AI Code Understanding

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Coalition for App Fairness

The Coalition for App Fairness (CAF) is a coalition comprised by companies, who aim to reach a fairer deal for the inclusion of their apps into the Apple App Store or the Google Play Store. The organization's executive director is Meghan DiMuzio and its headquarters are located in Washington, D.C. == Background == In July 2015, Spotify launched an email campaign to urge its App Store subscribers to cancel their subscriptions and start new ones through its website, bypassing the 30% transaction fee for in-app purchases required for iOS applications by technology company Apple Inc. A later update to the Spotify app on iOS was rejected by Apple, prompting Spotify's general counsel Horacio Gutierrez to write a letter to Apple's then-general counsel Bruce Sewell, stating: "This latest episode raises serious concerns under both U.S. and EU competition law. It continues a troubling pattern of behavior by Apple to exclude and diminish the competitiveness of Spotify on iOS and as a rival to Apple Music, particularly when seen against the backdrop of Apple's previous anticompetitive conduct aimed at Spotify … we cannot stand by as Apple uses the App Store approval process as a weapon to harm competitors." In August 2020, Epic Games updated their Fortnite Battle Royale game app on both Apple's App Store and Google's Google Play to include its own storefront that offered a 20% discount on V-Bucks, the in-game currency, if players bought through there rather than through the app stores' storefront, both which take a 30% revenue cut of the sale. Both Apple and Google removed the Fortnite app within hours, as this alternate storefront violated their terms of use that required all in-app purchases to be made through their storefronts. Epic immediately filed lawsuits against both companies challenging their storefront policies on antitrust principles, arguing that their non-negotiable 30% revenue cut is too high and the restrictions against alternate storefronts anticompetitive. Apple countersued Epic over its behavior, leading to a highly publicized 2021 bench trial. Ultimately, Epic largely lost its lawsuit against Apple, though the court did order Apple to allow developers to point users to alternative payment methods. Conversely, Epic won its antitrust lawsuit against Google in late 2023. == Foundation == On 24 September 2020, Epic Games joined forces with thirteen other prominent companies—including the music streaming platform Spotify, Tinder owner Match Group, the encrypted mail service Proton Mail, and the crypto currency website Blockchain.com—to establish the Coalition for App Fairness. It also includes Basecamp. The coalition criticizes the fact that for now the app stores of both Apple and Google charge their clients a 30% fee on any purchases made over their stores. Apple and Google defended themselves by arguing that the 30% transaction fee is a standard in the industry while the Coalition for App Fairness states that there is no other transaction fee which is even close to the 30%. In October 2020, it was reported that the coalition grew from 13 to 40 members since its foundation and received more than 400 applications for membership. In October 2025, X (formerly Twitter) joined CAF. This was seen as a larger pushback in the industry against Apple and Google, and a step towards hopefully passing the Bipartisan Open App Markets Act. == Aims == The group has broadened their demands for the app stores and now also aim for a better treatment for the apps available in the App Store. They claim that Apple favors its own services before other services available on the market and unjustifiably excludes other apps from their App Store. The group has also been viewing other transaction fees like the 5% fee which is charged by credit card companies, and states that Apple charges up to 600% more and would like the 30% fee, which was only included in 2011 by Apple, adapted to a comparable percentage that charge other providers of payment solutions. Its demands are mainly directed at Apple's strict control over its App Store, but to a lesser extent are also directed towards Google. Google allows apps to be downloaded over an independent web link or also another App Store, such as the Epic Game App Store. The organization emphasizes that no app developer should come into the position in which they are discriminated and are not granted the same rights as to the developers of the owner of the app store. == Reactions == In October 2020, Microsoft presented a new framework concerning the access to its Windows 10 operating system by app stores other than the one offered by Microsoft. The new framework is based on the demands of the Coalition for App Fairness. Microsoft emphasized though, that these principles would not apply to the Xbox. In December 2020, Apple announced that they would be lowering the revenue cut Apple takes for app developers making $1M or less from 30% to 15% if app developers fill out an application for the lowered revenue cut. In March 2021, Google followed suit by also lowering the revenue cut from the Play Store from 30% to 15% for the first million in revenue earned by a developer each year. == Notable members == Members listed are notable companies listed as members the groups website: Blockchain.com Deezer Epic Games European Digital SME Alliance Fanfix Life360 Masimo Nium Proton Mail Spotify TapTap Threema Vipps
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Instagram egg

The Instagram egg is a photo of an egg posted by the account @world_record_egg on the social media platform Instagram. It became a global phenomenon and an internet meme within days of its publication on 4 January 2019. It is the second most-liked Instagram post and was the most-liked Instagram post from 14 January 2019 until 20 December 2022, when it was overtaken by Lionel Messi's post showing him and his teammates celebrating after Argentina won the 2022 FIFA World Cup. The owner of the account was revealed to be Chris Godfrey, a British advertising creative, who later worked with his two friends Alissa Khan-Whelan and CJ Brown on a Hulu commercial featuring the egg, intended to raise mental health awareness. == Background == The photo was originally taken by Serghei Platanov, who then posted it to Shutterstock on 23 June 2015 with the title "eggs isolated on white background". == History == On 4 January 2019, the @world_record_egg account was created, and posted an image of a bird egg with the caption, "Let's set a world record together and get the most liked post on Instagram. Beating the current world record held by Kylie Jenner (18 million)! We got this." Jenner's previous record, the first photo of her daughter Stormi, had garnered a total of 18.4 million likes. The post quickly reached 18.4 million likes in just under 10 days, becoming the most-liked Instagram post at the time. It then continued to rise over 45 million likes in the next 48 hours, surpassing the "Despacito" music video and taking the world record for the most-liked online post (on any media platform) in history. After the account became verified on 14 January 2019, the post rose in popularity and likes, which snowballed into coverage in various media outlets. By 18 March 2019, the post had accumulated over 53.3 million likes, nearly three times the previous record of 18.4 million. It posted frequent updates for a few days in the form of Instagram Stories. Alongside the like tally, as of January 2023 the post has 3.8 million comments. Several individuals tried to claim that they were the account's creator, the claims being dismissed by "the egg" on Instagram direct messages. On 3 February 2019, the creator of the Instagram egg was revealed by Hulu and The New York Times to be Chris Godfrey, a British advertising creative. Alissa Khan-Whelan, his colleague, was also outed. On 18 January 2019, the account posted a second picture of an egg, almost identical to the first one apart from a small crack at the top left. As of 25 February 2019, the post accumulated 11.8 million likes. On 22 January 2019, the account posted a third picture of an egg, this time having two larger cracks. In less than 25 minutes, the post accumulated 1 million likes, and by 25 February 2019, it had accumulated 9.5 million likes. On 29 January 2019, a fourth picture of an egg was posted to the account which has another large crack on the right hand side, attracting 7.6 million likes by 25 February 2019. On 1 February 2019, a fifth picture of an egg was posted with stitching like that of a football, referencing the upcoming Super Bowl. That post had accumulated 6.5 million likes by 25 February 2019. The account promised that it would reveal what was inside the egg on 3 February, on the subscription video on demand service Hulu. The Hulu Instagram egg reveal was used to promote an animation about a mental health campaign. A caption from the clip read, "Recently I've started to crack, the pressure of social media is getting to me. If you're struggling too, talk to someone." The video was later posted on the @world_record_egg Instagram account, and this post received over 33 million views by May 2019. As of May 2020, it had received over 41 million views. On 16 July 2019, Chris Godfrey (the creator of the account) was listed as one of the top 25 most influential people on the internet. On 20 December 2022, the record for the most-liked Instagram post was surpassed by a post from Argentine footballer Lionel Messi, showing him and his teammates celebrating after winning the 2022 FIFA World Cup with their national team. The world record egg responded to being overtaken in likes by Messi with "Today [Lionel Messi] has taken the crown, for now. But I'm still left with one question… Who is the greatest of all time – Cristiano Ronaldo or Leo Messi?" The account sold to Dubai-based investor Mustafa El Fishawy in April 2024 for an undisclosed seven-figure sum. Reed Smith, who advised Godfrey, Brown, and Khan-Whelan in the transaction, stated they opted to sell it to "focus on new ventures." On 3 June, @world_record_egg posted an egg with the flag of Palestine in support of the country during the Gaza war; the post's caption described it as an "Egg for Peace" and hoped to "set a new world record together and get the most liked post on Instagram for a good cause." == Reception == In response to breaking the world record for the most-liked Instagram post, the account's owner wrote "This is madness. What a time to be alive." Hours later, Jenner posted a video on Instagram of her cracking open an egg and pouring its yolk onto the ground, with the caption: "Take that little egg." Pundits pontificated on the meaning of the egg picture's dominance over social media's "first family". As Vogue observed, tapping a heart pictogram is easy, and eggs are "lovable". More pointedly: [T]he attention economy is a scam based on requiring little to no labor from both producer and consumer despite commanding the most space, and therefore value, in our digital lives... but it very well could be: As a metaphor for the fragility of the influencer ecosystem, the egg has broken the Internet. The significance of the event and its massive republishing are a topic of discussion. A University of Westminster researcher of internet memes compared it to the movement to name a scientific research vessel in the United Kingdom as Boaty McBoatface. The Instagrammer's success is a rare victory for the unpaid viral campaign on social media. "There is a bit of an anti-celebrity revolt here – 'look what we can do with a simple egg'" The researcher suggests that the accomplishment of becoming such a widely heralded unpaid viral post may become increasingly rare, as social networks rely more on paid and business promotion. The post's spread has been characterized as a populist backlash against "consumerism" and is seen by some as a triumph of community over celebrity. However, propelled by their popular success, the creators promised to release 'egg-centric' memorabilia. Hundreds of games based on the Instagram egg have appeared on Apple's App Store. The creators of the Instagram egg also reached a deal to promote Hulu.
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SIGINT Activity Designator

A SIGINT Activity Designator (or SIGAD) identifies a signals intelligence (SIGINT) line of collection activity associated with a signals collection station, such as a base or a ship. For example, the SIGAD for Menwith Hill in the UK is USD1000. SIGADs are used by the signals intelligence agencies of Australia, Canada, New Zealand, the United Kingdom, and the United States (the Five Eyes). There are several thousand SIGADs including the substation SIGADs denoted with a trailing alpha character. Several dozen of these are significant. The leaked Boundless Informant reporting screenshot showed that it summarized 504 active SIGADs during a 30-day period in March 2013. == General format == A SIGAD consists of five to eight case insensitive alphanumeric characters. It takes the general form of an alphanumeric designator normally composed of a two- or three-letter prefix followed by one to three numbers. Often a dash is used to separate the alphabetic and numeric characters in the primary part of the designator, but less frequently a space is used as a separator or the alphabetic and numeric characters are concatenated together. An additional alphabetic character can be added to denote a sub-designator for a subset of the primary unit, such as a detachment. Lastly, a numeric character can be added after the aforementioned alphabetic to provide for a sub-sub-designator. In the examples below an X represents an alphabetic character and an N represents a numeric character that are part of the primary designator. Likewise, an x represents an alphabetic character and an n represents a numeric character that are part of a sub-designator. Here are valid generalized examples of SIGADs: The first two characters show which country operates the particular SIGINT facility, which can be US for the United States, UK for the United Kingdom, CA for Canada, AU for Australia and NZ for New Zealand. A third letter shows what sort of staff runs the station. SIGADs beginning with US without a third letter are used for intercept facilities run by the NSA. == PRISM SIGAD == One prominent SIGAD as of April 2013 is US-984XN, with an unclassified codename of PRISM. It is "the number one source of raw intelligence used for NSA analytic reports" according to National Security Agency sources in a document leaked by Edward Snowden. The President's Daily Brief, an all-source intelligence product, cited SIGAD US-984XN as a source in 1,477 items in 2012. The U.S. government operates the PRISM electronic surveillance collection program through NSA's Special Source Operations, an alliance with trusted telecommunications providers. == SIGADs for spy ships == The declassified SIGAD for the USS Liberty (AGTR-5) was USN-855. The USS Liberty incident occurred on 8 June 1967, during the Six-Day War, when Israeli Air Force jet fighter aircraft and Israeli Navy motor torpedo boats attacked the USS Liberty in international waters. The USS Pueblo (AGER-2) was a technical research ship, which was boarded and captured by North Korean forces on 23 January 1968, in what is known as the Pueblo incident. The declassified SIGAD for the NSA Direct Support Unit (DSU) from the Naval Security Group (NSG) on the USS Pueblo patrol involved in the incident was USN-467Y. The USS Pueblo, which officially remains a commissioned vessel of the United States Navy, is the only ship of the U.S. Navy currently being held captive. == Vietnam War SIGADs == The following are the Vietnam War-era declassified SIGADs from inside South Vietnam during the period of 1969 to 1975: Some locations have multiple SIGADs due to different types of collection activities and/or collection at different times during the period. The SIGADs beginning with USA were operated by the United States Air Force's United States Air Force Security Service (USAFSS). The SIGADs beginning with USM were operated by the United States Army's Army Security Agency (ASA). Lastly, the SIGADs beginning with USN were operated by the United States Navy's Naval Security Group (NAVSECGRU). All three of these units have been merged into other units or inactivated. The above list consists of the higher-echelon SIGADs. It does not include the numerous miscellaneous and temporary detachments, or direction finding stations belonging to major units or sites unless that detachment or site was the only one stationed in South Vietnam. Many of the "dets" were short-lived, often formed to support ongoing MACV operations or forward deployments of combat operational or maneuver units. These detachments usually were designated by a letter suffix attached to the higher-echelon SIGAD such as "USM-633J," which was a detachment of the 372d Radio Research Company, USM-633, supporting the United States Army's 25th Infantry Division. === Supporting Southeast Asia SIGADs === The following declassified SIGADs were highly relevant to the Vietnam Campaign, but were located in areas outside of South Vietnam in Southeast Asia. Again, detachments are not listed separately. In the case of the USS Maddox, naval Direct Support Units (DSUs) used the SIGAD USN-467 as a generic designator for their missions. Each specific patrol received a letter suffix for its duration. The subsequent mission would receive the next letter in an alphabetic sequence. Thus, SIGAD USN-467N specifically designates the USS Maddox patrol involved with the Gulf of Tonkin incident. == Joint Base SIGADs == In November 2005, the US Congress performed a fifth round of Base Realignment and Closure. This 2005 law also created twelve joint bases by merging adjacent installations belonging to different services in an effort to reduce costs and improve efficiencies. Joint bases with a primarily SIGINT mission have SIGADs that begin with USJ. A joint base would have a primary SIGAD in the general form of USJ-NNN, where NNN are numeric characters. An actual example is not given, since these units are currently active.
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Cloud Data Management Interface

ISO/IEC 17826 Information technology — Cloud Data Management Interface (CDMI) Version 2.0.0 is an international standard that specifies a protocol for self-provisioning, administering and managing access to data stored in cloud storage, object storage, storage area network and network attached storage systems. The CDMI standard is developed and maintained by the Storage Networking Industry Association, who makes a publicly accessible version of the specification available. CDMI defines new resource representations to enable standardized management of any URI-accessible data, and defines RESTful HTTP operations using these representations to discover the capabilities of the storage system, discover stored data, access and update management metadata, specify data storage protocols (such as iSCSI and NFS) through which the stored data is accessed, and provide cross-system and cross-cloud import and export in order to enable data portability. Management functions enabled by CDMI include managing data ownership, identity mapping, access controls, user-specified metadata, and to declaratively specify desired data protection, data retention, constraints on geographic placement, desired quality of service, data versioning and security requirements. CDMI also defines utility services to facilitate data management, such the ability to query data matching specific criteria, and includes extensions to perform bulk updates using CDMI Jobs. == Capabilities == Compliant implementations must provide access to a set of configuration parameters known as capabilities. These are either boolean values that represent whether or not a system supports things such as queues, export via other protocols, path-based storage and so on, or numeric values expressing system limits, such as how much metadata may be placed on an object. As a minimal compliant implementation can be quite small, with few features, clients need to check the cloud storage system for a capability before attempting to use the functionality it represents. Resource allocation assignments limited to the data management interface protocols must possess access bypass capabilities which extend beyond the layered framework. This integral function is vital to the prevention of transport layer session hijacking by unauthorized entities which may circumvent standard interfacing security parameters. == Containers == A CDMI client may access objects, including containers, by either name or object id (OID), assuming the CDMI server supports both methods. When storing objects by name, it is natural to use nested named containers; the resulting structure corresponds exactly to a traditional filesystem directory structure. == Objects == Objects are similar to files in a traditional file system, but are enhanced with an increased amount and capacity for metadata. As with containers, they may be accessed by either name or OID. When accessed by name, clients use URLs that contain the full pathname of objects to create, read, update and delete them. When accessed by OID, the URL specifies an OID string in the cdmi-objectid container; this container presents a flat name space conformant with standard object storage system semantics. Subject to system limits, objects may be of any size or type and have arbitrary user-supplied metadata attached to them. Systems that support query allow arbitrary queries to be run against the metadata. == Domains, Users and Groups == CDMI supports the concept of a domain, similar in concept to a domain in the Windows Active Directory model. Users and groups created in a domain share a common administrative database and are known to each other on a "first name" basis, i.e. without reference to any other domain or system. Domains also function as containers for usage and billing summary data. == Access Control == CDMI exactly follows the ACL and ACE model used for file authorization operations by NFSv4. This makes it also compatible with Microsoft Windows systems. == Metadata == CDMI draws much of its metadata model from the XAM specification. Objects and containers have "storage system metadata", "data system metadata" and arbitrary user specified metadata, in addition to the metadata maintained by an ordinary filesystem (atime etc.). == Queries == CDMI specifies a way for systems to support arbitrary queries against CDMI containers, with a rich set of comparison operators, including support for regular expressions. == Queues == CDMI supports the concept of persistent FIFO (first-in, first-out) queues. These are useful for job scheduling, order processing and other tasks in which lists of things must be processed in order. == Compliance == Both retention intervals and retention holds are supported by CDMI. A retention interval consists of a start time and a retention period. During this time interval, objects are preserved as immutable and may not be deleted. A retention hold is usually placed on an object because of judicial action and has the same effect: objects may not be changed nor deleted until all holds placed on them are removed. == Billing == Summary information suitable for billing clients for on-demand services can be obtained by authorized users from systems that support it. == Serialization == Serialization of objects and containers allows export of all data and metadata on a system and importation of that data into another cloud system. == Foreign protocols == CDMI supports export of containers as NFS or CIFS shares. Clients that mount these shares see the container hierarchy as an ordinary filesystem directory hierarchy, and the objects in the containers as normal files. Metadata outside of ordinary filesystem metadata may or may not be exposed. Provisioning of iSCSI LUNs is also supported. == Client SDKs == CDMI Reference Implementation Droplet libcdmi-java libcdmi-python .NET SDK
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Richardson–Lucy deconvolution

The Richardson–Lucy algorithm, also known as Lucy–Richardson deconvolution, is an iterative procedure for recovering an underlying image that has been blurred by a known point spread function. It was named after William Richardson and Leon B. Lucy, who described it independently. == Description == When an image is produced using an optical system and detected using photographic film, a charge-coupled device or a CMOS sensor, for example, it is inevitably blurred, with an ideal point source not appearing as a point but being spread out into what is known as the point spread function. Extended sources can be decomposed into the sum of many individual point sources, thus the observed image can be represented in terms of a transition matrix p operating on an underlying image: d i = ∑ j p i , j u j , {\displaystyle d_{i}=\sum _{j}p_{i,j}u_{j},} where u j {\displaystyle u_{j}} is the intensity of the underlying image at pixel j {\displaystyle j} , and d i {\displaystyle d_{i}} is the detected intensity at pixel i {\displaystyle i} . In general, a matrix whose elements are p i , j {\displaystyle p_{i,j}} describes the portion of light from source pixel j that is detected in pixel i. In most good optical systems (or in general, linear systems that are described as shift-invariant) the transfer function p can be expressed simply in terms of the spatial offset between the source pixel j and the observation pixel i: p i , j = P ( i − j ) , {\displaystyle p_{i,j}=P(i-j),} where P ( Δ i ) {\displaystyle P(\Delta i)} is called a point spread function. In that case the above equation becomes a convolution. This has been written for one spatial dimension, but most imaging systems are two-dimensional, with the source, detected image, and point spread function all having two indices. So a two-dimensional detected image is a convolution of the underlying image with a two-dimensional point spread function P ( Δ x , Δ y ) {\displaystyle P(\Delta x,\Delta y)} plus added detection noise. In order to estimate u j {\displaystyle u_{j}} given the observed d i {\displaystyle d_{i}} and a known P ( Δ i x , Δ j y ) {\displaystyle P(\Delta i_{x},\Delta j_{y})} , the following iterative procedure is employed in which the estimate of u j {\displaystyle u_{j}} (called u ^ j ( t ) {\displaystyle {\hat {u}}_{j}^{(t)}} ) for iteration number t is updated as follows: u ^ j ( t + 1 ) = u ^ j ( t ) ∑ i d i c i p i j , {\displaystyle {\hat {u}}_{j}^{(t+1)}={\hat {u}}_{j}^{(t)}\sum _{i}{\frac {d_{i}}{c_{i}}}p_{ij},} where c i = ∑ j p i j u ^ j ( t ) , {\displaystyle c_{i}=\sum _{j}p_{ij}{\hat {u}}_{j}^{(t)},} and ∑ j p i j = 1 {\displaystyle \sum _{j}p_{ij}=1} is assumed. It has been shown empirically that if this iteration converges, it converges to the maximum likelihood solution for u j {\displaystyle u_{j}} . Writing this more generally for two (or more) dimensions in terms of convolution with a point spread function P: u ^ ( t + 1 ) = u ^ ( t ) ⋅ ( d u ^ ( t ) ⊗ P ⊗ P ∗ ) , {\displaystyle {\hat {u}}^{(t+1)}={\hat {u}}^{(t)}\cdot \left({\frac {d}{{\hat {u}}^{(t)}\otimes P}}\otimes P^{}\right),} where the division and multiplication are element-wise, ⊗ {\displaystyle \otimes } indicates a 2D convolution, and P ∗ {\displaystyle P^{}} is the mirrored point spread function, or the inverse Fourier transform of the Hermitian transpose of the optical transfer function. In problems where the point spread function p i j {\displaystyle p_{ij}} is not known a priori, a modification of the Richardson–Lucy algorithm has been proposed, in order to accomplish blind deconvolution. == Derivation == In the context of fluorescence microscopy, the probability of measuring a set of number of photons (or digitalization counts proportional to detected light) m = [ m 0 , … , m K ] {\displaystyle \mathbf {m} =[m_{0},\dots ,m_{K}]} for expected values E = [ E 0 , … , E K ] {\displaystyle \mathbf {E} =[E_{0},\dots ,E_{K}]} for a detector with K + 1 {\displaystyle K+1} pixels is given by P ( m ∣ E ) = ∏ i K Poisson ⁡ ( E i ) = ∏ i K E i m i e − E i m i ! . {\displaystyle P(\mathbf {m} \mid \mathbf {E} )=\prod _{i}^{K}\operatorname {Poisson} (E_{i})=\prod _{i}^{K}{\frac {E_{i}^{m_{i}}e^{-E_{i}}}{m_{i}!}}.} Since in the context of maximum-likelihood estimation the aim is to locate the maximum of the likelihood function without concern for its absolute value, it is convenient to work with ln ⁡ ( P ) {\displaystyle \ln(P)} : ln ⁡ P ( m ∣ E ) = ∑ i K [ ( m i ln ⁡ E i − E i ) − ln ⁡ ( m i ! ) ] . {\displaystyle \ln P(\mathbf {m} \mid \mathbf {E} )=\sum _{i}^{K}[(m_{i}\ln E_{i}-E_{i})-\ln(m_{i}!)].} Moreover, since ln ⁡ ( m i ! ) {\displaystyle \ln(m_{i}!)} is a constant, it does not give any additional information regarding the position of the maximum, so consider α ( m ∣ E ) = ∑ i K [ m i ln ⁡ E i − E i ] , {\displaystyle \alpha (\mathbf {m} \mid \mathbf {E} )=\sum _{i}^{K}[m_{i}\ln E_{i}-E_{i}],} where α {\displaystyle \alpha } is something that shares the same maximum position as P ( m ∣ E ) {\displaystyle P(\mathbf {m} \mid \mathbf {E} )} . Now consider that E {\displaystyle \mathbf {E} } comes from a ground truth x {\displaystyle \mathbf {x} } and a measurement H {\displaystyle \mathbf {H} } which is assumed to be linear. Then E = H x , {\displaystyle \mathbf {E} =\mathbf {H} \mathbf {x} ,} where a matrix multiplication is implied. This can also be written in the form E m = ∑ n K H m n x n , {\displaystyle E_{m}=\sum _{n}^{K}H_{mn}x_{n},} where it can be seen how H {\displaystyle H} mixes or blurs the ground truth. It can also be shown that the derivative of an element of E {\displaystyle \mathbf {E} } , ( E i ) {\displaystyle (E_{i})} with respect to some other element of x j {\displaystyle x_{j}} can be written as It is easy to see this by writing a matrix H {\displaystyle \mathbf {H} } of, say, 5 × 5 and two arrays E {\displaystyle \mathbf {E} } and x {\displaystyle \mathbf {x} } of 5 elements and check it. This last equation can be interpreted as how much one element of x {\displaystyle \mathbf {x} } , say element i {\displaystyle i} , influences the other elements j ≠ i {\displaystyle j\neq i} (and of course the case i = j {\displaystyle i=j} is also taken into account). For example, in a typical case an element of the ground truth x {\displaystyle \mathbf {x} } will influence nearby elements in E {\displaystyle \mathbf {E} } but not the very distant ones (a value of 0 {\displaystyle 0} is expected on those matrix elements). Now, the key and arbitrary step: x {\displaystyle \mathbf {x} } is not known but may be estimated by x ^ {\displaystyle {\hat {\mathbf {x} }}} . Let's call x ^ old {\displaystyle {\hat {\mathbf {x} }}_{\text{old}}} and x ^ new {\displaystyle {\hat {\mathbf {x} }}_{\text{new}}} the estimated ground truths while using the RL algorithm, where the hat symbol is used to distinguish ground truth from estimator of the ground truth where ∂ ∂ x {\displaystyle {\frac {\partial }{\partial \mathbf {x} }}} stands for a K {\displaystyle K} -dimensional gradient. Performing the partial derivative of α ( m ∣ E ( x ) ) {\displaystyle \alpha (\mathbf {m} \mid \mathbf {E} (\mathbf {x} ))} yields the following expression: ∂ α ( m ∣ E ( x ) ) ∂ x j = ∂ ∂ x j ∑ i K [ m i ln ⁡ E i − E i ] = ∑ i K [ m i E i ∂ ∂ x j E i − ∂ ∂ x j E i ] = ∑ i K ∂ E i ∂ x j [ m i E i − 1 ] . {\displaystyle {\frac {\partial \alpha (\mathbf {m} \mid \mathbf {E} (\mathbf {x} ))}{\partial x_{j}}}={\frac {\partial }{\partial x_{j}}}\sum _{i}^{K}[m_{i}\ln E_{i}-E_{i}]=\sum _{i}^{K}\left[{\frac {m_{i}}{E_{i}}}{\frac {\partial }{\partial x_{j}}}E_{i}-{\frac {\partial }{\partial x_{j}}}E_{i}\right]=\sum _{i}^{K}{\frac {\partial E_{i}}{\partial x_{j}}}\left[{\frac {m_{i}}{E_{i}}}-1\right].} By substituting (1), it follows that ∂ α ( m ∣ E ( x ) ) ∂ x j = ∑ i K H i j [ m i E i − 1 ] . {\displaystyle {\frac {\partial \alpha (\mathbf {m} \mid \mathbf {E} (\mathbf {x} ))}{\partial x_{j}}}=\sum _{i}^{K}H_{ij}\left[{\frac {m_{i}}{E_{i}}}-1\right].} Note that H j i T = H i j {\displaystyle H_{ji}^{T}=H_{ij}} by the definition of a matrix transpose. And hence Since this equation is true for all j {\displaystyle j} spanning all the elements from 1 {\displaystyle 1} to K {\displaystyle K} , these K {\displaystyle K} equations may be compactly rewritten as a single vectorial equation ∂ α ( m ∣ E ( x ) ) ∂ x = H T [ m E − 1 ] , {\displaystyle {\frac {\partial \alpha (\mathbf {m} \mid \mathbf {E} (\mathbf {x} ))}{\partial \mathbf {x} }}=\mathbf {H} ^{T}\left[{\frac {\mathbf {m} }{\mathbf {E} }}-\mathbf {1} \right],} where H T {\displaystyle \mathbf {H} ^{T}} is a matrix, and m {\displaystyle \mathbf {m} } , E {\displaystyle \mathbf {E} } and 1 {\displaystyle \mathbf {1} } are vectors. Now, as a seemingly arbitrary but key step, let where 1 {\displaystyle \mathbf {1} } is a vector of ones of size K {\displaystyle K} (same as m {\displaystyle \mathbf {m} } , E {\displaystyle \mathbf {E} } and x {\displaystyle \mathbf {x} } ), and the d
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Thirst trap

A thirst trap is a type of social media post intended to entice viewers sexually. It refers to a viewer's "thirst", a colloquialism likening sexual frustration to dehydration, implying desperation, with the afflicted individual being described as "thirsty". The phrase entered into the lexicon in the late 1990s, but is most related to Internet slang that developed in the early 2010s. Its meaning has changed over time, previously referring to a graceless need for approval, affection or attention. == History == The term thirst trap originated within selfie culture, though its precise origins remain unclear. An early use of the phrase with reference to dehydration appears in the 1999 book Running for Dummies by Florence Griffith Joyner and John Hanc, where it referred to the deceptive sensation of thirst being quenched after initial fluid intake, advising continued hydration to avoid the so-called "thirst trap." The modern usage of thirst trap resurfaced around 2011 on platforms such as Twitter and Urban Dictionary, coinciding with the growing popularity of Snapchat, Instagram, and dating apps like Tinder and Grindr. In 2011, Urban Dictionary defined it as "any statement used to intentionally create attention or 'thirst'." By 2018, the term had entered mainstream discourse, appearing in outlets such as The New York Times and GQ without the need for explanation. == Usage of the term == Often, the term thirst trap describes an attractive picture of an individual that they post online. Thirst trap can also describe a digital heartthrob. For instance, former Canadian prime minister Justin Trudeau has been described as a political thirst trap. It has also been described as a modern form of "fishing for compliments". == Motivation == Thirst trapping may be driven by a variety of motives. Individuals often seek attention through "likes" and comments on social media, which can offer a temporary sense of validation and improved self-esteem. It can also serve as an outlet for expressing one's sexuality or enhancing a personal brand. In some cases, sharing such content may provide financial gain. Others might post thirst traps to cope with emotional distress, such as after breakup, or to spite a former lover. Sharing a thirst trap has also been used as a way to connect in times of social isolation (e.g. COVID-19 pandemic). From a physiological standpoint, endorphins and neurotransmitters like oxytocin and dopamine are released during sexual contact. It has been speculated outside of the academic setting that sharing and engaging with thirst traps may elicit similar pleasure responses. == Methodology == Methodologies have developed to take an optimal thirst trap photo. Reporting for Vice magazine, Graham Isador found several of his social network contacts spent a lot of time considering how to take the best photo and what text they should use. They considered angles and lighting. Sometimes they made use of the self-timer feature available on some cameras. Often, body parts are put on display without being too explicit (e.g. bulges of male genitalia, breast cleavage, abdominal muscles, pectoral muscles, backs, buttocks). Often, the thirst trap is accompanied by a caption. For instance, in October 2019, actress Tracee Ellis Ross posted bikini pictures on Instagram with a caption that included the message: "I've worked so hard to feel good in my skin and to build a life that truly matches me and I'm in it and it feels good. ... No filter, no retouch 47 year old thirst trap! Boom!" On Instagram, #ThirstTrapThursdays is a popular tag. Followers reply in turn after a posting. == Variations == "Gatsbying" is a variation of the thirst trap, where one puts posts on social media to attract the attention of a particular individual. The term alludes to the novel The Great Gatsby where the character Jay Gatsby would throw extravagant parties to attract the attention of his love interest, Daisy. "Instagrandstanding" is an alternative name for this. "Wholesome trapping" has developed, where one posts pictures of more meaningful aspects of life, such as spending time with friends or doing outdoor activities. == Criticism == Psychotherapist Lisa Brateman has criticized thirst traps as an unhealthy method of receiving external validation. This desire for external validation can be addictive. Thirst traps can cause pressure to maintain a good physical appearance, and therefore cause self-esteem issues. Additionally, thirst traps are often highly choreographed and thus present a distorted perception of reality. The manufacturing of thirst traps can be limited when one enters a relationship or with time as the body ages. In some cases, thirst traps can lead to harassment and online bullying. In April 2020, model Chrissy Teigen posted a video of herself wearing a black one-piece swimsuit, and she received a multitude of negative comments that constituted bullying and body shaming.
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Bus encryption

Bus encryption is the use of encrypted program instructions on a data bus in a computer that includes a secure cryptoprocessor for executing the encrypted instructions. Bus encryption is used primarily in electronic systems that require high security, such as automated teller machines, TV set-top boxes, and secure data communication devices such as two-way digital radios. Bus encryption can also mean encrypted data transmission on a data bus from one processor to another processor. For example, from the CPU to a GPU which does not require input of encrypted instructions. Such bus encryption is used by Windows Vista and newer Microsoft operating systems to protect certificates, BIOS, passwords, and program authenticity. PVP-UAB (Protected Video Path) provides bus encryption of premium video content in PCs as it passes over the PCIe bus to graphics cards to enforce digital rights management. The need for bus encryption arises when multiple people have access to the internal circuitry of an electronic system, either because they service and repair such systems, stock spare components for the systems, own the system, steal the system, or find a lost or abandoned system. Bus encryption is necessary not only to prevent tampering of encrypted instructions that may be easily discovered on a data bus or during data transmission, but also to prevent discovery of decrypted instructions that may reveal security weaknesses that an intruder can exploit. In TV set-top boxes, it is necessary to download program instructions periodically to customer's units to provide new features and to fix bugs. These new instructions are encrypted before transmission, but must also remain secure on data buses and during execution to prevent the manufacture of unauthorized cable TV boxes. This can be accomplished by secure crypto-processors that read encrypted instructions on the data bus from external data memory, decrypt the instructions in the cryptoprocessor, and execute the instructions in the same cryptoprocessor.
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Sex differences in social media use

Men and women use social media in different ways and with different frequencies. In general, several researchers have found that women tend to use social network services (SNSs) more than men and primiarly to socialize. == Differences == === Predilection for usage === Many studies have found that women are more likely to use either specific SNSs such as Facebook or MySpace or SNSs in general. In 2015, 73% of online men and 80% of online women used social networking sites. The gap in gender differences has become less apparent in LinkedIn. In 2015 about 26 percent of online men and 25% of online women used the business-and employee-oriented networking site. Researchers who have examined the gender of users of multiple SNSs have found contradictory results. Hargittai's groundbreaking 2007 study examining race, gender, and other differences between undergraduate college student users of SNSs found that women were not only more likely to have used SNSes than men but that they were also more likely to have used many different services, including Facebook, MySpace, and Friendster; these differences persisted in several models and analyses. Although she only surveyed students at one institution – the University of Illinois at Chicago – Hargittai selected that institution intentionally as "an ideal location for studies of how different kinds of people use online sites and services." In contrast, data collected by the Pew Internet & American Life Project found that men were more likely to have multiple SNS profiles. Although the sample sizes of the two surveys are comparable – 1,650 Internet users in the Pew survey compared with 1,060 in Hargittai's survey – the data from the Pew survey are newer and arguably more representative of the entire adult United States population. Pinterest, Facebook, and Instagram attract more females. Picture sharing sites overall are very popular among women. Pinterest alone attracts three times as many female users than male. However, use of Pinterest by men has increased from 5% in 2012. Facebook attracts about 77% of women online. Instagram is also more likely to attract women. Men are more likely to participate in online forums like Reddit, Digg or Slashdot. One in five men claim to be a part of an online forum. === Uses === In general, women seem to use SNSs more to explicitly foster social connections. A study conducted by Pew research centers found that women were more avid users of social media. In November 2010, the gap between men and women was as high as 15%. Female participants in a multi-stage study conducted in 2007 to discover the motivations of Facebook users scored higher on scales for social connection and posting of photographs. Studies have also been conducted on the differences between females and males with regards to blogging. The Pew Research Center found that younger females are more likely to blog than males their own age, even males that are older than them. Similarly, in a study of blogs maintained in MySpace, women were found to be more likely to not only write blogs but also write about family, romantic relationships, friendships, and health in those blogs. A study of Swedish SNS users found that women were more likely to have expressions of friendship, specifically in the areas of (a) publishing photos of their friends, (b) specifically naming their best friends, and (c) writing poems to and about their friends. Women were also more likely to have expressions related to family relationships and romantic relationships. One of the key findings of this research is that those men who do have expressions of romantic relationships in their profile had expressions just as strong as the women. However, the researcher speculated that this may be in part due to a desire to publicly express heterosexual behaviors and mannerisms instead of merely expressing romantic feelings. A large-scale study of gender differences in MySpace found that both men and women tended to have a majority of female Friends, and both men and women tended to have a majority of female "Top" Friends in the site. A later study found women to author disproportionately many (public) comments in MySpace, but an investigation into the role of emotion in public MySpace comments found that women both give and receive stronger positive emotion. It was hypothesised that women are simply more effective at using social networking sites because they are better able to harness positive emotion. A study focused on the influence of gender and personality on individuals' use of online social networking websites such as Facebook, reported that men use social networking sites with the intention of forming new relationships, whereas, women use them more for relationship maintenance. In addition to this, women are more likely to use Facebook or MySpace to compare themselves to others and also to search for information. Men, however, are more likely to look at other people's profiles with in the intention to find friends. Women were less successful at actually finding new friends, but more successful at "maintaining existing relationships, making new relationships, using for academic purposes and following specific agenda". Similarly, men also self-reported this motivation "while women reported using them more for relationship maintenance". === Personality === OCEAN personality traits are known to systematically vary between human males and females. In one study, the same women were more extraverted and agreeable, such as less neurotic while on social media than offline. Other studies associated neuroticism with female use of social media. === Privacy === Privacy has been the primary topic of many studies of SNS users, and many of these studies have found differences between male and female SNS users, although some studies have found results contradictory to those found in other studies. Some researchers have found that women are more protective of their personal information and more likely to have private profiles. Other researchers have found that women are less likely to post some types of information. Acquisti and Gross found that women in their sample were less likely to reveal their sexual orientation, personal address, or cell phone number. This is similar to Pew Internet & American Life research of children users of SNSs that found that boys and girls presented different views of privacy and behaviors, with girls being more concerned about and restrictive of information such as city, town, last name, and cell phone number that could be used to locate them. At least one group of researchers has found that women are less likely to share information that "identifies them directly – last name, cell phone number, and address or home phone number," linking that resistance to women's greater concerns about "cyberstalking", "cyberbullying", and security problems. Despite these concerns about privacy, researchers have found that women are more likely to maintain up-to-date photos of themselves. Further, Kolek and Saunders found in their sample of college student Facebook users that women were more likely to not only post a photograph of themselves in their profile but that they were more likely to have a publicly viewable Facebook account (a contradictory finding compared to many other studies), post photos, and post photo albums. Women were more likely to have: (a) a publicly viewable Facebook account, (b) more photo albums, (c) more photos, (d) a photo of themselves as their profile picture, (e) positive references to alcohol, partying, or drugs, and (f) more positive references to or about the institution or institution-related activities. In general, women were more likely to disclose information about themselves in their Facebook profile, with the primary exception of sharing their telephone number. Similarly, female respondents to Strano's study were more likely to keep their profile photo recent and choose a photo that made them appear attractive, happy, and fun-loving. Citing several examples, Strano opined that there may also be a difference in how men and women Facebook users display and interpret profile photos depicting relationships. Privacy has also been a concern for the SnapChat app, which allows you to send messages either text or photo or video which then disappear. One study has shown that security is not a major concern for the majority of users and that most do not use Snapchat to send sensitive content (although up to 25% may do so experimentally). As part of their research almost no statistically significant gender differences were found. === Cyberbullying === Past research carried out to investigate if there are any gender differences in cyber-bullying has found that boys commit more cyber verbal bullying, cyber forgery and more violence based on hidden identity or presenting themselves as other person. === Mansplaining === A 2021 article found that mansplaining could be seen more prominent online rather than offl
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TigerGraph

TigerGraph is a private company headquartered in Redwood City, California. It provides graph database and graph analytics software. == History == TigerGraph was founded in 2012 by programmer Yu, Ruoming, Li, Like and Mingxi, under the name GraphSQL. In September 2017, the company came out of stealth mode under the name TigerGraph with $33 million in funding. It raised an additional $32 million in funding in September 2019 and another $105 million in a series C round in February 2021. Cumulative funding as of March 2021 is $170 million. == Products == TigerGraph's hybrid transactional/analytical processing database and analytics software can scale to hundreds of terabytes of data with trillions of edges, and is used for data intensive applications such as fraud detection, customer data analysis (customer 360), IoT, artificial intelligence and machine learning. It is available using the cloud computing delivery model. The analytics uses C++ based software and a parallel processing engine to process algorithms and queries. It has its own graph query language that is similar to SQL. TigerGraph also provides a software development kit for creating graphs and visual representations. As of Mar 2024, TigerGraph version is up to version 4.2.0 TigerGraph offers free Community Edition for developers, researchers, and educators. It can be obtained from https://dl.tigergraph.com/ == Query Language == GSQL , designed by Mingxi Wu and Alin Deutsch in 2015, is a SQL-like Turing complete query language. GSQL includes additions to make it compliant with the Graph Query Language standard.
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Social commerce

Social commerce is a subset of electronic commerce that involves social media and online media that supports social interaction, and user contributions to assist online buying and selling of products and services. More succinctly, social commerce is the use of social network(s), and user-generated content in the context of e-commerce transactions. The term social commerce was introduced by Yahoo! in November 2005 which describes a set of online collaborative shopping tools such as shared pick lists, user ratings and other user-generated content of online product information and advice. The concept of social commerce was developed by David Beisel to denote user-generated advertorial content on e-commerce sites, and by Steve Rubel to include collaborative e-commerce tools that enable shoppers "to get advice from trusted individuals, find goods and services and then purchase them". The social networks that spread this advice have been found to increase the customer's trust in one retailer over another. Social commerce may assist companies in achieving the following purposes: Firstly, social commerce helps companies engage customers with their brands according to the customers' social behaviors. Secondly, it provides an incentive for customers to return to their website. Thirdly, it provides customers with a platform to talk about their brand on their website. Fourthly, it provides all the information customers need to research, compare, and ultimately choose you over your competitor, thus purchasing from you and not others. In these days, the range of social commerce has been expanded to include social media tools and content used in the context of e-commerce, especially in the fashion industry. Examples of social commerce include customer ratings and reviews, user recommendations and referrals, social shopping tools (sharing the act of shopping online), forums and communities, social media optimization, social applications and social advertising. Technologies such as augmented reality have also been integrated with social commerce, allowing shoppers to visualize apparel items on themselves and solicit feedback through social media tools. Some academics have sought to distinguish "social commerce" from "social shopping", with the former being referred to as collaborative networks of online vendors; the latter, the collaborative activity of online shoppers. == Timeline == 2005: The term "social commerce" was first introduced on Yahoo! in 2005. 2021: The Global Web Index associated one's use of social media to his/her eagerness to buy. Social media with its entertaining and inspirational content can increase a product's profitability. This explains why Instagram expanded its Checkout feature to similar content like IG Stories, IGTV, and Reels. == Elements == The attraction and effectiveness of Social Commerce can be understood in terms of Robert Cialdini's Principles of InfluenceInfluence: Science and Practice": Reciprocity – When a company gives a person something for free, that person will feel the need to return the favor, whether by buying again or giving good recommendations for the company. Community – When people find an individual or a group that shares the same values, likes, beliefs, etc., they find community. People are more committed to a community that they feel accepted within. When this commitment happens, they tend to follow the same trends as a group and when one member introduces a new idea or product, it is accepted more readily based on the previous trust that has been established. It would be beneficial for companies to develop partnerships with social media sites to engage social communities with their products. Social proof – To receive positive feedback, a company needs to be willing to accept social feedback and to show proof that other people are buying, and like, the same things that I like. This can be seen in a lot of online companies such as eBay and Amazon, that allow public feedback of products and when a purchase is made, they immediately generate a list showing purchases that other people have made in relation to my recent purchase. It is beneficial to encourage open recommendation and feedback. This creates trust for you as a seller. 55% of buyers turn to social media when they're looking for information. Authority – Many people need proof that a product is of good quality. This proof can be based on the recommendations of others who have bought the same product. If there are many user reviews about a product, then a consumer will be more willing to trust their own decision to buy this item. Liking – People trust based on the recommendations of others. If there are a lot of "likes" of a particular product, then the consumer will feel more confident and justified in making this purchase. Scarcity – As part of supply and demand, a greater value is assigned to products that are regarded as either being in high demand or are seen as being in a shortage. Therefore, if a person is convinced that they are purchasing something that is unique, special, or not easy to acquire, they will have more of a willingness to make a purchase. If there is trust established from the seller, they will want to buy these items immediately. This can be seen in the cases of Zara and Apple Inc. who create demand for their products by convincing the public that there is a possibility of missing out on being able to purchase them. == Types == === Onsite === Onsite social commerce refers to retailers including social sharing and other social functionality on their website. Some notable examples include Zazzle which enables users to share their purchases, Macy's which allows users to create a poll to find the right product, and Fab.com which shows a live feed of what other shoppers are buying. Onsite user reviews are also considered a part of social commerce. This approach has been successful in improving customer engagement, conversion and word-of-mouth branding according to several industry sources. === Offsite === Offsite social commerce includes activities that happen outside of the retailers' website. This may include posting products on social networks such as Facebook, X, and TikTok. It may also include advertising on shopping forums such as SlickDeals, Red Flag Deals, and LatestDeals.co.uk. == Measurements == Social commerce can be measured by any of the principle ways to measure social media. Return on Investment: measures the effect or action of social media on sales. Reputation: indices measure the influence of social media investment in terms of changes to online reputation – made up of the volume and valence of social media mentions. Reach: metrics use traditional media advertising metrics to measure the exposure rates and levels of an audience with social media. == Business applications == This category is based on individuals' shopping, selling, recommending behaviors. Social network-driven sales (Soldsie) – Facebook commerce and Twitter commerce belong to this part. Sales take place on established social network sites. Peer-to-peer sales platforms (eBay, Etsy, Amazon) – In these websites, users can directly communicate and sell products to other users. Group buying (Groupon, LivingSocial) – Users can buy products or services at a lower price when enough users agree to make this purchase. Peer recommendations and reviews (Amazon, Yelp, Bazaarvoice) – Users can see recommendations and reviews from other users. User-curated shopping (The Fancy, Lyst) – Users create and share lists of products and services for others to shop from. Participatory commerce (Betabrand, Threadless, Kickstarter) – Users can get involved in the production process. Social shopping (Squadded) – Allowing e-commerce to provide their users live chat sessions and shared shopping lists so they can communicate with their friends or other shoppers for advice. == Business examples == Here are some notable business examples of Social Commerce: Betabrand: an online brand using participatory design to release new, community-created ideas every week. Cafepress: an online retailer of stock and user-customized on demand products. Etsy: an e-commerce website focused on handmade or vintage items and supplies, as well as unique factory-manufactured items under Etsy's new guidelines. Eventbrite: an online ticketing service that allows event organizers to plan, set up ticket sales and promote events (event management) and publish them across Facebook, Twitter and other social-networking tools directly from the site's interface. Groupon: a deal-of-the-day website that features discounted gift certificates usable at local or national companies. Houzz: a web site and online community about architecture, interior design and decorating, landscape design and home improvement. LivingSocial: an online marketplace that allows clients to buy and share things to do in their city. Lockerz: an international social commerce website based in Seattle, Washington. OpenSky: is a r
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NYSERNet

NYSERNet, Inc. (New York State Education and Research Network), is a non-profit Internet service provider in New York State. It mainly provides Internet access to universities, colleges, museums, health care facilities, primary and secondary schools, and research institutions. == History == NYSERNet was founded in 1986 in Troy, New York. Its founders compared NYSERNet's network with the Erie Canal and considered it the next step in two centuries to draw the country together. NYSERNet's network reaches from Buffalo to New York City. Completed in 1987, it was the first statewide regional IP network in the United States.[1] Initial speed of 56 kbps was upgraded to T1 in 1989 and T3 in 1994. It was the original assignee of AS174 according to RFC1117. This ASN is used today by Cogent Communications for their global network.
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Factorization of polynomials over finite fields

In mathematics and computer algebra the factorization of a polynomial consists of decomposing it into a product of irreducible factors. This decomposition is theoretically possible and is unique for polynomials with coefficients in any field, but rather strong restrictions on the field of the coefficients are needed to allow the computation of the factorization by means of an algorithm. In practice, algorithms have been designed only for polynomials with coefficients in a finite field, in the field of rationals or in a finitely generated field extension of one of them. All factorization algorithms, including the case of multivariate polynomials over the rational numbers, reduce the problem to this case; see polynomial factorization. It is also used for various applications of finite fields, such as coding theory (cyclic redundancy codes and BCH codes), cryptography (public key cryptography by the means of elliptic curves), and computational number theory. As the reduction of the factorization of multivariate polynomials to that of univariate polynomials does not have any specificity in the case of coefficients in a finite field, only polynomials with one variable are considered in this article. == Background == === Finite field === The theory of finite fields, whose origins can be traced back to the works of Gauss and Galois, has played a part in various branches of mathematics. Due to the applicability of the concept in other topics of mathematics and sciences like computer science there has been a resurgence of interest in finite fields and this is partly due to important applications in coding theory and cryptography. Applications of finite fields introduce some of these developments in cryptography, computer algebra and coding theory. A finite field or Galois field is a field with a finite order (number of elements). The order of a finite field is always a prime or a power of prime. For each prime power q = pr, there exists exactly one finite field with q elements, up to isomorphism. This field is denoted GF(q) or Fq. If p is prime, GF(p) is the prime field of order p; it is the field of residue classes modulo p, and its p elements are denoted 0, 1, ..., p−1. Thus a = b in GF(p) means the same as a ≡ b (mod p). === Irreducible polynomials === Let F be a finite field. As for general fields, a non-constant polynomial f in F[x] is said to be irreducible over F if it is not the product of two polynomials of positive degree. A polynomial of positive degree that is not irreducible over F is called reducible over F. Irreducible polynomials allow us to construct the finite fields of non-prime order. In fact, for a prime power q, let Fq be the finite field with q elements, unique up to isomorphism. A polynomial f of degree n greater than one, which is irreducible over Fq, defines a field extension of degree n which is isomorphic to the field with qn elements: the elements of this extension are the polynomials of degree lower than n; addition, subtraction and multiplication by an element of Fq are those of the polynomials; the product of two elements is the remainder of the division by f of their product as polynomials; the inverse of an element may be computed by the extended GCD algorithm (see Arithmetic of algebraic extensions). It follows that, to compute in a finite field of non prime order, one needs to generate an irreducible polynomial. For this, the common method is to take a polynomial at random and test it for irreducibility. For sake of efficiency of the multiplication in the field, it is usual to search for polynomials of the shape xn + ax + b. Irreducible polynomials over finite fields are also useful for pseudorandom number generators using feedback shift registers and discrete logarithm over F2n. The number of irreducible monic polynomials of degree n over Fq is the number of aperiodic necklaces, given by Moreau's necklace-counting function Mq(n). The closely related necklace function Nq(n) counts monic polynomials of degree n which are primary (a power of an irreducible); or alternatively irreducible polynomials of all degrees d which divide n. === Example === The polynomial P = x4 + 1 is irreducible over Q but not over any finite field. On any field extension of F2, P = (x + 1)4. On every other finite field, at least one of −1, 2 and −2 is a square, because the product of two non-squares is a square and so we have If − 1 = a 2 , {\displaystyle -1=a^{2},} then P = ( x 2 + a ) ( x 2 − a ) . {\displaystyle P=(x^{2}+a)(x^{2}-a).} If 2 = b 2 , {\displaystyle 2=b^{2},} then P = ( x 2 + b x + 1 ) ( x 2 − b x + 1 ) . {\displaystyle P=(x^{2}+bx+1)(x^{2}-bx+1).} If − 2 = c 2 , {\displaystyle -2=c^{2},} then P = ( x 2 + c x − 1 ) ( x 2 − c x − 1 ) . {\displaystyle P=(x^{2}+cx-1)(x^{2}-cx-1).} === Complexity === Polynomial factoring algorithms use basic polynomial operations such as products, divisions, gcd, powers of one polynomial modulo another, etc. A multiplication of two polynomials of degree at most n can be done in O(n2) operations in Fq using "classical" arithmetic, or in O(nlog(n) log(log(n)) ) operations in Fq using "fast" arithmetic. A Euclidean division (division with remainder) can be performed within the same time bounds. The cost of a polynomial greatest common divisor between two polynomials of degree at most n can be taken as O(n2) operations in Fq using classical methods, or as O(nlog2(n) log(log(n)) ) operations in Fq using fast methods. For polynomials h, g of degree at most n, the exponentiation hq mod g can be done with O(log(q)) polynomial products, using exponentiation by squaring method, that is O(n2log(q)) operations in Fq using classical methods, or O(nlog(q)log(n) log(log(n))) operations in Fq using fast methods. In the algorithms that follow, the complexities are expressed in terms of number of arithmetic operations in Fq, using classical algorithms for the arithmetic of polynomials. == Factoring algorithms == Many algorithms for factoring polynomials over finite fields include the following three stages: Square-free factorization Distinct-degree factorization Equal-degree factorization An important exception is Berlekamp's algorithm, which combines stages 2 and 3. === Berlekamp's algorithm === Berlekamp's algorithm is historically important as being the first factorization algorithm which works well in practice. However, it contains a loop on the elements of the ground field, which implies that it is practicable only over small finite fields. For a fixed ground field, its time complexity is polynomial, but, for general ground fields, the complexity is exponential in the size of the ground field. === Square-free factorization === The algorithm determines a square-free factorization for polynomials whose coefficients come from the finite field Fq of order q = pm with p a prime. This algorithm firstly determines the derivative and then computes the gcd of the polynomial and its derivative. If it is not one then the gcd is again divided into the original polynomial, provided that the derivative is not zero (a case that exists for non-constant polynomials defined over finite fields). This algorithm uses the fact that, if the derivative of a polynomial is zero, then it is a polynomial in xp, which is, if the coefficients belong to Fp, the pth power of the polynomial obtained by substituting x by x1/p. If the coefficients do not belong to Fp, the pth root of a polynomial with zero derivative is obtained by the same substitution on x, completed by applying the inverse of the Frobenius automorphism to the coefficients. This algorithm works also over a field of characteristic zero, with the only difference that it never enters in the blocks of instructions where pth roots are computed. However, in this case, Yun's algorithm is much more efficient because it computes the greatest common divisors of polynomials of lower degrees. A consequence is that, when factoring a polynomial over the integers, the algorithm which follows is not used: one first computes the square-free factorization over the integers, and to factor the resulting polynomials, one chooses a p such that they remain square-free modulo p. Algorithm: SFF (Square-Free Factorization) Input: A monic polynomial f in Fq[x] where q = pm Output: Square-free factorization of f R ← 1 # Make w be the product (without multiplicity) of all factors of f that have # multiplicity not divisible by p c ← gcd(f, f′) w ← f/c # Step 1: Identify all factors in w i ← 1 while w ≠ 1 do y ← gcd(w, c) fac ← w / y R ← R · faci w ← y; c ← c / y; i ← i + 1 end while # c is now the product (with multiplicity) of the remaining factors of f # Step 2: Identify all remaining factors using recursion # Note that these are the factors of f that have multiplicity divisible by p if c ≠ 1 then c ← c1/p R ← R·SFF(c)p end if Output(R) The idea is to identify the product of all irreducible factors of f with the same multiplicity. This is done in two steps. The first step uses the formal d
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ImageMixer

ImageMixer is a brand name of video editing software that edits digital video and still image in camcorders and authors to VCD and DVD. It is a second-party Japanese product, distributed by Pixela Corporation, a Japanese manufacturer of PC peripheral hardware and multimedia software. == Bundling == ImageMixer is widely used for several camcorder brands, such as JVC, Hitachi and Canon. Also, Sony has chosen to package ImageMixer with its DVD and HDD Handycam. == ImageMixer series == ImageMixer has other series of software for digital camera, such as ImageMixer Label Maker and ImageMixer DVD dubbing. ImageMixer also has movie editing solution for Macintosh. == Windows Vista version of ImageMixer == A Windows Vista version of ImageMixer has been developed (ImageMixer3).
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HashClash

HashClash was a volunteer computing project running on the Berkeley Open Infrastructure for Network Computing (BOINC) software platform to find collisions in the MD5 hash algorithm. It was based at Department of Mathematics and Computer Science at the Eindhoven University of Technology, and Marc Stevens initiated the project as part of his master's degree thesis. The project ended after Stevens defended his M.Sc. thesis in June 2007. However, SHA1 was added later, and the code repository was ported to git in 2017. The project was used to create a rogue certificate authority certificate in 2009.
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Unknown key-share attack

As defined by Blake-Wilson & Menezes (1999), an unknown key-share (UKS) attack on an authenticated key agreement (AK) or authenticated key agreement with key confirmation (AKC) protocol is an attack whereby an entity A {\displaystyle A} ends up believing she shares a key with B {\displaystyle B} , and although this is in fact the case, B {\displaystyle B} mistakenly believes the key is instead shared with an entity E ≠ A {\displaystyle E\neq A} . In other words, in a UKS, an opponent, say Eve, coerces honest parties Alice and Bob into establishing a secret key where at least one of Alice and Bob does not know that the secret key is shared with the other. For example, Eve may coerce Bob into believing he shares the key with Eve, while he actually shares the key with Alice. The “key share” with Alice is thus unknown to Bob.
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