In mathematics, the sieve of Pritchard is an algorithm for finding all prime numbers up to a specified bound. Like the ancient sieve of Eratosthenes, it has a simple conceptual basis in number theory. It is especially suited to quick hand computation for small bounds. Whereas the sieve of Eratosthenes marks off each non-prime for each of its prime factors, the sieve of Pritchard avoids considering almost all non-prime numbers by building progressively larger wheels, which represent the pattern of numbers not divisible by any of the primes processed thus far. It thereby achieves a better asymptotic complexity, and was the first sieve with a running time sublinear in the specified bound. Its asymptotic running-time has not been improved on, and it deletes fewer composites than any other known sieve. It was created in 1979 by Paul Pritchard. Since Pritchard has created a number of other sieve algorithms for finding prime numbers, the sieve of Pritchard is sometimes singled out by being called the wheel sieve (by Pritchard himself) or the dynamic wheel sieve. == Overview == A prime number is a natural number that has no natural number divisors other than the number 1 and itself. To find all the prime numbers less than or equal to a given integer N, a sieve algorithm examines a set of candidates in the range 2, 3, …, N, and eliminates those that are not prime, leaving the primes at the end. The sieve of Eratosthenes examines all of the range, first removing all multiples of the first prime 2, then of the next prime 3, and so on. The sieve of Pritchard instead examines a subset of the range consisting of numbers that occur on successive wheels, which represent the pattern of numbers left after each successive prime is processed by the sieve of Eratosthenes. For i > 0, the ith wheel Wi represents this pattern. It is the set of numbers between 1 and the product Pi = p1 · p2 ⋯ pi of the first i prime numbers that are not divisible by any of these prime numbers (and is said to have an associated length Pi). This is because adding Pi to a number does not change whether it is divisible by one of the first i prime numbers, since the remainder on division by any one of these primes is unchanged. So W1 = {1} with length P1 = 2 represents the pattern of odd numbers; W2 = {1,5} with length P2 = 6 represents the pattern of numbers not divisible by 2 or 3; etc. Wheels are so-called because Wi can be usefully visualized as a circle of circumference Pi with its members marked at their corresponding distances from an origin. Then rolling the wheel along the number line marks points corresponding to successive numbers not divisible by one of the first i prime numbers. The animation shows W2 being rolled up to 30. It is useful to define Wi → n for n > 0 to be the result of rolling Wi up to n. Then the animation generates W2 → 30 = {1,5,7,11,13,17,19,23,25,29}. Note that up to 52 − 1 = 24, this consists only of 1 and the primes between 5 and 25. The sieve of Pritchard is derived from the observation that this holds generally: for all i > 0, the values in Wi → (p2i+1 − 1) are 1 and the primes between pi+1 and p2i+1. It even holds for i = 0, where the wheel has length 1 and contains just 1 (representing all the natural numbers). So the sieve of Pritchard starts with the trivial wheel W0 and builds successive wheels until the square of the wheel's first member after 1 is at least N. Wheels grow very quickly, but only their values up to N are needed and generated. It remains to find a method for generating the next wheel. Note in the animation that W3 = {1,5,7,11,13,17,19,23,25,29} − {5 · 1 , 5 · 5} can be obtained by rolling W2 up to 30 and then removing 5 times each member of W2.This also holds generally: for all i ≥ 0, Wi+1 = (Wi → Pi+1) − {pi+1 · w | w ∈ Wi}. Rolling Wi past Pi just adds values to Wi, so the current wheel is first extended by getting each successive member starting with w = 1, adding Pi to it, and inserting the result in the set. Then the multiples of pi+1 are deleted. Care must be taken to avoid a number being deleted that itself needs to be multiplied by pi+1. The sieve of Pritchard as originally presented does so by first skipping past successive members until finding the maximum one needed, and then doing the deletions in reverse order by working back through the set. This is the method used in the first animation above. A simpler approach is just to gather the multiples of pi+1 in a list, and then delete them. Another approach is given by Gries and Misra. If the main loop terminates with a wheel whose length is less than N, it is extended up to N to generate the remaining primes. The algorithm, for finding all primes up to N, is therefore as follows: Start with a set W = {1} and length = 1 representing wheel 0, and prime p = 2. As long as p2 ≤ N, do the following: if length < N, then extend W by repeatedly getting successive members w of W starting with 1 and inserting length + w into W as long as it does not exceed p · length or N; increase length to the minimum of p · length and N. repeatedly delete p times each member of W by first finding the largest ≤ length and then working backwards. note the prime p, then set p to the next member of W after 1 (or 3 if p was 2). if length < N, then extend W to N by repeatedly getting successive members w of W starting with 1 and inserting length + w into W as long as it does not exceed N; On termination, the rest of the primes up to N are the members of W after 1. === Example === To find all the prime numbers less than or equal to 150, proceed as follows. Start with wheel 0 with length 1, representing all natural numbers 1, 2, 3...: 1 The first number after 1 for wheel 0 (when rolled) is 2; note it as a prime. Now form wheel 1 with length 2 × 1 = 2 by first extending wheel 0 up to 2 and then deleting 2 times each number in wheel 0, to get: 1 2 The first number after 1 for wheel 1 (when rolled) is 3; note it as a prime. Now form wheel 2 with length 3 × 2 = 6 by first extending wheel 1 up to 6 and then deleting 3 times each number in wheel 1, to get 1 2 3 5 The first number after 1 for wheel 2 is 5; note it as a prime. Now form wheel 3 with length 5 × 6 = 30 by first extending wheel 2 up to 30 and then deleting 5 times each number in wheel 2 (in reverse order), to get 1 2 3 5 7 11 13 17 19 23 25 29 The first number after 1 for wheel 3 is 7; note it as a prime. Now wheel 4 has length 7 × 30 = 210, so we only extend wheel 3 up to our limit 150. (No further extending will be done now that the limit has been reached.) We then delete 7 times each number in wheel 3 until we exceed our limit 150, to get the elements in wheel 4 up to 150: 1 2 3 5 7 11 13 17 19 23 25 29 31 37 41 43 47 49 53 59 61 67 71 73 77 79 83 89 91 97 101 103 107 109 113 119 121 127 131 133 137 139 143 149 The first number after 1 for this partial wheel 4 is 11; note it as a prime. Since we have finished with rolling, we delete 11 times each number in the partial wheel 4 until we exceed our limit 150, to get the elements in wheel 5 up to 150: 1 2 3 5 7 11 13 17 19 23 25 29 31 37 41 43 47 49 53 59 61 67 71 73 77 79 83 89 91 97 101 103 107 109 113 119 121 127 131 133 137 139 143 149 The first number after 1 for this partial wheel 5 is 13. Since 13 squared is at least our limit 150, we stop. The remaining numbers (other than 1) are the rest of the primes up to our limit 150. Just 8 composite numbers are removed, once each. The rest of the numbers considered (other than 1) are prime. In comparison, the natural version of Eratosthenes sieve (stopping at the same point) removes composite numbers 184 times. == Pseudocode == The sieve of Pritchard can be expressed in pseudocode, as follows: algorithm Sieve of Pritchard is input: an integer N >= 2. output: the set of prime numbers in {1,2,...,N}. let W and Pr be sets of integer values, and all other variables integer values. k, W, length, p, Pr := 1, {1}, 2, 3, {2}; {invariant: p = pk+1 and W = Wk ∩ {\displaystyle \cap } {1,2,...,N} and length = minimum of Pk,N and Pr = the primes up to pk} while p2 <= N do if (length < N) then Extend W,length to minimum of plength,N; Delete multiples of p from W; Insert p into Pr; k, p := k+1, next(W, 1) if (length < N) then Extend W,length to N; return Pr ∪ {\displaystyle \cup } W - {1}; where next(W, w) is the next value in the ordered set W after w. procedure Extend W,length to n is {in: W = Wk and length = Pk and n > length} {out: W = Wk → {\displaystyle \rightarrow } n and length = n} integer w, x; w, x := 1, length+1; while x <= n do Insert x into W; w := next(W,w); x := length + w; length := n; procedure Delete multiples of p from W,length is integer w; w := p; while pw <= length do w := next(W,w); while w > 1 do w := prev(W,w); Remove pw from W; where prev(W, w) is the previous value in the ordered set W before w. The algorithm can be initialized with W0 instead of W1 at the minor complication of making next(W, 1) a special case when k = 0. This a
Color reproduction
Color reproduction is an aspect of color science concerned with producing light spectra that evoke a desired color, either through additive (light emitting) or subtractive (surface color) models. It converts physical correlates of color perception (CIE 1931 XYZ color space tristimulus values and related quantities) into light spectra that can be experienced by observers. In this way, it is the opposite of colorimetry. It is concerned with the faithful reproduction of a color in one medium, with a color in another, so it is a central concept in color management and relies heavily on color calibration. For example, food packaging must be able to faithfully reproduce the colors of the foods therein in order to appeal to a customer. This involves proper color calibration of at least four devices: Lighting, which must have a high color rendering index and not give a color cast to the object. Camera, which measures the reflected spectrum of the object and converts to a trichromatic color space (e.g. RGB). Screen, which reproduces color so a designer can proof the captured image and make color corrections as necessary. Printer, which reproduces the final color on paper.
Philco computers
Philco was one of the pioneers of transistorized computers, also known as second-generation computers. After the company developed the surface-barrier transistor, which was much faster than previous point-contact types, it was awarded contracts for military and government computers. Commercialized derivatives of some of these designs became successful business and scientific computers. The TRANSAC (Transistor Automatic Computer) Model S-1000 was released as a scientific computer. The TRANSAC S-2000 mainframe computer system was first produced in 1958, and a family of compatible machines, with increasing performance, was released over the next several years. However, the mainframe computer market was dominated by IBM. Other companies could not deploy resources for development, customer support and marketing on the scale that IBM could afford, making competition in this segment difficult after the introduction of the IBM 360 family. Philco went bankrupt and was purchased in 1961 by Ford Motor Company, but the computer division carried on until the Philco division of Ford exited the computer business in 1963. The Ford company maintained one Philco mainframe in use until 1981. == The surface-barrier transistor == The surface-barrier transistor developed by Philco in 1953 had a much higher frequency response than the original point-contact transistors. The transistor was made of a thin crystal of germanium, which was electrolytically etched with pits on either side forming a very thin base region, on the order of 5 micrometers. Philco's process for etching was United States patent number 2,885,571. Philco surface-barrier transistors were used in TX-0, and in early models of what would become the DEC PDP product line. Although relatively fast, the small size of the devices limited their power to circuits operating at a few tens of milliwatts. == Military and government == Between 1955 and 1957, Philco built transistor computers for use in aircraft, models C-1000, C-1100, and C-1102, intended for airborne real-time applications. By 1957, the C-1102 had been used by a civilian sector customer. The BASICPAC AN/TYK 6V (first delivery in 1961), COMPAC AN/TYK 4V (not completed), and LOGICPAC systems were built for the US Army as transportable computer systems for use with their Fieldata concept of integrated information management. BASICPAC was a transistorized computer with up to 28,672 words of 38-bit core memory (including sign and parity), available in several configurations from a minimum system, to a truck-borne mobile version, to a fully expanded system. Basic clock periods was 1 microsecond (which gives a clock rate of 1 MHz), with 12 microsecond memory access and a fixed-point multiplication taking 242 microseconds. Input/output was by paper tape reader and punch, or through a teletypewriter. With additional hardware, magnetic tape storage was also available, with up to seven I/O devices. The instruction set had 31 basic operation codes and nine opcodes for I/O === CXPQ === Philco was contracted by the US Navy to build the CXPQ computer. One model was completed and installed at the David Taylor Model Basin. This design was later adapted to become the commercial TRANSAC S-2000. Only one CXPQ was built. The CXPQ is a 48-bit transistorized computer. === SOLO === In 1955, the National Security Agency through the US Navy contracted with Philco to produce a computer suitable for use as a workstation, with an architecture based on the vacuum-tube computer system called Atlas II already in use at the NSA, and similar to the commercial UNIVAC 1103. At the time, Philco was the largest producer of surface barrier transistors, which were the only type available with the speed and quantities required for a computer. The SOLO prototype was delivered in 1958, but required extensive debugging at NSA. Difficulties were encountered with core memory and power supplies. SOLO used paper tape and teleprinter machines for input and output. SOLO cost about $1 million US, and contained 8,000 transistors. While the system was extensively used for training, testing, research and development, no additional units were ordered. SOLO was removed from active service in 1963. The design of the SOLO became commercialized as Philco's TRANSAC Model S-1000. == Commercial == === S-1000 === The TRANSAC S-1000 was a scientific computer with a 36-bit word length and 4096 words of core memory. It was packaged in a container about the size of a large office desk, and used only 1.2 kilowatts, much less than vacuum-tube-based computers of similar capacity. In a 1961 survey, about 15 S-1000 computer installations had been identified. It weighed about 1,650 pounds (750 kg). === S-2000 === The TRANSAC S-2000 was a large mainframe system intended for both business and scientific work. It had a 48-bit word length and supported calculations in fixed point, floating point and binary-coded decimal formats. The original S-2000 "TRANSAC" (Transistor Automatic Computer) released in 1958 was later designated Model 210; it was used internally at Philco. Similar to the Control Data Corporation Model 1604, it was a 48-bit fully transistorized computer. Three succeeding models were released in the series, all compatible with the software of the original model. The Model 211 was introduced in 1960, using micro-alloy diffused field-effect transistors, requiring significant redesign of circuits compared to the original. The TRANSAC S-2000/Philco 210/211 weighed about 2,000 pounds (910 kg). By 1964, eighteen Model 210, eighteen Model 211 and seven Model 212 systems had been sold. After Philco was purchased by Ford Motor Company, the Model 212 was introduced in 1962 and released in 1963. It had 65,535 words of 48-bit memory. Initially made with 6-microsecond core memory, it had better performance than the IBM 7094 transistor computer. It was later upgraded in 1964 to 2-microsecond core memory, which gave the machine floating-point performance greater than the IBM 7030 Stretch computer. A Model 213 was announced in 1964 but never built. By that time competition from IBM had made the Philco computer operations no longer profitable for Ford, and the division was closed down. The Model 212 could carry out a floating-point multiplication in 22 microseconds. Each word contained two 24-bit instructions with 16 bits of address information and eight bits for the opcode. There were 225 different valid opcodes in the Model 212; invalid opcodes were detected and halted the machine. The CPU had an accumulator register of 48 bits, three general-purpose registers of 24 bits, and 32 index registers of 15 bits. Main memory size ranged from 4K words to 64K words. Only the first model had a magnetic drum memory; later editions used tape drives. The Model 212 weighed about 6,500 pounds (3.3 short tons; 2.9 t). Software for the S-2000 initially consisted of TAC (Translator-Assembler-Compiler), and ALTAC, a FORTRAN II-like language with some differences from the IBM 704 FORTRAN implementation. A COBOL compiler was also available, targeted at business applications. The Philco 2400 was the input/output system for the S-2000. Operations such as reading cards or printing were carried out through magnetic tapes, thereby offloading the S-2000 from relatively slow input/output processing. The 2400 had a 24-bit word length and could be supplied with 4K to 32K characters (1K to 8K words) of core memory, rated at 3-microsecond cycle time. The instruction set was aimed at character I/O use. The idea of base registers, implemented in Philco computers, influenced the design of IBM/360. The last Philco TRANSAC S-2000 Model 212 was taken out of service in December 1981, after 19 years of service at Ford.
Pivot to video
"Pivot to video" is a phrase referring to the trend, starting in 2015, of media publishing companies cutting staff resources for written content (generally published on their own web sites) in favor of short-form video content (often published on third-party platforms such as Facebook, Instagram, Twitter, YouTube, Snapchat, and TikTok). These moves were generally presented by publishers as a response to changes in social media traffic or to changes in the media consumption habits of younger audiences. However, many media commentators have argued that this shift was primarily motivated by advertising revenue, and that only advertisers, not consumers, prefer video over text. The pivot's contribution to job loss in the media industry has given the phrase "pivot to video" an association with decline, especially in a business context. Commentators have also noted a lack of transparency and accuracy in the viewership metrics reported by platforms such as Facebook, pointing out that abrupt shifts in platforms' proprietary algorithms can have devastating effects on publishers' viewership, traffic, and revenue. Following a scandal in which Facebook revealed it had artificially inflated numbers to its advertisers about how long viewers watched ads, many journalists and industry analysts concluded that the shift to video was based on such misleading or inaccurate metrics, which created a false impression that there was customer demand for additional video content. == History == Streaming media technology has been available since the early 1990s, though it was relatively low-fidelity and not widely available until the mid-2000s. In 2007, traditional media publishers including the New York Times, Washington Post and Time Inc. created new divisions to develop web videos, and Facebook launched its video platform. Twitter purchased micro-video service Vine in October 2012, began adding native video streaming in late 2014, and acquired video-streaming service Periscope in January 2015. An August 2014 profile on BuzzFeed noted the publisher's large investment into video production, and observed that "the future of BuzzFeed may not even be on BuzzFeed.com. One of the company’s nascent ideas, BuzzFeed Distributed, will be a team of 20 people producing content that lives entirely on other popular platforms, like Tumblr, Instagram or Snapchat." On 7 January 2015, Facebook issued a statement about "the shift to video," reporting that "since June 2014, Facebook has averaged more than 1 billion video views every day." Media critic John Herrman argued that "What the shift to Facebook video means is that Facebook is more interested in hosting the things media companies make than just spreading them, that it views links to outside pages as a problem to be solved, and that it sees Facebook-hosted video as an example of the solution." In February 2015, the digital video-journalism publisher NowThis announced that it would operate without a home page, producing content to be published directly on social media platforms. In April 2016, Mashable fired much of its editorial staff, attempting to pivot away from hard news coverage while "growing Mashable across every platform" and doubling down on branded content and video. By December 2017, following a sale to Ziff Davis, Mashable retreated from this focus on video; Bernard Gershon, president of GershonMedia, said that the announcement of many such "pivots" were actually aimed primarily at investors. By 2017, "advertiser interest in video [was] insatiable... Any CFO is going to say 'How can we get more video?'" according to an executive of the publishers' trade association Digital Content Next. Publishers such as Vanity Fair, the Washington Post, and Sports Illustrated began adapting their own articles into cheap video content, either dictated by a newsreader or animated as a slideshow with captions, which could be shared on social platforms or even played alongside the articles themselves. June 2017 saw numerous high-profile pivots to video. Vocativ laid off at least 20 staff, including its entire newsroom, explaining that "as the industry evolves, we are undertaking a strategic shift to focus exclusively on video content that will be distributed via social media and other platforms." Fox Sports eliminated its entire writing staff to focus on creating "premium video across all platforms." And MTV News announced a restructuring that would cut its writing team. Less than two years earlier, MTV News had hired Grantland co-founder Dan Fierman to lead a significant investment in "longform" political and cultural reporting, but Fierman left in April 2017, and in June MTV announced it was "shifting resources into short-form video content more in line with young people's media consumption habits." In July, Vice Media laid off at least 60 employees, including the editor-in-chief of Vice Sports, while expanding video production. August 2017 saw Mic cut ten writers and directed the remainder of the newsroom to generate videos for social platforms. CEO Chris Altchek said "When you think about how many hours people spend watching video versus reading, the audience has already spoken." The move was ultimately unsuccessful, and Mic laid off the majority of its staff a year later before being sold to Bustle Media Group for a fraction of its former value. In September 2017, the for-profit wiki-hosting company Fandom began adding commercially produced videos to its otherwise user-generated wiki subdomains, explicitly citing the need to "keep up with user and advertiser expectations" by "diversifying our content," claiming without substantiation that "consumer patterns are changing," necessitating the addition of "complementary video" to accommodate that supposed need. Objection to the content in these videos and its sharp contrast against the content of the wiki sites to which they were applied led to vocal user backlash, leading Fandom CCO Dorth Raphaely to offer the following non-committal response: "I agree that with these videos in particular we did not deliver the right type of content experience." Movie Pilot CEO Tobi Bauckhage explained his company's fall 2017 layoffs as part of moving "from a text-based publishing model to video... a reaction to the fact that Facebook has changed their algorithms in favor of video instead of referral traffic over the last 12 months and we were losing money in the publishing bit of our business." As part of the company's change in direction, the majority of its staff was laid off and its parent company was sold to Webedia. In November 2017, magazine publisher Condé Nast cut jobs, reduced the frequency of several magazines, and shut down the print edition of Teen Vogue, then invested significant new resources in video production, with a senior executive saying "In the next 24 months, I hope that video is half our business... It’s critical. It’s the macro trend of content consumption." In February 2018, Vox Media cut approximately 50 employees, primarily those assigned to "social video," as Vox CEO Jim Bankoff admitted that those efforts were not "viable audience or revenue growth drivers." In August 2020, Facebook Inc. (now Meta Platforms) pivoted Instagram to video in an effort to replicate the success of TikTok and appeal to a younger audience, introducing "reels" as a form of video and promoting them aggressively. Reels accounted more than half the 20 most-viewed posts on Facebook; however, most of these reels were anonymous aggregations of content from TikTok. Elon Musk declared in early 2024 that X (formerly Twitter) was now a "video-first platform", which has been described by critics as a "pivot to video". == As euphemism == In 2017, Journalist Brian Feldman said that "'Pivoting to video' has become a business strategy for digital publishers common enough in recent months to be a kind of cliché — a slick way to describe something else: layoffs." In response, writers use the phrase as gallows humor shorthand for death or cancellation, as in "how do i tell my bf i want our relationship to pivot to video" (SkyNews' Mollie Goodfellow) or "Horse broke its leg, so we had to take it out back and help it 'pivot to video'" (blogger Anil Dash). == Facebook metrics controversy == In September 2016, Facebook admitted that it had reported artificially inflated numbers to its advertisers about how long viewers watched ads leading to an overestimation of 60-80%. Plaintiffs in a later court case allege the discrepancy was as high as 150-900%. Facebook apologized in an official statement and in multiple staff appearances at New York Advertising Week. Two months later, Facebook disclosed additional discrepancies in audience metrics. In October 2018, a California federal court unsealed the text of a class action lawsuit filed by advertisers against Facebook, alleging that Facebook had known since 2015 that its viewership numbers were highly inflated, that internal records showed it "was far from an hon
Format-transforming encryption
In cryptography, format-transforming encryption (FTE) refers to encryption where the format of the input plaintext and output ciphertext are configurable. Descriptions of formats can vary, but are typically compact set descriptors, such as a regular expression. Format-transforming encryption is closely related to, and a generalization of, format-preserving encryption. == Applications of FTE == === Restricted fields or formats === Similar to format-preserving encryption, FTE can be used to control the format of ciphertexts. The canonical example is a credit card number, such as 1234567812345670 (16 bytes long, digits only). However, FTE does not enforce that the input format must be the same as the output format. === Censorship circumvention === FTE is used by the Tor Project to circumvent deep packet inspection by pretending to be some other protocols. The implementation is fteproxy; it was written by the authors who came up with the FTE concept.
Content as a service
Content as a service (CaaS) or managed content as a service (MCaaS) is a service-oriented model, where the service provider delivers the content on demand to the service consumer via web services that are licensed under subscription. The content is hosted by the service provider centrally in the cloud and offered to a number of consumers that need the content delivered into any applications or system, hence content can be demanded by the consumers as and when required. Content as a Service is a way to provide raw content (in other words, without the need for a specific human compatible representation, such as HTML) in a way that other systems can make use of it. Content as a Service is not meant for direct human consumption, but rather for other platforms to consume and make use of the content according to their particular needs. This happens usually on the cloud, with a centralized platform which can be globally accessible and provides a standard format for your content. With Content as a Service, you centralize your content into a single repository, where you can manage it, categorize it, make it available to others, search for it, or do whatever you wish with it. == Overview == The content delivered typically could be one or more of the following The technical terminology related to equipment or spares that is required to procure or design the materials The industrial terminology of the equipment or spares Technical values pertaining to various types, specifications, applications, characteristics of equipment or spares Sourcing information which will help in procurement or supply-chain management of equipment or spares Descriptive specifications of equipment or spares based on the product reference number or identifier UNSPSC codes or industry practiced classifications ISO, IEC compliant terminology Ontology or Technical Dictionary of products & services Predefined content for specific business needs The term "Content as a service" (CaaS) is considered to be part of the nomenclature of cloud computing service models & Service-oriented architecture along with Software as a service (SaaS), Infrastructure as a service (IaaS), and Platform as a service (PaaS).
Social media stock bubble
The social media bubble is a hypothesis stating that there was a speculative boom and bust phenomenon in the field of social media in the 2010s, particularly in the United States. The Wall Street Journal defined a bubble as stocks "priced above a level that can be justified by economic fundamentals," but this bubble includes social media. Social networking services (SNS) have seen huge growth since 2006, but some investors believed around 2014-2015, that the "bubble" was similar to the dot-com bubble of the late 1990s and early 2000s. In 2015, Mark Cuban, owner of the Dallas Mavericks NBA team and star of the TV show, Shark Tank, sounded an alarm on his personal blog over the social media bubble, calling it worse than the tech bubble in 2000 due to the lack of liquidity in social media stocks. A year prior, however, Cuban told CNBC that he did not believe social media stocks were on the verge of a bubble. In a letter to investors in 2014, David Einhorn, who runs the hedge-fund Greenlight Capital, wrote that "we are witnessing our second tech bubble in 15 years." He went on to write, "What is uncertain is how much further the bubble can expand, and what might pop it." Einhorn cited several factors supporting the existence an over-exuberance including "rejection of conventional valuation methods" and "huge first day IPO pops for companies that have done little more than use the right buzzwords and attract the right venture capital." Since those claims, services like Facebook, Twitter, Instagram, and Snapchat have grown to become multi-billion-dollar corporations generating enormous revenues, though some continue to lose money. == History of social networking services == Social networking services have grown and evolved with time since the launch of SixDegrees.com in 1997. Cutting edge at its time, SixDegrees.com allowed users to create a profile, invite friends, and connect within its platform. At its peak, SixDegrees.com had more than 3.5 million users. Between 1997 and 2001 more social sites aimed at allowing users to connect with others for personal, professional, or dating reasons. Friendster and MySpace were next to enter the social SNS arena, followed by Facebook in 2004. Even though MySpace had a following of more than 300 million users, it could not compete with Facebook, which now has overtaken the social networking world. However, as development of SNS started to emerge, a market saturation began to take effect. Some classrooms have begun to incorporate technology in daily learning as well as social channels specific to student's course work. Traditional social media sites are used, as are educational oriented sites such as ShowMe and Educreations Interactive Whiteboard. == Controversies == While SNS continue to play an influential role in helping people form real-world connections via the Internet, renewed concerns over the social media bubble have surfaced due to recent controversies. These threats include growing concerns about breaches in data, the rise of bot accounts, and the sharing of fake news on SNS platforms. There are also concerns that big data figures associated with these SNS are inflated or fake, as well as worries about the role the platforms played in national elections (see Russian interference in the 2016 United States elections). These issues have resulted in a lack of trust among the sites' users.