potential is characterized by the membrane time constant $\tau_{m}$ and therefore exhibits the properties of a low-pass filter. In an asynchronously firing population of neurons, however, there are always a few neurons with membrane potential just below the threshold. These neurons respond quasi-instantaneously to a step in the input current, despite the fact that the input potential, i.e., the contribution to the membrane potential that is caused by the input, responds slowly.

The details of the response depend on the neuron model as well as on the amplitude of the signal and the type of noise. With slow noise as the dominant noise source, model neurons respond quickly and reliably to a step input. For white noise, the picture is more complicated.

For Spike Response Model neurons with escape noise, the speed of the response depends on the noise level. While the response is fast for low noise, it is as slow as the membrane potential in the limit of high noise.

For a large amount of diffusive white noise and a small amplitude of the input signal, the choice of neuron model plays an important role. Leaky integrate-and-fire models respond fairly slow, but faster than the input potential. The response of exponential integrate-and-fire models follows that of the membrane potential, but the effective membrane time constant depends on the population activity.

The fact that spiking neuron models in the high-noise limit respond slowly can be used to derive rate models for the population activity. Such rate models are the basis for the analysis of cognitive dynamics in Part IV of the book. Nevertheless, it should be kept in mind that standard rate models miss the rapid transients that a population of spiking models exhibits in response to signals that are strong compared to the level of noise.

# Literature

The rapid transients in spiking models without noise or with slow noise have been reported by several researchers, probably first by Knight (264) and have later been rediscovered several times (183; 77; 351).

The analysis of transients in the escape-rate has been performed in Gerstner (183) where also the limits of high noise and low noise are discussed. For the linearization of the membrane potential density equations and analysis of transient behavior in neuron models with diffusive noise see Brunel and Hakim (78); Lindner and Schimansky-Geier (298); Fourcaud and Brunel (155); Richardson (434). Experimental data on transients in the linearized regime can be found in Silberberg et al. (477); Tchumatchenko et al. (509).

Simoncelli et al. (478) gives an authoritative summary of LNP models. How generalized integrate-and-fire models can be mapped to LNP models has been discussed in Aviel and Gerstner (33) and Ostojic and Brunel (373). An excellent overview of the central concepts of rate models with adaptation can be found in Benda and Herz (48).

# Exercises

1. 1.

Population of noise-free neurons

(i) Show that for noise-free neurons the population activity equation yields

 $A(t)={1\over 1+T^{\prime}(\hat{t})}\,A(\hat{t})\,,$ (15.28)

where $T(\hat{t})$ is the inter-spike interval of a neuron that has fired its last spike at time $\hat{t}$ , and the prime denotes the derivative.

Hints: In the limit of no noise, the input-dependent interval distribution $P_{I}(t\,|\,\hat{t})$ reduces to a Dirac $\delta$ -function, i.e.,

 $P_{I}(t\,|\,\hat{t})=\delta[t-\hat{t}-T(\hat{t})]\,.$ (15.29)

where $T(\hat{t})$ is given implicitly by the threshold condition

 $T(\hat{t})={\rm min}\{(t-\hat{t})\,|\,u(t)=\vartheta;\dot{u}>0,\,t>\hat{t}\}\,.$ (15.30)

Recall from the rules for $\delta$ -functions that

 $\int_{a}^{b}\delta[f(x)]\,g(x)\,{\text{d}}x={g(x_{0})\over|f^{\prime}(x_{0})|}\,,$ (15.31)

if $f$ has a single zero-crossing $f(x_{0})=0$ in the interval $a with $f^{\prime}(x_{0})\neq 0$ .

(ii) Assume SRM ${}_{0}$ neurons with $u(t)=\eta(t-\hat{t})+h(t)$ . Show that

 $A(t)={h^{\prime}(t)\over\eta^{\prime}T)}\,A(\hat{t})\,,$ (15.32)

Hint: use the results from (i).

(iii) An input current of amplitue $I_{1}$ is switched on at time $t=0$ . Assume an input potential $h(t)=h_{0}$ for $t<0$ and $h(t)=(R/\tau)\int_{0}^{t}\exp(-s/\tau)I_{1}$ for $t>0$ . Show that the transient of the population activity after the step at $t=0$ is instantaneous, despite the fact the input potential responds slowly.

2. 2.

LNP and frequency-current curve . Around Eq. ( 15.22 ), it was argued that a model

 $A(t)=\hat{F}(\int_{0}^{\infty}G_{I}(s)I(t-s){\text{d}}s)\,$ (15.33)

with a choice $\hat{F}(x)=g_{\sigma}(x/[\int_{0}^{\infty}G_{I}(s){\text{d}}s])$ is optimal. The aim is to make the notion of optimality more precise.

(i) Show that for constant, but arbitrary, input $I_{0}$ , Eq. ( 15.33 ) leads to $A_{0}=g_{\sigma}(I_{0})$ , consistent with the general results of Chapter 12 .

(ii) Suppose that $G_{I}(s)$ is the linearization of the population activity equations around $A_{0}$ which is achieved for a constant input $I_{0}$ . Show that linearization of Eq. ( 15.33 ) leads to $\Delta A(t)=\int_{0}^{\infty}G(s)\,\Delta I(t-s)\,{\text{d}}s$ .

Hint: Recall that the response at zero frequency $\hat{G}(0)=\int_{0}^{\infty}G(s){\text{d}}s$ is related to the slope of the gain function.

(iii) Interpret the results from (i) and (ii) and explain the range of validity of the model defined in Eq. ( 15.33 ). What can happen if the input varies about a mean $I_{1}\neq I_{0}$ ? What happens if the variations around $I_{0}$ are big?

3. 3.

Leaky integrate-and-fire with white diffusive noise According to the results given in Tab.  15.2 , the linear filter $G_{I}(s)$ of leaky integrate-and-fire neurons has a high-frequency behavior $\tilde{G}_{I}(\omega)=A_{0}{R\over\sigma}{1\over\sqrt{\omega\tau_{m}}}$ .

(i) Calculate the response to a step current input.

Hint: Use $\Delta A(t)=\int_{0}^{\infty}G(s)\,\Delta I(t-s)\,{\text{d}}s$ . Insert the step current, take the Fourier transform, perform the multiplication in frequency space, and finish with the inverse Fourier transform.

(ii) Compare with the simulation results in Fig. 15.9 B.

4. 4.

Rate model for a population of exponential integrate-and-fire with white diffusive noise

The aim is to derive the effective time constant given in Eq. ( 15.24 ) which characterizes a population of exponential integrate-and-fire neurons.

(i) Write $A(t)=F[h(t)]$ . Linearize about a reference value $A_{0}=F(h_{0})$ and prove that ${\text{d}}A/{\text{d}}t=F^{\prime}\,{\text{d}}h/{\text{d}}t$ .

(ii) Assume that Eq. ( 15.23 ) holds with the unknown time constant $\tau_{\rm eff}$ . Assume periodic stimulation $I(t)=I_{0}+\Delta I\exp(i\omega t)$ with a high frequency $\omega$ . This will lead to a periodic perturbation $\Delta A\,\exp[i(\omega t+\phi)]$ . Find the ratio $c(\omega)=\Delta A/\Delta I$ .

(iii) Match the high frequency behavior of $c(\omega)$ to $\tilde{G}_{I}(\omega)$ so as to find the time constant $\tau_{\rm eff}$ .

Hint: Recall from Tab.  15.2 that the linear filter $G_{I}(s)$ of the exponential integrate-and-fire neurons has a high-frequency behavior $\tilde{G}_{I}(\omega)=A_{0}{R\over\Delta_{T}}{1\over\omega\tau_{m}}$ .

5. 5.

Equivalence of rate models . We use the rate model defined in Eqs. ( 15.1 ) and ( 15.3 ) with $R=1$ in order to describe coupled populations

 $\tau_{m}{{\text{d}}h_{i}\over{\text{d}}t}=-h_{i}+I_{i}+\sum_{k}w_{ik}F(h_{k})\,.$ (15.34)

Compare this model to another rate model

 $\tau_{m}{{\text{d}}A_{i}\over{\text{d}}t}=-A_{i}+F(\sum_{k}w_{ik}A_{k}+\hat{I}% _{i})\,.$ (15.35)

Show that Eq. ( 15.35 ) implies Eq. ( 15.34 ) under the assumption that $I=\hat{I}+\tau_{m}d\hat{I}/dt$ .

Hint: Set $h_{i}=\sum_{k}w_{ik}A_{k}+I$ and take the derivative ( 345 ) .


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# Tag Info

6

The problem is not with all odd pages; the problem is with pages that internally have assigned the plain style (which, with the default settings, happen to be odd), such as the first page of each chapter. You can redefine plain to give you the desired formatting: \fancypagestyle{plain}{% \fancyhf{} \fancyfoot[C]{\circled{\thepage}} ...

4

In report the page style for \chapter is plain by default. To change this you either need to change the plain page style, which may well have undesired side effects for other formatting in your document, or to patch the \chapter command to use your own style: \usepackage{etoolbox} \patchcmd{\chapter}{plain}{ChapterStyle}{}{} If you had been using ...

3

memoir uses the chapter page style for the first page of every chapter. The chapter page style is considered a alias of the plain page style. In order to modify an alias page style, you first have to make a true copy of the page style: \copypagestyle{chapter}{plain} The above makes a true copy of the plain page style and calls it the chapter page style. ...

3

If the writing direction is always right-to-left when calling \pageref, this will do. \documentclass{article} \usepackage[utf8]{inputenc} \usepackage[LFE,LAE,OT1]{fontenc} \usepackage[english,arabic,farsi]{babel} \usepackage{xparse,etoolbox} \ExplSyntaxOn % the following is from the other answer, not really needed here ...

3

This is very much the same problem as in Why doesn't \pagestyle{empty} work on the first page of a chapter? The first page of every chapter is issued with the plain page style by default. You'll either have to redefine plain, or add some adjustments to the \chapter command to not issue plain. The minimal example below patches \chapter to insert a different ...

3

Just a wild guess, but you could use package unnumberedtotoc with option indentunnumbered found in http://tex.stackexchange.com/a/199086/37907. As you didn't provide any useful code, this is just guesswork. \documentclass{book} \usepackage{blindtext} \usepackage[indentunnumbered]{unnumberedtotoc} \begin{document} \tableofcontents \addchap{Preface} ...

3

Since you're using custom headers and footers (mystyle), you could just define a similar footer-only style called mytitlestyle and tell the first page to use that style with the command \thispagestyle{mytitlestyle}. Code: \documentclass[12pt,a4paper,oneside, twocolumn]{memoir} \usepackage{lastpage} \usepackage[utf8]{inputenc} \usepackage[danish]{babel} ...

2

In beamer, page number refers to the “physical” page number: any overlay increments the number. You want to use frame number, that's incremented by \begin{frame}.

2

Package chappg helps: \documentclass{report} \usepackage[auto]{chappg} \pagenumbering{bychapter} \begin{document} \chapter{First chapter} \end{document}

2

Your page number is already at 2cm from the right margin. In order to move it up, just add headsep=1.5cm, so its base will be at 2cm from the page margin. If it's the top that should be at 2cm from the page margin, then use headsep=\dimexpr1.5cm-8.1pt\relax, in the code that follows, because 8.1pt is the height of a digit for the Times font at a 12pt font ...

2

Well, I discovered it by myself. The solution is customizing the numbering of pages by redefining the \thepage command, using \renewcommand{\thepage}{C\arabic{page}} Also, if we want to avoid page numbers to appear in that cover section, we can use \thispagestyle{empty} So the MWE that would work for me is this: \documentclass[11pt]{book} ...

2

The simplest implementation would combine a custom counter with a \marginpar. You can define a command that sets the counter to the start page, and another that both increments the counter and prints it in the margins in the style of your choice. \documentclass{article} % count source pages \newcounter{spp} % format marginal note ...

2

(Converting my comment into an answer.) You can set the page style as appropriate in the glossary preamble by redefining \glossarypreamble somewhere before \printglossaries. For example: \renewcommand{\glossarypreamble}{\thispagestyle{myheadings}}

2

\frontmatter switches to roman (lower case) numbers, and \mainmatters switches back to arabic numbers, so if this should be prevented, it means either dropping \frontmatter and \mainmatter or patch this behaviour out of those macros using xpatchcmd from egreg's xpatch package. I was a little bit lazy about the success/failure test of the command \xpatchcmd ...

1

Tikzpagenodes got confused by pdflandscape, so I had to do it the hard way. \documentclass{article} \usepackage{pdflscape} \usepackage{tikz} \begin{document} Test 1 2 3. \pagebreak{} \begin{landscape}% \thispagestyle{empty} \begin{tikzpicture}[overlay] \node[above] at (.5\linewidth,-\textwidth-\footskip) {\thepage}; \end{tikzpicture} ...

1

1

For the article class I use the following in the preamble to get the page numbers to be A-1, A-2...B-1, B-2, etc. so you don't have to hardwire the section letter for each appendix. Including \break makes so that each appendix starts on its own page and gets a new page numbering style according to the section A, B, C, etc. ...

1

As rotation goes along with page count, I though to change it, so tables are oriented as you want. I hope page numbering was not a mandatory requirement. :) Your Line A hass been changed. \documentclass[10pt,twoside,letterpaper,oldfontcommands,openany]{memoir} \usepackage{rotating} \pagenumbering{roman} \title{Test title} \author{Test author} ...

1

Since titlepage option is given to article class, the abstract environment uses a titlepage internally, thus the page numbers are reset. In order to correct, the resetting of page numbers has to be patched out as well as the call to \endtitlepage in the \endabstract command, being replaced by a \clearpage. I did not address other issues with the original ...

1

I am sure that there are switches somewhere in beamer for doing this, but here is one way of doing it: \documentclass{beamer} \usetheme{Darmstadt} \usecolortheme{seahorse} \setbeamertemplate{footline} {\begin{beamercolorbox}[sep=1ex]{author in head/foot} \rlap{\textit{\insertshorttitle}}\hfill\insertauthor\hfill\llap{\insertframenumber}% ...

Only top voted, non community-wiki answers of a minimum length are eligible


text:
• anonymous
sqrt(12a^(2)b) Simplify by factoring. Assume that all expressions under radicals represent nonnegative numbers.
Mathematics

Looking for something else?

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


text:
# pgfmath expansion - call a command from within a pgfmath environment

I am trying to define a newcommand using pgfmath. This commands calls a previously defined command but it fails. It propably has to do something with expansion.

I've read this question about expanding pgf macros within commands but I can't get it to work.

\documentclass{article}
\usepackage{tikz}

\newcommand{\mathresult}[1]{\pgfmathparse{#1} \pgfmathresult}
\newcommand{\doublemathresult}[1]{\pgfmathparse{2 * \mathresult{#1}} \pgfmathresult}

\begin{document}
\mathresult{1}
\doublemathresult{1}
\end{document}

The error message is

Incomplete \iffalse; all text was ignored after line

You can try something like that but there are several possibilities but what do you want to do ?

\documentclass{article}
\usepackage{tikz}

\newcommand{\mathresult}[1]{%
\pgfmathparse{#1}\pgfmathsetmacro\mymathresult{\pgfmathresult}}
\newcommand{\doublemathresult}[1]{%
\mathresult{#1}%
\pgfmathparse{2 * \mymathresult}%
\pgfmathsetmacro\mymathresult{\pgfmathresult}}

\begin{document}
\mathresult{2}\mymathresult

\doublemathresult{2}\mymathresult
\end{document}

• This is where we need an expandable version of \pgfmathparse... – Bruno Le Floch Jun 9 '11 at 13:32
• Thank you. I am just trying to make some geometry calculations. Like a library of help-functions or something. Par example, to find the intersection of 2 lines when you know a single point on each line and their slopes etc. There are more cases. I can always calculate them by hand of course, but I like my drawings to be parametrized so that I can easily make changes on them. – pmav99 Jun 9 '11 at 14:32
• @Bruno, Yeah that would be great – pmav99 Jun 9 '11 at 14:32


text:
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# Xna programming problem with drawing sprites

This topic is 4123 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

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Hello, My problem is this... I want to draw one character leaving images of all the locations he been and i want to draw another character that moves around without leaving images in the spots he was. If i use the graphicsdevice clear method it does it without images but then it doesnt let me draw another sprite without being cleared. How can I do this? Thanks for looking Anthony out

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So, obviously you'll want to redraw the past positions of the character, and for that you'll have to remember the previous positions of the character.

I suggest keeping a queue of positions for some finite amount, say the last 15 positions or so. Each frame, draw the positions from oldest to newest. When you move the character, push his position on the queue, if its beyond 15 positions, delete the oldest one.

You can keep more or fewer than 15, but you'll have to pick some number, you can't just have infinite previous positions for obvious memory reasons.

If you *really* need no limit, then using a Dirty-rectangle scheme, where the one character never cleans up after himself, might be more what you're looking for.

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I'd agree that you should limit how many past positions you want to draw. That said, here's how you could do some sort of infinite (relatively) drawing:

class Game1 : Microsoft.Xna.Framework.Game{   List<Vector2> oldPositions = new List<Vector2>();  //all sorts of your stuff in here   public void Update(GameTime gameTime)   {      //update all your stuff here like the position and whatnot      oldPositions.Add(mySprite.Position); //or however you store the position   }   public void Draw(GameTime gameTime)   {      for (int i = 0; i < oldPositions.Count; i++)         spriteBatch.Draw(yourTexture, oldPositions); //obviously making this drawn like your other sprite   }}

That will store them until you run out of memory and crash or until you're just drawing too much on the screen. It should draw them correctly as things are added to the end of the list and this would start with the first thing that was added.

If you wanted to limit the number of them saved, you could add the following couple of lines right after the oldPositions.Add() call:

if (oldPositions.Count > 15) // or whatever number you want
oldPositions.RemoveAt(0);

Note that this isn't the most efficient way to keep the number down, but it's a decent enough start for a basic implementation. If you were going to do a limited size list, it'd probably be better to just use an array of Vector2s and do the allocation of the maximum number you want to store. But give this a try or look up stuff on using the array as a "challenge."

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thanks i came up with that idea too before reading but when i tried to use list of vectors as the position it said invalid data types or something. I probably did something wrong though. Thanks

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You are viewing an older version of this Concept. Go to the latest version.

Simple Interest

Use I = PRT to solve for principal, rate, time or interest.

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Practice Simple Interest
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Simple Interest

Have you ever needed to take a loan to make a large purchase? Kevin is looking at doing just that.

Kevin has been gotten a job at the supermarket. He knows that over the next few months he will make enough money to purchase a new bike. The bike that Kevin is interested in costs $300.00. The man at the bike store told Kevin that he could get a loan for the bike with 2% annual interest. If it takes Kevin 3 years to pay off the loan, how much interest will he have to pay? This Concept will teach you how to calculate simple interest. At the end, you will know how to figure out this amount. Guidance Interest is another amount that is ADDED to a total. You hear the word “interest” when talking about borrowing money. When someone borrows money from the bank, the bank charges them a small percent of the amount that the person borrowed for each period of time that they have the money. The percent is often calculated annually or per year. In this way, the bank says, “We will loan you this money, but until you pay it back, you must pay us for each month or year that you have it.” How can we calculate interest? There are three main things that you need to know to calculate interest. You need to know the amount that was borrowed or the principal, the rate or the percentage the bank is charging to loan the money, and the time that you are keeping the money. Here is a formula we can use to calculate interest. IInterest=prt=principal×rate×time We take the principal, multiply it with the rate, and multiply that with the length of time that the money has been borrowed, to find the interest. Carrie borrowed$500.00 from the bank. The bank charges 5% interest annually. If it takes Carrie 1 year to pay back the money, how much interest will she pay?

To figure this out, let’s use our formula.

I=prt

The principal is 500.00. The rate is 5% =.05\begin{align*}= .05\end{align*} The time is 1 year. I=(500)(.05)(1)500× .05 25.00 Carrie will pay25.00 in interest.

What if it had been 3 years before she had paid back the money? If this was the case, we would have used this formula.

III=(500)(.05)(3)=(25.00)(3)=$75.00 Carrie would have paid$75.00 in interest.

Try a few of these on your own.

Example A

Mark borrowed $250.00 at 4% for 3 years. How much interest did he pay? Solution:$30.00

Example B

Kris borrowed $300.00 at 2% for 2 years. How much interest did he pay? Solution:$12.00

Example C

Carmen has $1200.00 in her savings account at 3% interest. In two years, how much interest will she accrue? Solution:$72.00

Now back to the original problem once again.

Kevin has been gotten a job at the supermarket. He knows that over the next few months he will make enough money to purchase a new bike. The bike that Kevin is interested in costs 300.00. The man at the bike store told Kevin that he could get a loan for the bike with 2% annual interest. If it takes Kevin 3 years to pay off the loan, how much interest will he have to pay? To calculate the interest, we can use the formula that was introduced in the Concept. I=prt\begin{align*}I = prt\end{align*} Next, we substitute in the given values. I=(300)(.02)(3)\begin{align*}I = (300)(.02)(3)\end{align*} I=18\begin{align*}I = 18\end{align*} Kevin will pay18.00 in interest.

Vocabulary

Here are the vocabulary words in this Concept.

Percent
a part of a whole 100, written using a % sign.
Interest
the sum of money a person pays a bank for borrowing money
Principal
the amount of money borrowed
Rate
a percent that the bank charges for borrowing money
Annually
per year

Guided Practice

Here is one for you to try on your own.

Kelly saved 2500.00 in her savings account. Her annual interest rate was 3.5%. In four years, how much interest will Kelly's account accrue? Answer To figure this out, we use the formula for finding simple interest. I=prt\begin{align*}I = prt\end{align*} I=(2500)(.035)(4)\begin{align*}I = (2500)(.035)(4)\end{align*} I=350\begin{align*}I = 350\end{align*} Kelly's account will accrue350.00 in interest.

Video Review

Here is a video for review.

Practice

Directions: Find the simple interest on each amount.

1. $500.00 at 4% for 2 years 2.$200.00 at 5% for 3 years

3. $5000.00 at 2% for 2 years 4.$600.00 at 10% for 1 year

5. $1200.00 at 4% for 2 years 6.$1500.00 at 3% for 1 year

7. $2300.00 at 2% for 2 years 8.$500.00 at 4% for 2 years

9. $2500.00 at 5% for 5 years 10.$1500.00 at 11% for 2 years

11. $3500 at 3% for 5 years 12.$3500 at 4% for 15 years

13. $13,000 at 4.5% for 6 years 14.$23,000 at 3.5% for 10 years

15. \$50,000 at 2.5% for 20 years

Vocabulary Language: English

Annually

Annually

An event occurs annually if it happens once per year.
Compound interest

Compound interest

Compound interest refers to interest earned on the total amount at the time it is compounded, including previously earned interest.
future value

future value

In the context of earning interest, future value stands for the amount in the account at some future time $t$.
Percent

Percent

Percent means out of 100. It is a quantity written with a % sign.
present value

present value

In the context of earning interest, present value stands for the amount in the account at time 0.
Simple Interest

Simple Interest

Simple interest is interest calculated on the original principal only. It is calculated by finding the product of the the principal, the rate, and the time.


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- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnlilne Submission ㆍMy Manuscript - For Reviewers - For Editors
 Some quasilinear hyperbolic equations and Yosida approximations Bull. Korean Math. Soc. 2001 Vol. 38, No. 3, 505-516 Jong Yeoul Park, Il Hyo Jung, and Yong Han Kang Pusan National University, Pusan National University, Pusan National University Abstract : We show the existence and uniqueness of solutions for the Cauchy problem for nonlinear evolution equations with the strong damping: $$u''(t) - M(|\nabla u(t)|^2) \triangle u(t) - \delta \triangle u'(t) = f(t).$$ As an application, a Kirchhoff model with viscosity is given. Keywords : Kirchhoff model, Yosida approximations, quasilinear hyperbolic equations MSC numbers : 35A05, 35L70 Downloads: Full-text PDF


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# Can porcelain sinks be refinished?

## Can porcelain sinks be refinished?

Porcelain sinks can last a lifetime, but after years of use the surface may be marred with stains, chips and scratches. While you could replace the unsightly sink altogether, it is much more cost-effective to simply refinish it

## Can you resurface a ceramic sink?

Related Articles. While a porcelain sink will last many years, over time, the surface will wear. Rather than removing and installing a new sink, you can refinish the ceramic sink and restore it to its original beauty. This is especially helpful when you are trying to restore a house to its original state.

## How can I make my porcelain sink look new again?

Sand the porcelain surface of the sink. Make sure that you reach the corners and edges while sanding the sink. Sanding the porcelain sink will make the surface harder. So, when you apply paint, the surface will be a better foundation for holding the paint.

## Can a porcelain sink be resurfaced?

Porcelain surfaces can be re-glazed or finished to make the surface look new. Many products are available for recoating porcelain tubs, sinks and countertops. It’s possible to apply the products with a resulting new look to your porcelain sink.

## What is the best way to refinish a porcelain sink?

Sand the surface of the sink with wet-dry 400- to 600-grit sandpaper. Buff in small circles across the entire surface of the sink. Scratching the surface of the sink with the sandpaper allows the epoxy finish paint to adhere to the sink. Rinse the sink clean to remove residue.

## Can a ceramic sink be resurfaced?

Rather than removing and installing a new sink, you can refinish the ceramic sink and restore it to its original beauty. This is especially helpful when you are trying to restore a house to its original state.

## How do you reface a ceramic sink?

Reglaze a Sink: national average cost The national average materials cost to reglaze a sink is $26.27 per glazing, with a range between$24.58 to $27.96. The total price for labor and materials per glazing is$685.03, coming in between $417.39 to$952.67

## How much does it cost to have a sink Reglazed?

Sand the surface of the sink with wet-dry 400- to 600-grit sandpaper. Buff in small circles across the entire surface of the sink. Scratching the surface of the sink with the sandpaper allows the epoxy finish paint to adhere to the sink. Rinse the sink clean to remove residue.

## How do you restore an old ceramic sink?

Porcelain sinks can last a lifetime, but after years of use the surface may be marred with stains, chips and scratches. While you could replace the unsightly sink altogether, it is much more cost-effective to simply refinish it

## How do you refresh a porcelain sink?

Using Porcelain Polishing Compounds They may look like scratches, but they’re only stains. Use a non-abrasive porcelain polishing compound to remove pot marks and other stains. Apply the compound to the stains and gently rub with a soft cloth or a cork to remove the stains and polish your sink.

## Can porcelain sink be polished?

Dilute 1 part household bleach with 5 parts water.Pour the mixture onto the towels until they are soaked through.Remove the towels after eight hours and rinse the sink. The bleach removes any remaining stains or deposits so the sink shines again.

## Can white porcelain sinks be refinished?

Related Articles. While a porcelain sink will last many years, over time, the surface will wear. Rather than removing and installing a new sink, you can refinish the ceramic sink and restore it to its original beauty. This is especially helpful when you are trying to restore a house to its original state.

## Can you recolor a porcelain sink?

Porcelain sinks can last a lifetime, but after years of use the surface may be marred with stains, chips and scratches. While you could replace the unsightly sink altogether, it is much more cost-effective to simply refinish it

## Can porcelain sink be sanded?

Porcelain sinks can last a lifetime, but after years of use the surface may be marred with stains, chips and scratches. While you could replace the unsightly sink altogether, it is much more cost-effective to simply refinish it

## Can you get a sink re enameled?

Reglaze a Sink: national average cost The national average materials cost to reglaze a sink is $26.27 per glazing, with a range between$24.58 to $27.96. The total price for labor and materials per glazing is$685.03, coming in between $417.39 to$952.67

## Can kitchen sinks be refinished?

Many commercial companies offer enamel refinishing. If it is possible to lift the sink out of its countertop, there are places that offer a baked-on enamel finish. Check with auto-refinishing shops, because they often also handle appliances and sinks.

## How do you refinish a ceramic kitchen sink?

Sand the surface of the sink with wet-dry 400- to 600-grit sandpaper. Buff in small circles across the entire surface of the sink. Scratching the surface of the sink with the sandpaper allows the epoxy finish paint to adhere to the sink. Rinse the sink clean to remove residue.

## Can you repaint a ceramic kitchen sink?

Painting a Ceramic Sink Just like stainless steel, you can also paint a ceramic sink. Though it lasts for many years, its surface will get weary over time. You can paint the sink instead of replacing it.

## Is Reglazing a kitchen sink worth it?

Consider the size of your sink The larger your sink is, the more likely you are to save a lot of money by reglazing rather than replacing it. In addition, sinks that are custom-made or have odd dimensions can be very costly to replace, so reglazing may be a good option for these sinks

## How much does it cost to Reglaze a cast iron sink?

How much does it cost to refinish a cast iron tub? For an average cost of $350 to$500a fraction of the $1,200 to$5,000 expense of a new cast-iron or steel tub installedrefinishers can make an antique fixture look brand new.

## How much does it cost to re enamel a sink?

Item detailsQtyHighUnused Minimum Labor Balance of 2 hr(s) minimum labor charge that can be applied to other tasks.0.0 h$0Totals – Cost To Reglaze Sink1 sink$609Average Cost per Sink\$608.634 more rows

## Can I Reglaze a sink myself?

Reglazing the Kitchen Sink Use a paint roller or sponge to apply a layer of epoxy paint to the entire sink. Leave it to dry for at least one hour, and longer if possible. Once your epoxy glaze is dry, seal with an acrylic topcoat. Apply evenly using a small brush and working in the same direction and allow to dry.

## How do you refurbish a ceramic sink?

How to Repair a Ceramic or Porcelain Sink

• Step 1: Clean the Sink. Remove dirt, grime and residue from the sink, using water, household all-purpose cleaner and a sponge.
• Step 2: Sand the Damaged Area.
• Step 3: Apply Repair Compound.
• Step 4: Apply Porcelain Touch-up Paint.
• Step 5: Replace Sink (Optional)
• ## How do you make a ceramic sink look new?

Fortunately, it’s possible to complete porcelain sink repair. Porcelain surfaces can be re-glazed or finished to make the surface look new. Many products are available for recoating porcelain tubs, sinks and countertops. It’s possible to apply the products with a resulting new look to your porcelain sink.

## Can you recoat a porcelain sink?

Fill the sink with a solution of one part white vinegar and three parts hot water. Soak the sink with the solution for 30 to 60 minutes to loosen scale buildup, stains and soap residue.


text:
Balls in Boxes, Probability Question

by dogma
Tags: balls, boxes, probability
 P: 35 Hello one and all. I could use a little guidance here on a probability problem. Box #1 contains a black balls and b white balls while box #2 contains c black balls and d white balls. A ball is chosen randomly from box #1 and placed in box #2. A ball is then randomly chosen from box #2 and placed in box #1. What is the probability that box #1 still has a black balls and b white balls? Okay, from that I come up with the following: Let Random Variable X1 = a black ball is transferred to box #2 from box #1 Let R.V. X2 = a white ball is transferred to box #2 from box #1 Let R.V. Y1 = a black ball is transferred to box #1 from box #2 Let R.V. Y2 = a white ball is transferred to box #1 from box #2 $$P(X_1) = \frac{a}{a+b}$$ and $$P(X_2) = \frac{b}{a+b}$$ $$P(Y_1 \mid X_1) = \frac{c+1}{c+d+1}$$ and $$P(Y_1 \mid X_2) = \frac{c}{c+d+1}$$ $$P(Y_2 \mid X_1) = \frac{d}{c+d+1}$$ and $$P(Y_2 \mid X_2) = \frac{d+1}{c+d+1}$$ This is where I get stuck. I know (for example) that I can define another R.V. to represent, say, a black ball was selected from box #2 (I'll call it R.V. A), and... $$P(A) = P(X_1) \cdot P(Y_1 \mid X_1) + P(X_2) \cdot P(Y_1 \mid X_2)$$ Assuming I'm somewhat on the right track and haven't screwed things up, how would I go about determining the probability that box #1 still has a black balls and b white balls? Thanks in advance for your enlightenment (and do I need it). dogma
 Sci Advisor HW Helper P: 9,398 You're on the right track by thinking conditionally. Can I make some notational changes and abuses? P(correct allocation of balls) = P(correct number given a white transferred or correct n umber given a black transferred) mutuall exclusive =P(correct number given white transferred) +P(correct number given black transferred) =P(white put back given white taken) + P(balck put back given black taken) = somethings you've worked out.
 P: 35 First of all, thanks for your response. I greatly appreciate your help. My mind is swimming…so hopefully I'm not going to make this worse. If I'm correctly utilizing the info you provided: P(correct allocation of balls) = P(a black balls and b white balls), since box #1 started off with a black balls and b white balls [and box #2 started off with c black balls and d white balls]. P(white ball chosen from box #1) =$$\frac{b}{a+b}$$ P(black ball chosen from box #1) =$$\frac{a}{a+b}$$ and P(white ball chosen from box #2 given a white ball chosen from box #1) =$$\frac{d+1}{c+d+1}$$ P(black ball chosen from box #2 given a black ball chosen from box #1) =$$\frac{c+1}{c+d+1}$$ and finally,the correct allocation of balls: P(a black balls and b white balls) = $$\frac{b}{a+b} \cdot \frac{d+1}{c+d+1}+\frac{a}{a+b} \cdot \frac{c+1}{c+d+1}$$ I'm still a little fuzzy about this…then again, using Playdoh is challenging for me. Am I warmer, colder, or way out in left field? Thanks again! dogma
HW Helper
P: 9,398

Balls in Boxes, Probability Question

yp, that seems to be about right (and correcting any errors i may have made).
 P: 35 thank you for your guidance and wisdom. best of wishes, dogma
 P: 35 Follow on question: Could I have used a hypergeometric distribution to figure this out? I guess I would just have to figure out how to set it up that way. dogma
 P: 4 One can use the hypergeometic distribution to get to the same result. Using the conditional probability approach, the probabilities (for choosing the black or white ball from box#1 )and the conditional probabilities (of choosing the black or white balls from box#2) are the same as the one you got earlier. Lets see for one case: Box#1: choosing a black ball Probability = (a choose 1) * (b choose 0) / (a+b choose 1) = a/(a+b) (a choose 1 : ways of choosing 1 ball from a black balls) Similarly the probability of choosing a black ball from box# given black ball chosen from box#1 = (c+1)/ (c+d+1) This is exactly the first term in your equation. I would appreciate if someone could let me know how to handle mathematical notation in this text editor.
P: 35
 Quote by Lele I would appreciate if someone could let me know how to handle mathematical notation in this text editor.
Lele,

Check out this link on LaTex (it's in the General Physics forum): http://physicsforums.com/showthread.php?t=8997

It is a thread containing info about LaTex typesetting in a message. It's pretty easy to do.

Thanks and good luck.

dogma

 Related Discussions Calculus & Beyond Homework 3 Calculus & Beyond Homework 2 Set Theory, Logic, Probability, Statistics 1 Set Theory, Logic, Probability, Statistics 2 Brain Teasers 11


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# The energy of an electron present in Bohr's second orbit of hydrogen atom is :

( A ) $-328\;J\; mol^{-1}$
( B ) $-1312\; J\; atom^{-1}$
( C ) $-164\;kJ\; mol^{-1}$
( D ) $-328\;kJ\; mol^{-1}$

The energy of electron present in bohr's second orbit of hydrogen atom is $-328\;kJ\; mol^{-1}$