The r-to-1 collision problem is an important theoretical problem in complexity theory, quantum computing, and computational mathematics. The collision problem most often refers to the 2-to-1 version: given n {\displaystyle n} even and a function f : { 1 , … , n } → { 1 , … , n } {\displaystyle f:\,\{1,\ldots ,n\}\rightarrow \{1,\ldots ,n\}} , we are promised that f is either 1-to-1 or 2-to-1. We are only allowed to make queries about the value of f ( i ) {\displaystyle f(i)} for any i ∈ { 1 , … , n } {\displaystyle i\in \{1,\ldots ,n\}} . The problem then asks how many such queries we need to make to determine with certainty whether f is 1-to-1 or 2-to-1. == Classical solutions == === Deterministic === Solving the 2-to-1 version deterministically requires n 2 + 1 {\textstyle {\frac {n}{2}}+1} queries, and in general distinguishing r-to-1 functions from 1-to-1 functions requires n r + 1 {\textstyle {\frac {n}{r}}+1} queries. This is a straightforward application of the pigeonhole principle: if a function is r-to-1, then after n r + 1 {\textstyle {\frac {n}{r}}+1} queries we are guaranteed to have found a collision. If a function is 1-to-1, then no collision exists. Thus, n r + 1 {\textstyle {\frac {n}{r}}+1} queries suffice. If we are unlucky, then the first n / r {\displaystyle n/r} queries could return distinct answers, so n r + 1 {\textstyle {\frac {n}{r}}+1} queries is also necessary. === Randomized === If we allow randomness, the problem is easier. By the birthday paradox, if we choose (distinct) queries at random, then with high probability we find a collision in any fixed 2-to-1 function after Θ ( n ) {\displaystyle \Theta ({\sqrt {n}})} queries. == Quantum solution == The BHT algorithm, which uses Grover's algorithm, solves this problem optimally by only making O ( n 1 / 3 ) {\displaystyle O(n^{1/3})} queries to f. The matching lower bound of Ω ( n 1 / 3 ) {\displaystyle \Omega (n^{1/3})} was proved by Aaronson and Shi using the polynomial method.
Second-order co-occurrence pointwise mutual information
In computational linguistics, second-order co-occurrence pointwise mutual information (SOC-PMI) is a method used to measure semantic similarity, or how close in meaning two words are. The method does not require the two words to appear together in a text. Instead, it works by analyzing the "neighbor" words that typically appear alongside each of the two target words in a large body of text (corpus). If the two target words frequently share the same neighbors, they are considered semantically similar. For example, the words "cemetery" and "graveyard" may not appear in the same sentence often, but they both frequently appear near words like "buried," "dead," and "funeral." SOC-PMI uses this shared context to determine that they have a similar meaning. The method is called "second-order" because it doesn't look at the direct co-occurrence of the target words (which would be first-order), but at the co-occurrence of their neighbors (a second level of association). The strength of these associations is quantified using pointwise mutual information (PMI). == History == The method builds on earlier work like the PMI-IR algorithm, which used the AltaVista search engine to calculate word association probabilities. The key advantage of a second-order approach like SOC-PMI is its ability to measure similarity between words that do not co-occur often, or at all. The British National Corpus (BNC) has been used as a source for word frequencies and contexts for this method. == Methodology == The SOC-PMI algorithm measures the similarity between two words, w 1 {\displaystyle w_{1}} and w 2 {\displaystyle w_{2}} , in several steps. === Step 1: Score neighboring words with PMI === First, for each target word ( w 1 {\displaystyle w_{1}} and w 2 {\displaystyle w_{2}} ), the algorithm identifies its "neighbor" words within a certain text window (e.g., within 5 words to the left or right) across a large corpus. The strength of the association between a target word t i {\displaystyle t_{i}} and its neighbor w {\displaystyle w} is calculated using pointwise mutual information (PMI). A higher PMI value means the two words appear together more often than would be expected by chance. The PMI between a target word t i {\displaystyle t_{i}} and a neighbor word w {\displaystyle w} is calculated as: f pmi ( t i , w ) = log 2 f b ( t i , w ) × m f t ( t i ) f t ( w ) {\displaystyle f^{\text{pmi}}(t_{i},w)=\log _{2}{\frac {f^{b}(t_{i},w)\times m}{f^{t}(t_{i})f^{t}(w)}}} where: f b ( t i , w ) {\displaystyle f^{b}(t_{i},w)} is the number of times t i {\displaystyle t_{i}} and w {\displaystyle w} appear together in the context window. f t ( t i ) {\displaystyle f^{t}(t_{i})} is the total number of times t i {\displaystyle t_{i}} appears in the corpus. f t ( w ) {\displaystyle f^{t}(w)} is the total number of times w {\displaystyle w} appears in the corpus. m {\displaystyle m} is the total number of tokens (words) in the corpus. === Step 2: Create a semantic 'signature' for each word === For each target word ( w 1 {\displaystyle w_{1}} and w 2 {\displaystyle w_{2}} ), the algorithm creates a list of its most significant neighbors. This is done by taking the top β {\displaystyle \beta } neighbor words, sorted in descending order by their PMI score with the target word. This list of top neighbors, X w {\displaystyle X^{w}} , acts as a semantic "signature" for the word w {\displaystyle w} . X w = { X i w } {\displaystyle X^{w}=\{X_{i}^{w}\}} , for i = 1 , 2 , … , β {\displaystyle i=1,2,\ldots ,\beta } The size of this list, β {\displaystyle \beta } , is a parameter of the method. === Step 3: Compare the signatures === The algorithm then compares the signatures of w 1 {\displaystyle w_{1}} and w 2 {\displaystyle w_{2}} . It looks for words that are present in both signatures. The similarity of w 1 {\displaystyle w_{1}} to w 2 {\displaystyle w_{2}} is calculated by summing the PMI scores of w 2 {\displaystyle w_{2}} with every word in w 1 {\displaystyle w_{1}} 's signature list. The β {\displaystyle \beta } -PMI summation function defines this score. The score for w 1 {\displaystyle w_{1}} with respect to w 2 {\displaystyle w_{2}} is: f ( w 1 , w 2 , β ) = ∑ i = 1 β ( f pmi ( X i w 1 , w 2 ) ) γ {\displaystyle f(w_{1},w_{2},\beta )=\sum _{i=1}^{\beta }(f^{\text{pmi}}(X_{i}^{w_{1}},w_{2}))^{\gamma }} This sum only includes terms where the PMI value is positive. The exponent γ {\displaystyle \gamma } (with a value > 1) is used to give more weight to neighbors that are more strongly associated with w 2 {\displaystyle w_{2}} . This calculation is done in both directions: The similarity of w 1 {\displaystyle w_{1}} with respect to w 2 {\displaystyle w_{2}} : f ( w 1 , w 2 , β 1 ) = ∑ i = 1 β 1 ( f pmi ( X i w 1 , w 2 ) ) γ {\displaystyle f(w_{1},w_{2},\beta _{1})=\sum _{i=1}^{\beta _{1}}(f^{\text{pmi}}(X_{i}^{w_{1}},w_{2}))^{\gamma }} The similarity of w 2 {\displaystyle w_{2}} with respect to w 1 {\displaystyle w_{1}} : f ( w 2 , w 1 , β 2 ) = ∑ i = 1 β 2 ( f pmi ( X i w 2 , w 1 ) ) γ {\displaystyle f(w_{2},w_{1},\beta _{2})=\sum _{i=1}^{\beta _{2}}(f^{\text{pmi}}(X_{i}^{w_{2}},w_{1}))^{\gamma }} === Step 4: Calculate final similarity score === Finally, the total semantic similarity is the average of the two scores from the previous step. S i m ( w 1 , w 2 ) = f ( w 1 , w 2 , β 1 ) β 1 + f ( w 2 , w 1 , β 2 ) β 2 {\displaystyle \mathrm {Sim} (w_{1},w_{2})={\frac {f(w_{1},w_{2},\beta _{1})}{\beta _{1}}}+{\frac {f(w_{2},w_{1},\beta _{2})}{\beta _{2}}}} This score can be normalized to fall between 0 and 1. For example, using this method, the words cemetery and graveyard achieve a high similarity score of 0.986 (with specific parameter settings).
Far-Play
Far-Play (stylized fAR-Play, from augmented reality) was a software platform developed at the University of Alberta, for creating location-based, scavenger-hunt style games which use the GPS and web-connectivity features of a player's smartphone. According to the development team, "our long-term objective is to develop a general framework that supports the implementation of AARGs that are fun to play and also educational". It utilizes Layar, an augmented reality smartphone application, QR codes located at particular real-world sites, or a phone's web browser, to facilitate games which require players to be in close physical proximity to predefined "nodes". A node, referred to by the developers as a Virtual Point of Interest (vPOI), is a point in space defined by a set of map coordinates; fAR-Play uses the GPS function of a player's smartphone — or, for indoor games, which are not easily tracked by GPS satellites, specially-created QR codes— to confirm that they are adequately near a given node. Once a player is within a node's proximity, Layar's various augmented reality features can be utilized to display a range of extra content overlaid upon the physical play-space or launch another application for extra functionality. == Development and features == fAR-Play began development in 2008, emerging from a collaborative project undertaken by a group of University of Alberta students from the Computer Science and Humanities Computing departments. fAR-Play is still under development, but a beta version is available for testing by request. fAR-Play's development is managed by a team of interdisciplinary professors and students at the University of Alberta. Currently, the developing team's roster includes Supervising Professors Geoffrey Rockwell and Eleni Stroulia, Developers Lucio Gutierrez and Matthew Delaney, and Website Developers Calen Henry and Garry Wong. === Technology === fAR-Play relies on a number of open- and closed-source web technologies as tools to create, and enhance the users' experience. Layar is the recommended client-side frontend for delivering game content to the player; it is available on Android and iOS, which covers over 91% of smartphones. While Layar is not a requirement to play fAR-Play games, the application does supply additional augmented reality functionality; Layar also includes a built-in QR scanner. Depending on the design of the particular game, the player may instead use a dedicated QR code scanner; the developers recommend BeeTagg, but any such application will do. Layar or a QR code scanner are the maximum software requirements to play a fAR-Play game, making implementation of games on a wide variety of platforms relatively straightforward. fAR-Play games can also be designed for play strictly within a mobile phone's web browser. On the server side, fAR-Play's engine is composed of an Apache server which manages the system's web interface, including the mobile and desktop versions of the fAR-Play website, and a Java-based REST framework for managing the database of nodes. === Features === As a platform for designing AR games, as opposed to an AR game itself, fAR-Play offers little in the way of explicit shapes or patterns for games to take; instead, these elements are left to the game designer or players to develop. However, the nonspecific nature of nodes, the many options they offer for content delivery, and the open design of the platform are such that these elements can be developed extensively. Functionally, fAR-Play is a tool for tracking arbitrary points in space and a given player's proximity to them; what it does beyond that is up to the developers' and players' discretion. However, the fAR-Play website contains a leaderboard which tracks registered user's total scores. Players are assigned levels based on their total score, ranging from Novice — Super Player. Player profiles will display nodes that the player has recently caught, and any achievements the player has gained. Additionally, players can share their adventure progress, achievements, and the capture of vPOIs on Facebook. == How to play == In order to participate in the locative aspects of fAR-Play games, users must have an Android or iOS mobile device and access to wireless internet. Players can participate in fAR-Play anonymously, or create and sign into a fAR-Play account. Those who choose to play anonymously will lose the ability to track their progress across multiple games. When signed in, the player is presented with a list of games that are currently available for play. Each game includes a brief description and the various "adventures" available to the player. Once the game has been started, the player has three different methods for capturing nodes: they may scan a QR in the physical space, discover a node through the Layar camera virtual view, or receive a link in their device's web browser. === QR codes and Layar === QR codes can only be used as a method for capturing nodes and initiating games when there is a physical code present. In order to scan a QR code, players are required to have an application which can capture and recognize QR codes. If the player is utilizing a QR scanning application that has a built in browser, they will be required to log into fAR-Play through the app. Layar is a free to download augmented reality app, containing a built in QR code scanner, which enables its users to participate in fAR-Play games. === Capturing nodes === Layar permits the player to see nodes on their mobile device, guiding the player to their goal. Using this application, the player is able to navigate to their objective with map provided by Google Maps' API or by using their camera — Layar overlays a virtual image onto the real-world scene presented by the camera. The representations on screen expand in size as the player approaches the node destination, simulating relative distance. If the player taps any of the nodes that are presented on the screen, they will be provided additional information about that node, including the node's name and a brief description. Nodes can be captured by tapping the "capture" button. === Playing on browsers === The player can also play fAR-Play games within their mobile device's browser. By visiting https://archive.today/20131123223038/http://farplay.ualberta.ca/far-play/ on a mobile device, players will be presented with a fully realized user interface, permitting full interaction with the games. The player can capture the in game vPOIs through their browser by tapping the "nodes" button. This will bring up a list of all the accessible nodes, complete with a brief description for each location. By clicking on one of the nodes, the player is shown to a screen with a mapped location of the vPOI, an in-depth description of it, and hints. At the top of the page, the player can tap "CAPTURE THIS NODE" and advance in the game. When attempting to capture a node, the developer may or may not associate a challenge with the node. For example, in the game "Zombies ate my Campus", when players are attempting to capture a node, they're presented with a multiple choice question associated with the current node. === Game types === Players complete an adventure when they have captured all of the nodes within it. fAR-Play provides two game modes: in a Virtual Scavenger Hunt, nodes must be captured in a specific order; in a Virtual Treasure Hunt, the order is unimportant. == Existing fAR-Play games == Games currently available through fAR-Play include: Giselle Ever After Thought Hub Comics Arts Capture Challenge Pioneering Edmonton The Intelliphone Challenge A Tour of Atwater Zombies ate my Campus == For developers == fAR-Play's ultimate goal is to provide a simple, effective platform for the creation of locative augmented reality games, but the developer tools are still under active development and not openly available to the public. Access can be granted on a case-by-case basis, however, and a developer's manual is available. Users with development privileges can create new games or edit their existing games, in addition to playing their own or others' games. === Adventures === Games that are developed with fAR-Play are segmented into components called "Adventures". To progress through each game adventure, the player must reach and capture virtual points of interest, referred to in the game as vPOIs. In order to capture a vPOI, the player must travel to a physical location that is set by the developer. It is the developer's choice to include a challenge question to capture the vPOI, though it is not mandatory. A deduction of points can be implemented if the player submits an incorrect answer to a challenge question. === Points and achievements === Each of the nodes will reward the player with a predetermined number of points once they have been captured by the player. These points are added to the player's total points. Each of the adventures that are created require a predetermined number of vPOIs
Raseef22
Raseef22 (Arabic: رصيف22) is a liberal Arabic media network founded in 2013 based in Beirut, Lebanon. It publishes content in Arabic and English from different Arab states and describes itself as an independent media platform. International Media Support mentions Raseef22 along with HuffPost Arabic and Al Jazeera as one of the biggest Pan-Arab online platforms. == Name == The Arabic word raseef (رَصِيف) means platform or pavement, and the number 22 refers to the number of states in the Arab League. == History == Kareem Sakka co-founded Raseef22 in the aftermath of the Arab Spring, which he cites as a source of inspiration. In an article in The Washington Post, he wrote that Raseef22 was created as a "digital space for those eager to know what was going on around them." Raseef22 was one of the 500 websites censored in Egypt in late 2017 after it published an article on Egyptian security agencies' vies to influence the media. After the site was blocked in Egypt, it was targeted in a cyber attack that took it offline in locations around the world. Jamal Khashoggi wrote for Raseef22 regularly. One of his notable articles was "Notes on the Freedom of the Arabs from Oslo, Norway," published June 5, 2018. The site was blocked in Saudi Arabia December 2018 when the Saudi Ministry of Communications and Information Technology ordered its censorship due to its "unprecedented response to the assassination of Jamal Khashoggi in Istanbul." This decision might have also been related to Raseef22's coverage of Saudi-Israeli relations and interviews with activists later imprisoned or placed under house arrest coverage In 2019 the Association of LGBT Journalists (AJL) in Paris gave Raseef22 a golden foreign press award for its six-month series of articles on gender and sexuality issues. == Readership == According to its publisher in 2019, the news agency counted 12 million readers annually from 22 Arab nations. Of the readership, he wrote that it "believes in the talent and promise of the Arab mind and sees the ugliness of tyranny, patriarchy, misogyny and the futility of proxy rulers and wars." Al-Quds Al-Arabi described Raseef22 as "oriented to the youth."
FactorDaily
FactorDaily is an Indian digital media publication founded in 2016 by Pankaj Mishra and Jayadevan PK. Mishra was formerly an Editor at TechCrunch and the Economic Times. The digital publication was launched with an intent to produce stories on the impact of technology on life in India. == History == FactorDaily began publishing in May 2016, with daily reported stories on technology, culture and life in India. Prior to its launch, the company had raised $1 million in seed funding from Accel India, Blume Ventures, Girish Mathrubootham of Freshdesk, Vijay Shekhar Sharma of PayTm, and Jay Vijayan of Tekion. Josey Puliyenthuruthel John, formerly Managing Editor at Business Today and National Corporate Editor at Mint, later joined the company as a Consulting Editor. In January 2017, FactorDaily launched its first Podcast called The Outliers. The inaugural episode featured a conversation with Manish Sharma of Printo on his journey starting up. == Awards == The FactorDaily team won the Bengaluru Editors Lab 2017, a journalism hackathon organised by the Global Editors Network (GEN). The story titled "India has 3,800 psychiatrists for 1.2bn people. Can tech step in to manage mental health?" won the first prize in the online category of the fifth Schizophrenia Research Foundation’s (SCARF) ‘Media for Mental Health’ awards. The story titled 'The dark hand of tech that stokes sex trafficking in India', won the Stop Slavery media Awards by the Thomson Reuters Foundation for the year 2020.
Superquadrics
In mathematics, the superquadrics or super-quadrics (also superquadratics) are a family of geometric shapes defined by formulas that resemble those of ellipsoids and other quadrics, except that the squaring operations are replaced by arbitrary powers. They can be seen as the three-dimensional relatives of the superellipses. The term may refer to the solid object or to its surface, depending on the context. The equations below specify the surface; the solid is specified by replacing the equality signs by less-than-or-equal signs. The superquadrics include many shapes that resemble cubes, octahedra, cylinders, lozenges and spindles, with rounded or sharp corners. Because of their flexibility and relative simplicity, they are popular geometric modeling tools, especially in computer graphics. It becomes an important geometric primitive widely used in computer vision, robotics, and physical simulation. Some authors, such as Alan Barr, define "superquadrics" as including both the superellipsoids and the supertoroids. In modern computer vision literatures, superquadrics and superellipsoids are used interchangeably, since superellipsoids are the most representative and widely utilized shape among all the superquadrics. Comprehensive coverage of geometrical properties of superquadrics and methods of their recovery from range images and point clouds are covered in several computer vision literatures. == Formulas == === Implicit equation === The surface of the basic superquadric is given by | x | r + | y | s + | z | t = 1 {\displaystyle \left|x\right|^{r}+\left|y\right|^{s}+\left|z\right|^{t}=1} where r, s, and t are positive real numbers that determine the main features of the superquadric. Namely: less than 1: a pointy octahedron modified to have concave faces and sharp edges. exactly 1: a regular octahedron. between 1 and 2: an octahedron modified to have convex faces, blunt edges and blunt corners. exactly 2: a sphere greater than 2: a cube modified to have rounded edges and corners. infinite (in the limit): a cube Each exponent can be varied independently to obtain combined shapes. For example, if r=s=2, and t=4, one obtains a solid of revolution which resembles an ellipsoid with round cross-section but flattened ends. This formula is a special case of the superellipsoid's formula if (and only if) r = s. If any exponent is allowed to be negative, the shape extends to infinity. Such shapes are sometimes called super-hyperboloids. The basic shape above spans from -1 to +1 along each coordinate axis. The general superquadric is the result of scaling this basic shape by different amounts A, B, C along each axis. Its general equation is | x A | r + | y B | s + | z C | t = 1. {\displaystyle \left|{\frac {x}{A}}\right|^{r}+\left|{\frac {y}{B}}\right|^{s}+\left|{\frac {z}{C}}\right|^{t}=1.} === Parametric description === Parametric equations in terms of surface parameters u and v (equivalent to longitude and latitude if m equals 2) are x ( u , v ) = A g ( v , 2 r ) g ( u , 2 r ) y ( u , v ) = B g ( v , 2 s ) f ( u , 2 s ) z ( u , v ) = C f ( v , 2 t ) − π 2 ≤ v ≤ π 2 , − π ≤ u < π , {\displaystyle {\begin{aligned}x(u,v)&{}=Ag\left(v,{\frac {2}{r}}\right)g\left(u,{\frac {2}{r}}\right)\\y(u,v)&{}=Bg\left(v,{\frac {2}{s}}\right)f\left(u,{\frac {2}{s}}\right)\\z(u,v)&{}=Cf\left(v,{\frac {2}{t}}\right)\\&-{\frac {\pi }{2}}\leq v\leq {\frac {\pi }{2}},\quad -\pi \leq u<\pi ,\end{aligned}}} where the auxiliary functions are f ( ω , m ) = sgn ( sin ω ) | sin ω | m g ( ω , m ) = sgn ( cos ω ) | cos ω | m {\displaystyle {\begin{aligned}f(\omega ,m)&{}=\operatorname {sgn}(\sin \omega )\left|\sin \omega \right|^{m}\\g(\omega ,m)&{}=\operatorname {sgn}(\cos \omega )\left|\cos \omega \right|^{m}\end{aligned}}} and the sign function sgn(x) is sgn ( x ) = { − 1 , x < 0 0 , x = 0 + 1 , x > 0. {\displaystyle \operatorname {sgn}(x)={\begin{cases}-1,&x<0\\0,&x=0\\+1,&x>0.\end{cases}}} === Spherical product === Barr introduces the spherical product which given two plane curves produces a 3D surface. If f ( μ ) = ( f 1 ( μ ) f 2 ( μ ) ) , g ( ν ) = ( g 1 ( ν ) g 2 ( ν ) ) {\displaystyle f(\mu )={\begin{pmatrix}f_{1}(\mu )\\f_{2}(\mu )\end{pmatrix}},\quad g(\nu )={\begin{pmatrix}g_{1}(\nu )\\g_{2}(\nu )\end{pmatrix}}} are two plane curves then the spherical product is h ( μ , ν ) = f ( μ ) ⊗ g ( ν ) = ( f 1 ( μ ) g 1 ( ν ) f 1 ( μ ) g 2 ( ν ) f 2 ( μ ) ) {\displaystyle h(\mu ,\nu )=f(\mu )\otimes g(\nu )={\begin{pmatrix}f_{1}(\mu )\ g_{1}(\nu )\\f_{1}(\mu )\ g_{2}(\nu )\\f_{2}(\mu )\end{pmatrix}}} This is similar to the typical parametric equation of a sphere: x = x 0 + r sin θ cos φ y = y 0 + r sin θ sin φ ( 0 ≤ θ ≤ π , 0 ≤ φ < 2 π ) z = z 0 + r cos θ {\displaystyle {\begin{aligned}x&=x_{0}+r\sin \theta \;\cos \varphi \\y&=y_{0}+r\sin \theta \;\sin \varphi \qquad (0\leq \theta \leq \pi ,\;0\leq \varphi <2\pi )\\z&=z_{0}+r\cos \theta \end{aligned}}} which give rise to the name spherical product. Barr uses the spherical product to define quadric surfaces, like ellipsoids, and hyperboloids as well as the torus, superellipsoid, superquadric hyperboloids of one and two sheets, and supertoroids. == Plotting code == The following GNU Octave code generates a mesh approximation of a superquadric:
Digital media service
A digital media service (DMS) is an online service provider that sells access to digital library of content such as films, software, games, images, literature, etc. While no transfer of property is made, a nearly perfect duplicate of the data (song movie, etc.) is made on a customer's computer. Content is either primarily hosted on a dedicated server, which is owned by the service provider, or it is hosted primarily on the hard drives of its customers using a P2P protocol with, perhaps, a dedicated server to supplement. == History == One example of the older business model is the iTunes Store, which still markets and prices data as individual retail products. There are no examples of the latter business model in operation yet, but one is currently in development by Global Gaming Factory X and expected to begin operation some time after they acquire The Pirate Bay domain on August 27, 2009. A key difference between the two models is that the model which relies on its customer base for offering their bandwidth for other customers to access customer hosted data can operate at significantly lower costs than a company that seeks to limit data access to a per-download fee in order to supplement the cost of using its own hosting and bandwidth. The P2P model holds the potential for companies to offer unlimited access to the largest data library in the history of the internet to its customers for a reasonably low membership rate that is relevant to the cost of operation. While the market is virtually untouched, the P2P supplemented model will need entrepreneurs who are able to overcome a series of challenges in order to compete with the older business model as well as that which is offered for free (and often against the wishes of copyright holders) by hundreds of P2P communities on the internet. These challenges include, but are not limited to: Offering better data quality, speed, convenience and ease of use, protocol, sense of security, indexing and search organization, site up time, data library size, customer support, advertising, artist/copyright holder incentives and compensation, incentives and compensation for customers hosting data and providing bandwidth, guaranteed seeding (available access to indexed data at all times), than competitors.