Whitehead's algorithm

Whitehead's algorithm

Whitehead's algorithm is a mathematical algorithm in group theory for solving the automorphic equivalence problem in the finite rank free group Fn. The algorithm is based on a classic 1936 paper of J. H. C. Whitehead. It is still unknown (except for the case n = 2) if Whitehead's algorithm has polynomial time complexity. == Statement of the problem == Let F n = F ( x 1 , … , x n ) {\displaystyle F_{n}=F(x_{1},\dots ,x_{n})} be a free group of rank n ≥ 2 {\displaystyle n\geq 2} with a free basis X = { x 1 , … , x n } {\displaystyle X=\{x_{1},\dots ,x_{n}\}} . The automorphism problem, or the automorphic equivalence problem for F n {\displaystyle F_{n}} asks, given two freely reduced words w , w ′ ∈ F n {\displaystyle w,w'\in F_{n}} whether there exists an automorphism φ ∈ Aut ⁡ ( F n ) {\displaystyle \varphi \in \operatorname {Aut} (F_{n})} such that φ ( w ) = w ′ {\displaystyle \varphi (w)=w'} . Thus the automorphism problem asks, for w , w ′ ∈ F n {\displaystyle w,w'\in F_{n}} whether Aut ⁡ ( F n ) w = Aut ⁡ ( F n ) w ′ {\displaystyle \operatorname {Aut} (F_{n})w=\operatorname {Aut} (F_{n})w'} . For w , w ′ ∈ F n {\displaystyle w,w'\in F_{n}} one has Aut ⁡ ( F n ) w = Aut ⁡ ( F n ) w ′ {\displaystyle \operatorname {Aut} (F_{n})w=\operatorname {Aut} (F_{n})w'} if and only if Out ⁡ ( F n ) [ w ] = Out ⁡ ( F n ) [ w ′ ] {\displaystyle \operatorname {Out} (F_{n})[w]=\operatorname {Out} (F_{n})[w']} , where [ w ] , [ w ′ ] {\displaystyle [w],[w']} are conjugacy classes in F n {\displaystyle F_{n}} of w , w ′ {\displaystyle w,w'} accordingly. Therefore, the automorphism problem for F n {\displaystyle F_{n}} is often formulated in terms of Out ⁡ ( F n ) {\displaystyle \operatorname {Out} (F_{n})} -equivalence of conjugacy classes of elements of F n {\displaystyle F_{n}} . For an element w ∈ F n {\displaystyle w\in F_{n}} , | w | X {\displaystyle |w|_{X}} denotes the freely reduced length of w {\displaystyle w} with respect to X {\displaystyle X} , and ‖ w ‖ X {\displaystyle \|w\|_{X}} denotes the cyclically reduced length of w {\displaystyle w} with respect to X {\displaystyle X} . For the automorphism problem, the length of an input w {\displaystyle w} is measured as | w | X {\displaystyle |w|_{X}} or as ‖ w ‖ X {\displaystyle \|w\|_{X}} , depending on whether one views w {\displaystyle w} as an element of F n {\displaystyle F_{n}} or as defining the corresponding conjugacy class [ w ] {\displaystyle [w]} in F n {\displaystyle F_{n}} . == History == The automorphism problem for F n {\displaystyle F_{n}} was algorithmically solved by J. H. C. Whitehead in a classic 1936 paper, and his solution came to be known as Whitehead's algorithm. Whitehead used a topological approach in his paper. Namely, consider the 3-manifold M n = # i = 1 n S 2 × S 1 {\displaystyle M_{n}=\#_{i=1}^{n}\mathbb {S} ^{2}\times \mathbb {S} ^{1}} , the connected sum of n {\displaystyle n} copies of S 2 × S 1 {\displaystyle \mathbb {S} ^{2}\times \mathbb {S} ^{1}} . Then π 1 ( M n ) ≅ F n {\displaystyle \pi _{1}(M_{n})\cong F_{n}} , and, moreover, up to a quotient by a finite normal subgroup isomorphic to Z 2 n {\displaystyle \mathbb {Z} _{2}^{n}} , the mapping class group of M n {\displaystyle M_{n}} is equal to Out ⁡ ( F n ) {\displaystyle \operatorname {Out} (F_{n})} ; see. Different free bases of F n {\displaystyle F_{n}} can be represented by isotopy classes of "sphere systems" in M n {\displaystyle M_{n}} , and the cyclically reduced form of an element w ∈ F n {\displaystyle w\in F_{n}} , as well as the Whitehead graph of [ w ] {\displaystyle [w]} , can be "read-off" from how a loop in general position representing [ w ] {\displaystyle [w]} intersects the spheres in the system. Whitehead moves can be represented by certain kinds of topological "swapping" moves modifying the sphere system. Subsequently, Rapaport, and later, based on her work, Higgins and Lyndon, gave a purely combinatorial and algebraic re-interpretation of Whitehead's work and of Whitehead's algorithm. The exposition of Whitehead's algorithm in the book of Lyndon and Schupp is based on this combinatorial approach. Culler and Vogtmann, in their 1986 paper that introduced the Outer space, gave a hybrid approach to Whitehead's algorithm, presented in combinatorial terms but closely following Whitehead's original ideas. == Whitehead's algorithm == Our exposition regarding Whitehead's algorithm mostly follows Ch.I.4 in the book of Lyndon and Schupp, as well as. === Overview === The automorphism group Aut ⁡ ( F n ) {\displaystyle \operatorname {Aut} (F_{n})} has a particularly useful finite generating set W {\displaystyle {\mathcal {W}}} of Whitehead automorphisms or Whitehead moves. Given w , w ′ ∈ F n {\displaystyle w,w'\in F_{n}} the first part of Whitehead's algorithm consists of iteratively applying Whitehead moves to w , w ′ {\displaystyle w,w'} to take each of them to an "automorphically minimal" form, where the cyclically reduced length strictly decreases at each step. Once we find automorphically these minimal forms u , u ′ {\displaystyle u,u'} of w , w ′ {\displaystyle w,w'} , we check if ‖ u ‖ X = ‖ u ′ ‖ X {\displaystyle \|u\|_{X}=\|u'\|_{X}} . If ‖ u ‖ X ≠ ‖ u ′ ‖ X {\displaystyle \|u\|_{X}\neq \|u'\|_{X}} then w , w ′ {\displaystyle w,w'} are not automorphically equivalent in F n {\displaystyle F_{n}} . If ‖ u ‖ X = ‖ u ′ ‖ X {\displaystyle \|u\|_{X}=\|u'\|_{X}} , we check if there exists a finite chain of Whitehead moves taking u {\displaystyle u} to u ′ {\displaystyle u'} so that the cyclically reduced length remains constant throughout this chain. The elements w , w ′ {\displaystyle w,w'} are not automorphically equivalent in F n {\displaystyle F_{n}} if and only if such a chain exists. Whitehead's algorithm also solves the search automorphism problem for F n {\displaystyle F_{n}} . Namely, given w , w ′ ∈ F n {\displaystyle w,w'\in F_{n}} , if Whitehead's algorithm concludes that Aut ⁡ ( F n ) w = Aut ⁡ ( F n ) w ′ {\displaystyle \operatorname {Aut} (F_{n})w=\operatorname {Aut} (F_{n})w'} , the algorithm also outputs an automorphism φ ∈ Aut ⁡ ( F n ) {\displaystyle \varphi \in \operatorname {Aut} (F_{n})} such that φ ( w ) = w ′ {\displaystyle \varphi (w)=w'} . Such an element φ ∈ Aut ⁡ ( F n ) {\displaystyle \varphi \in \operatorname {Aut} (F_{n})} is produced as the composition of a chain of Whitehead moves arising from the above procedure and taking w {\displaystyle w} to w ′ {\displaystyle w'} . === Whitehead automorphisms === A Whitehead automorphism, or Whitehead move, of F n {\displaystyle F_{n}} is an automorphism τ ∈ Aut ⁡ ( F n ) {\displaystyle \tau \in \operatorname {Aut} (F_{n})} of F n {\displaystyle F_{n}} of one of the following two types: There is a permutation σ ∈ S n {\displaystyle \sigma \in S_{n}} of { 1 , 2 , … , n } {\displaystyle \{1,2,\dots ,n\}} such that for i = 1 , … , n {\displaystyle i=1,\dots ,n} τ ( x i ) = x σ ( i ) ± 1 {\displaystyle \tau (x_{i})=x_{\sigma (i)}^{\pm 1}} Such τ {\displaystyle \tau } is called a Whitehead automorphism of the first kind. There is an element a ∈ X ± 1 {\displaystyle a\in X^{\pm 1}} , called the multiplier, such that for every x ∈ X ± 1 {\displaystyle x\in X^{\pm 1}} τ ( x ) ∈ { x , x a , a − 1 x , a − 1 x a } . {\displaystyle \tau (x)\in \{x,xa,a^{-1}x,a^{-1}xa\}.} Such τ {\displaystyle \tau } is called a Whitehead automorphism of the second kind. Since τ {\displaystyle \tau } is an automorphism of F n {\displaystyle F_{n}} , it follows that τ ( a ) = a {\displaystyle \tau (a)=a} in this case. Often, for a Whitehead automorphism τ ∈ Aut ⁡ ( F n ) {\displaystyle \tau \in \operatorname {Aut} (F_{n})} , the corresponding outer automorphism in Out ⁡ ( F n ) {\displaystyle \operatorname {Out} (F_{n})} is also called a Whitehead automorphism or a Whitehead move. ==== Examples ==== Let F 4 = F ( x 1 , x 2 , x 3 , x 4 ) {\displaystyle F_{4}=F(x_{1},x_{2},x_{3},x_{4})} . Let τ : F 4 → F 4 {\displaystyle \tau :F_{4}\to F_{4}} be a homomorphism such that τ ( x 1 ) = x 2 x 1 , τ ( x 2 ) = x 2 , τ ( x 3 ) = x 2 x 3 x 2 − 1 , τ ( x 4 ) = x 4 {\displaystyle \tau (x_{1})=x_{2}x_{1},\quad \tau (x_{2})=x_{2},\quad \tau (x_{3})=x_{2}x_{3}x_{2}^{-1},\quad \tau (x_{4})=x_{4}} Then τ {\displaystyle \tau } is actually an automorphism of F 4 {\displaystyle F_{4}} , and, moreover, τ {\displaystyle \tau } is a Whitehead automorphism of the second kind, with the multiplier a = x 2 − 1 {\displaystyle a=x_{2}^{-1}} . Let τ ′ : F 4 → F 4 {\displaystyle \tau ':F_{4}\to F_{4}} be a homomorphism such that τ ′ ( x 1 ) = x 1 , τ ′ ( x 2 ) = x 1 − 1 x 2 x 1 , τ ′ ( x 3 ) = x 1 − 1 x 3 x 1 , τ ′ ( x 4 ) = x 1 − 1 x 4 x 1 {\displaystyle \tau '(x_{1})=x_{1},\quad \tau '(x_{2})=x_{1}^{-1}x_{2}x_{1},\quad \tau '(x_{3})=x_{1}^{-1}x_{3}x_{1},\quad \tau '(x_{4})=x_{1}^{-1}x_{4}x_{1}} Then τ ′ {\displaystyle \tau '} is actually an inner automorphism of F 4 {\displaystyle F_{4}} given by conjugation by x 1 {\displaystyle x_{1}} , and, moreover, τ ′ {\displaystyle \

Equalized odds

Equalized odds, also referred to as conditional procedure accuracy equality and disparate mistreatment, is a measure of fairness in machine learning. A classifier satisfies this definition if the subjects in the protected and unprotected groups have equal true positive rate and equal false positive rate, satisfying the formula: P ( R = + | Y = y , A = a ) = P ( R = + | Y = y , A = b ) y ∈ { + , − } ∀ a , b ∈ A {\displaystyle P(R=+|Y=y,A=a)=P(R=+|Y=y,A=b)\quad y\in \{+,-\}\quad \forall a,b\in A} For example, A {\displaystyle A} could be gender, race, or any other characteristics that we want to be free of bias, while Y {\displaystyle Y} would be whether the person is qualified for the degree, and the output R {\displaystyle R} would be the school's decision whether to offer the person to study for the degree. In this context, higher university enrollment rates of African Americans compared to whites with similar test scores might be necessary to fulfill the condition of equalized odds, if the "base rate" of Y {\displaystyle Y} differs between the groups. The concept was originally defined for binary-valued Y {\displaystyle Y} . In 2017, Woodworth et al. generalized the concept further for multiple classes.

Social media and suicide

Since the rise of social media, there have been numerous cases of individuals being influenced towards committing suicide or self-harm through their use of social media, and even of individuals arranging to broadcast suicide attempts, some successful, on social media. Researchers have studied social media and suicide to determine what, if any, risks social media poses in terms of suicide, and to identify methods of mitigating such risks, if they exist. The search for a correlation has not yet uncovered a clear answer. == Background == Suicide is one of the leading causes of death worldwide, and as of 2020, the second leading cause of death in the United States for those aged 15–34. According to the Center for Disease Control and Prevention, suicide was the third leading cause of death among adolescents in the US, from 1999 to 2006. In 2020, people in the US had a suicide rate of 13.5 per 100,000. Suicide was a leading cause of death in the United States accounting for 48,183 deaths in 2021. Suicide rates increased by 30 per cent from 2000 to 2018 and declined in 2019 and 2020. Suicide remains a significant public health issue worldwide, despite prevention efforts and treatments. Suicide has been identified not only as an individual phenomenon but also as being influenced by social and environmental factors. There is growing evidence that online activity has influenced suicide-related behavior. The use of social media throughout the 21st century has grown exponentially. For this reason, there are a variety of sources that are accessible to the public in various forms, especially social media sites such as Facebook, Instagram, Twitter, YouTube, Snapchat, TikTok and many more. Although these platforms were intended to allow people to connect virtually, these platforms can lead to cyber-bullying, insecurity, and emotional distress, and sometimes may influence a person to attempt suicide. Bullying, whether on social media or elsewhere, physical or not, significantly increases victims' risk of suicidal behavior. Since social media was introduced some people have taken their lives as a result of cyberbullying. Furthermore, suicide rates among teenagers have increased from 2010 to 2022 as social media has become something that people interact with more throughout their day-to-day lives. Media algorithms tend to popularize videos and posts to inform the country of the rising trouble, which may create a popular appeal to the young and immature minds of teenagers. This is why, social media could provide higher risks with the promotion of different kinds of pro-suicidal sites, message boards, chat rooms, and forums. Moreover, the Internet not only reports suicide incidents but documents suicide methods (for example, suicide pacts, an agreement between two or more people to kill themselves at a particular time and often by the same lethal means). Therefore, the role the Internet plays, particularly social media, in suicide-related behavior is a topic of growing interest. == Cyberbullying == There is substantial evidence that the Internet and social media can influence suicide-related behavior. Such evidence includes an increase in exposure to graphic content. A research study conducted by Sameer Hinduja and Justin Patchin found a correlation between cyberbullying and suicide. According to their findings, cyber-bullying increases suicidal thoughts by 14.5 percent and suicide attempts by 8.7 percent. Particularly alarming is the fact that children and young people under 25 who are victims of cyberbullying are more than twice as likely to self-harm and engage in suicidal behavior. Overall, teen suicide rates have increased within the past decade.This presents a significant public health concern, with over 40,000 suicides in the United States and nearly one million worldwide annually. Adolescents involved in cyberbullying often downplay its seriousness by calling it a joke or blaming the victim. These moral disengagement strategies can normalize harmful behavior and reduce feelings of guilt. This normalization may increase emotional distress and contribute to risks like depression and suicidal thoughts. Recent data from the Centers for Disease Control and Prevention reveals that 14.9 per cent of teenagers have experienced online bullying, while 13.6 per cent of teenagers have seriously attempted suicide. Both of these incidents are in increasing numbers in the United States. Furthermore, in numerous recent incidents, cyber-bullying led the victim to commit suicide; this phenomenon is now known as cyberbullicide. Many parents and children are unaware of the dangers and potential legal consequences of cyberbullying. As a response, anti-bullying regulations implemented by schools aim to prevent any form of bullying, including through technology, and protect students from online harassment. While some states have enacted laws against cyberbullying, there are currently no federal regulations addressing this issue. == Social media's influence on suicide == The media may portray suicidal behavior or language which can potentially influence people to act on these suicidal ideation. This may include news reports of actual suicides that have occurred or television shows and films that reenact suicides. Some organizations have proposed guidelines about how the media should report suicide. There is evidence that compliance with the guidelines varies. Some research showed that it is unclear whether the guidelines have successfully reduced the number of suicides. On the contrary, other research studies stated that the guidelines have worked in some cases. == Impact of pro-suicidal sites, message boards, chat rooms and forums == Social media platforms have transformed traditional methods of communication by allowing instantaneous and interactive sharing of information created and controlled by individuals, groups, organizations, and governments. As of the third quarter of 2022, Facebook had 266 million monthly active users, between Canada and the US. An immense quantity of information on the topic of suicide is available on the Internet and via social media. The information available on social media on the topic of suicide can influence suicidal behavior, both negatively and positively. The social cognitive theory plays a vital role in suicide attempts influenced through social media. This theory is demonstrated when one is influenced by what they see through various processes that form into modeled behaviors. This can be shown when people post their suicide attempts online or promote suicidal behavior in general. Contributors to these social media platforms may also exert peer pressure and encourage others to take their own lives, idolize those who have killed themselves, and facilitate suicide pacts. These pro-suicidal sites reported the following. For example, on a Japanese message board in 2008, it was shared that people can kill themselves using hydrogen sulfide gas. Shortly afterwards, 220 people attempted suicide in this way, and 208 were successful. Biddle et al. conducted a systematic Web search of 12 suicide-associated terms (e.g., suicide, suicide methods, how to kill yourself, and best suicide methods) to analyze the search results, and found that pro-suicide sites and chat rooms that discussed general issues associated with suicide most often occurred within the first few hits of a search. In another study, 373 suicide-related websites were found using Internet search engines and examined. Among them, 31% were suicide-neutral, 29% were anti-suicide, and 11% were pro-suicide. Together, these studies have shown that obtaining pro-suicide information on the Internet, including detailed information on suicide methods, is very easy. While social media has been prevalent in young adult suicide, some young adults find comfort and solace through these platforms. Young adults are making connections with people in like situations that are helping them feel less lonely. Although the public opinion is that message boards are harmful, the following studies show how they point to suicide prevention and have positive influences. A study using content analysis analyzed all of the postings on the AOL Suicide Bulletin Board over 11 months and concluded that most contributions contained positive, empathetic, and supportive postings. Then, a multi-method study was able to demonstrate that the users of such forums experience a great deal of social support and only a small amount of social strain. Lastly, in the survey participants were asked to assess the extent of their suicidal thoughts on a 7-level scale (0, absolutely no suicidal thoughts, to 7, very strong suicidal thoughts) for the time directly before their first forum visit and at the time of the survey. The study found a significant reduction after using the forum. The study however cannot conclude the forum is the only reason for the decrease. Together, these studies show how forums can reduce the number of

Storyful

Storyful (stylized as storyful.) is a social media intelligence company headquartered in Dublin, Ireland that is a subsidiary of News Corp, offering services such as social news monitoring, video licensing, and reputation risk management tools for corporate clients. The startup was launched as the first social media newswire, a content aggregator, verifying news sources and online content in Dublin in 2010 by Mark Little, a former journalist with RTÉ News. Storyful was acquired by News Corp in 2013 for USD$25 million. == Background == Mark Little, who had worked as a television journalist for RTÉ One, founded startup Storyful in Dublin, Ireland, in 2010, as a service that "verified news sources and online content". According to Nieman Lab, Storyful had a reputation for content aggregation as a social news agency—finding, verifying, distributing, licensing, and commercializing user-generated content, social media and online content from social networking services, including videos about stories in the news, such as the Syrian Civil War, Arab Spring protests, as well as "smaller viral moments". Storyful aimed to provide authority through its verification and monitoring tools while providing authenticity through user-generated content. On 20 December 2013 News Corp purchased Storyful for US$25 million and opened a New York office in the same building as Fox News' main studios. Little left Storyful in 2015 and Gavin Sheridan, Storyful's director of innovation left in 2014. News Corp CEO Robert Thomson said that through Storyful, News Corp would "define the opportunities that the digital landscape presents, rather than simply adapt to them." After the acquisition, the company expanded its service to include "commercial and creative work". After Murdoch acquired the company, from 2014 through to February 2018, losses "swelled", requiring a series of cash injections from News Corp. During that time the company expanded aggressively globally with a staff of about 200 worldwide up from about 30 in 2014. According to The Guardian, in 2016, journalists were encouraged by Storyful to use the social media monitoring software called Verify developed by Storyful. By installing Verify's web browser extension on their computers, Verify would inform the journalists when social media content had been "verified and cleared". The Guardian revealed that through the Verify plugin, dozens of staff in four offices had access to the journalists browsing activity without them knowing. This data allowed Storyful to actively monitor its own clients' activities on social media and to "turn it into an internal feed" at Storyful that "updates in real time". In November 2018, when a video circulated by Infowars' Paul Joseph Watson appeared to prove that CNN's Jim Acosta's contact with a White House intern was a physical blow, Storyful was able to prove that the 15-second-long clip had been doctored. According to a 21 January 2019 article in CNN Business, Rob McDonagh, the editor of Storyful's U.S. news team, had proven that one of the viral videos that served as catalysts in the January 2019 Lincoln Memorial confrontation at 18 January 2019 Indigenous Peoples March, was posted by a suspicious account, under the handle @2020fight. McDonagh's team validates videos and posts before adding them to their "digest", distinguishing true stories from those that are not. Storyful attempts to validate each post or video before including it in its digest. McDonagh reviewed previous content from @2020fight's account, and found it suspicious because it had a high follower count, a "highly polarized and yet inconsistent political messaging", an "unusually high rate of tweets", and "the use of someone else's image in the profile photo." reporter Donie O'Sullivan said that the @2020fight video that had been posted on 18 January, which had 2.5 million views by 22 January, was the one that "helped frame the news cycle". Currently the website offers a service by which video can be commercially brokered. == Services == Services include a newswire service—one of their "core pillars"—and social news monitoring. By February 2018, Storyful was developing "risk and reputation monitoring" services through which they would source and verify social news, fact-checking it and contextualising it for corporate clients. They were "developing tech tools" to "explore obscure or closed networks" for their intelligence team. can use to explore obscure or closed networks. They "track deviations in social conversations around brands and organisations and catch potential risks before they blow up. Like an alerts system." The company "released a re-booted version of its Newswire platform in 2018. According to FORA, Storyful was developing new tools to combat fake news online. == Clients == When Storyful was acquired by News Corp in 2013, the company already had the Wall Street Journal, the BBC, New York Times, YouTube, ITN and Channel 4 News as clients. By 2018 their clients included CNN, ABC News and Fox News, The New York Times, the Washington Post, in the United States, the Australian Broadcasting Corporation and all of News Corp’s own publications. Most of their "reputation-conscious corporate customers" clients prefer to not be named.

IBM remote batch terminals

The IBM 2780 and the IBM 3780 are devices developed by IBM for performing remote job entry (RJE) and other batch functions over telephone lines; they communicate with the mainframe via Binary Synchronous Communications (BSC or Bisync) and replaced older terminals using synchronous transmit-receive (STR). In addition, IBM has developed workstation programs for the 1130, 360/20, 2922, System/360 other than 360/20, System/370 and System/3. == 2780 Data Transmission Terminal == The 2780 Data Transmission Terminal first shipped in 1967. It consists of: A line printer similar to the IBM 1443 that can print up to 240 lines per minute (lpm), or 300 lpm using an extremely restricted character set. A card reader/punch unit, similar to an IBM 1442, that can read up to 400 cards per minute (cpm) and can punch up to 355 cpm. A line buffer that stores data received or to be transmitted over the communications line. A binary synchronous adapter which controls the flow of data over the communications line. The 2780 is capable of local (offline) card to print operation. It comes in four models: Model 1: Can read punched cards and transmit the data to a remote host computer, and can receive and print data sent by the host. Model 2: Same as Model 1 but adds the ability to punch card data received from the host. Model 3: Can only print data received from the host, but not send data to it. Model 4: Can read and punch card data, but has no printing capabilities. The 2780 uses a dedicated communication line at speeds of 1200, 2000, 2400 or 4800 bits per second. It is a half duplex device, although full duplex lines can be used with some increase in throughput. It can communicate in Transcode (a 6-bit code), 8-bit EBCDIC, or 7-bit ASCII. == 2770 Data Communication System == The 2770, announced in 1969, "was said to surpass all other IBM terminals in the variety of available input-output devices." The 2770 was developed by the IBM General Products Division (GPD) in Rochester, MN. It comes standard with a desktop terminal with keyboard. The printer and other devices (any two in any combination) can be attached to the 2772 Multi-Purpose Control unit. Possible devices include: 50 Magnetic Data Inscriber 545 Card Punch Model 3 (non-printing) or Model 4 (printing) 1017 Paper Tape Reader 1018 Paper Tape Punch 1053 Printer Model 1 1255 Magnetic Character Reader Models 1, 2 or 3 2203 Printer Model A1 or A2 2213 Printer Model 1 or 2 2265 Display Station Model 2 2502 Card Reader Model A1 or A2 5496 Data Recorder == 3780 Data Communications Terminal == In May 1972, IBM announced the IBM 3780, an enhanced version of the 2780. The 3780 was developed by IBM's Data Processing Division (DPD). There is one model, with an optional card punch. The 3780 drops Transcode support and incorporates several performance enhancements. It supports compression of blank fields in data using run-length encoding. It provides the ability to interleave data between devices, introduces double buffering, and adds support for the Wait-before-transmit ACKnowledgement (WACK) and Temporary Text Delay (TTD) Binary Synchronous control characters. The integrated punched card unit can read cards at 600 cards per minute. The integrated printer is rated at 300, 350 or 425 lines per minute based on characters set (63, 52 or 39 characters). The 3781 Card Punch is an optional feature. It punches 160 columns per second, or 91 cards per minute if all 80 columns are punched. The IBM 2780 and 3780 were later emulated on various types of equipment, including eventually the personal computer. A notable early emulation was the DN60, by Digital Equipment Corporation in the late 1970s. == 3770 Data Communications System == In 1974 IBM Data Processing Division (DPD) offered a successor to the 3780, called the 3770 Data Communications System, supporting SDLC, BSC, BSC Multi-leaving and SNA, depending on the configuration. The 3770 is a family of desk console style terminals that offers a variety of keyboard and printer combinations as well as I/O equipment attachment and communications features. The terminals come built into a desk and include the following models: 3771 Communication Terminal (optional card reader, optional card punch, wire matrix printer) Models 1 (40 cps printer), 2 (80 cps printer), and 3 (120 cps printer). 3773 Communication Terminal (diskette, wire matrix printer) Models 1 (40 cps printer), 2 (80 cps printer), and 3 (120 cps printer). Each model has a P version which adds some programming features. 3774 Communication Terminal (optional card reader, optional card punch, optional belt printer, wire matrix printer) Models 1 (80 cps printer), and 2 (120 cps printer). Each model has a P version which adds some programming features, a 480-character display and a non-removable diskette. 3775 Communication Terminal (optional card reader, optional card punch, optional diskette, belt printer) Model 1 (120 lpm printer). The model P1 adds some programming features, a 480-character display and a non-removable diskette. 3776 Communication Terminal (optional card reader, optional card punch, optional diskette, belt printer) Models 1 (300 lpm printer) and 2 (400 lpm printer). Models 3 and 4 are similar to models 1 and 2. 3777 Communication Terminal (optional card reader, optional diskette, train printer) Model 1 (up to 1000 lpm printer depending on character set). Model 2 adds an optional card punch, model 3 adds an optional magnetic tape drive and model 4 replaces the train printer with a slower model called the IBM 3262. The model 4 also allows a second, optional, 3262. The following I/O devices can be attached to a 3770 terminal: IBM 2502 Card Reader: Models A1 (up to 150 card per minute), A2 (up to 300 cards per minute) or A3 (up to 400 cards per minute) IBM 3203 Printer Model 3: 1000 LPM using 48 character set IBM 3501 Card Reader: Up to 50 cards per minute desktop unit IBM 3521 Card Punch: Up to 50 cards per minute IBM 3782 Card Attachment unit, which allows the 2502 or 3521 to be attached to any terminal except the 3777 IBM 3784 Line Printer, can be attached to a 3774 as a second printer. Up to 155 LPM with 48 characters set print belt. == Workstation programs == IBM distributes workstation programs with systems software including OS/360 Attached Support Processor (ASP) Houston Automatic Spooling Priority (HASP and HASP II) Operating System/Virtual Storage 1 (OS/VS1) Operating System/Virtual Storage 2 (OS/VS2 MVS) Release 2 through 3.8 MVS versions from MVS/SP Version 1 through z/OS Priority Output Writers, Execution processors and input Readers (POWER) Remote Spooling Communications Subsystem (RSCS) Except for the RJE workstation programs in OS/360, these programs use a variation of BSC known as Multi-leaving. In addition, IBM provides separately ordered workstation programs using BSC. Systems Network Architecture (SNA) and TCP/IP. Workstation programs are available from IBM and third-party vendors to support all of these protocols: 2770/3770 2780/3780 Multileaving Network Job Entry (NJE) OS/360 RJE SNA TCP/IP

Mooky (app)

Mooky was a location-based social and dating application, designed to help its users to find the perfect match by providing a large scale of filters. Mooky was free of charge. The app made use of mobile devices' geolocation, a feature of smart phones and other devices which allows users to locate other users who are nearby. == History == Mooky was published on Google Play on April 17, 2016, by Mooky BV. The latest version of this application was version 1.0.6. == Overview == === How it works === Mooky used Facebook to build a user profile with photos and basic information, like the user's surname and age. From there on the user had to fill in their Mooky profile, which contains information about the user's height, posture, hair color, eye color, ethnicity and religion. After this the user could select its preferences to find matches nearby. === User verification === Mooky asked their users to take a selfie holding a piece of paper saying 'Mooky'. Mooky would then manually accept or decline the user verification.

Social trading

Social trading is a form of investing that allows investors to observe the trading behavior of their peers and expert traders. The primary objective is to follow their investment strategies using copy trading or mirror trading. Social trading requires little or no knowledge about financial markets. == History == One of the first social trading platforms was Collective2] which began offering a social trading functionality to retail traders as early as 2003 (preceding ZuluTrade by four years). In 2010, social trading started to achieve a greater degree of mainstream appeal with eToro, followed by Wikifolio in 2012. Europe-based NAGA, listed on Frankfurt Stock Exchange since 2017, claims more than EUR 27 billion was traded on its platform in the second half of 2019. Some of the other contemporary social trading platforms and tech providers are Trading Motion, Brokeree Solutions, iSystems, and FX Junction, among others. === Research === MIT Computer Scientist and researcher Yaniv Altshuler described social trading networks as complex adaptive systems, and in his 2014 research on eToro's OpenBook, wrote that "Having the inherent ability to share ideas and information between each others, OpenBook's users are given a new source of information they can use in order to enhance their trading performance. As the users are not playing against each other but rather – against the market, this situation becomes a non zero-sum game, hence incentivizing the users to share as much information as possible." His paper concludes that "social trading provides much better opportunities for profiting compared with individual trading," but that users make "excellent but sometimes not optimal decisions in selecting experts when they can see others' choices." A 2015 World Economic Forum report described social trading networks as disruptors, which "have emerged to provide low-cost, sophisticated alternatives to traditional wealth managers. These solutions cater to a broader customer base and empower customers to have more control of their wealth management," and "pose a tangible threat to the traditional practices of the wealth management industry". Economist Nouriel Roubini's thinktank predicted in 2016 that "newer forms of investment, such as socially responsible investments and social trading will bring some of the largest industry growth in the coming years." A 2017 St. John's University study found that 'leader' traders, or those with followers, are more susceptible to the disposition effect than investors that are not being followed by any other traders, with the authors suggesting the observation may be explained by "leaders feeling responsible towards their followers and an urge to not let them down, by fear of losing followers when admitting a bad investment decision and signaling confidence in their initial investment choice, or by an attempt of newly appointed leaders to manage their self-image." Social trading may potentially also change how much risk investors take. A recent experimental study argues that merely providing information on the success of others may lead to a significant increase in risk taking. This increase in risk taking may even be larger when subjects are provided with the option to directly copy others. == Characteristics == Social trading is an alternative way of analyzing financial data by looking at what other traders are doing and comparing and copying their techniques and strategies. Prior to the advent of social trading, investors and traders were relying on fundamental or technical analysis to form their investment decisions. Using social trading investors and traders could integrate into their investment decision-process social indicators from trading data-feeds of other traders. Social trading platforms or networks can be considered a subcategory of social networking services. Social trading allows traders to trade online with the help of others and some have claimed shortens the learning curve from novice to experienced trader. Traders can interact with others, watch others take trades, then duplicate their trades and learn what prompted the top performer to take a trade in the first place. By copying trades, traders can learn which strategies work and which do not work. Social trading is used to do speculation; in the moral context speculative practices are considered negatively and to be avoided by each individual. who conversely should maintain a long-term horizon avoiding any types of short term speculation. Social Media has permeated the trading world such that two main types of trading has evolved: Traditional Trades Single (or non-social) trade: Trader A places a normal trade by himself or herself; This can by manual or automated Social Trading There are two main types of social trading: Copy trade: Trader A places exactly the same trade as trader B's one single trade; (iii) Mirror trade: Trader A automatically executes trader B's every single trade, i.e., trader A follows exactly trader B's trading activities. Other variations offered on some platforms allow users to copy another trader's portfolio (copy portfolio), and follow a trader's dividends (copy dividends), where whenever a followed trader withdraws money from his or her account, a proportional amount of money will be withdrawn from the balance of their follower, in real time. === Key features === Information flow: Unencumbered access to information is important in financial markets and that makes the free exchange of information of interest to small scale as well as individual investors. Cooperative trading: Social trading offers traders the opportunity to work together in trading teams which can trade the markets collaboratively, whether by pooling funds, dividing research or through sharing information. Monetization: As with social networks in the broader sense, monetization strategies are not always clear. As with social networks in general, it is possible, however, that the long-term worth of such websites may come from the variety and depth of data about their users which their active communities are likely to generate. Transparency: Social trading platforms reveal traders' performance stats, open and past positions, and market sentiment, giving members complete information to assess the credibility of the contributors they follow on the platform.