AI Chatbot That Sends Pictures

AI Chatbot That Sends Pictures — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

Relational data mining

Relational data mining is the data mining technique for relational databases. Unlike traditional data mining algorithms, which look for patterns in a single table (propositional patterns), relational data mining algorithms look for patterns among multiple tables (relational patterns). For most types of propositional patterns, there are corresponding relational patterns. For example, there are relational classification rules (relational classification), relational regression tree, and relational association rules. There are several approaches to relational data mining: Inductive Logic Programming (ILP) Statistical Relational Learning (SRL) Graph Mining Propositionalization Multi-view learning == Algorithms == Multi-Relation Association Rules: Multi-Relation Association Rules (MRAR) is a new class of association rules which in contrast to primitive, simple and even multi-relational association rules (that are usually extracted from multi-relational databases), each rule item consists of one entity but several relations. These relations indicate indirect relationship between the entities. Consider the following MRAR where the first item consists of three relations live in, nearby and humid: “Those who live in a place which is near by a city with humid climate type and also are younger than 20 -> their health condition is good”. Such association rules are extractable from RDBMS data or semantic web data. == Software == Safarii: a Data Mining environment for analysing large relational databases based on a multi-relational data mining engine. Dataconda: a software, free for research and teaching purposes, that helps mining relational databases without the use of SQL. == Datasets == Relational dataset repository: a collection of publicly available relational datasets.
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Mosaik Solutions

Mosaik Solutions (formerly American Roamer) was a company that specializes in wireless coverage data and wireless coverage maps, based in Memphis, Tennessee before being acquired by Ookla. The company collects and crowdsources carrier signal quality from major telecommunications providers or users who have its consumer or enterprise mobile application installed. The data is used to provide insights into places around the world without access to cellular coverage and the development of new coverage patterns, as well as to provide maps showing what provider offers the best service in an area. In 2011, the Federal Communications Commission (FCC), recognized Mosaik Solutions as the "industry standard" for the presence of wireless service at the census-block level. == History == In 2016, Mosaik purchased Sensorly, a free app developed to crowdsource cellular network performance service and provide coverage mapping for wireless networks worldwide. == Products and services == === MapELEMENTS === MapELEMENTS software is a visualization tool that allows users to analyze data from the largest cellular coverage database in the world. === CellMaps === CellMaps is an interactive mapping solution that allows companies to show their network coverage directly on their website through an iframe or API. In 2013 Mosaik launched an android app for CellMaps that provides data directly from carriers so that users can determine what carrier meets their needs in a given area. On the map you can overlay multiple carriers, zoom to street-view level, and drop a pin onto any given spot to get a breakdown of carrier service in that area. === Signal Insights App === Signal Insights is an SaaS platform service available for android users that measures and analyzes the customer's experience in cellular or Wi-Fi networks. Indoor mode allows a user to upload a building floor plan and then map and test specific points in the building for cellular or Wi-Fi connectivity. === Sensorly App === Sensorly is a free app that crowdsources cellular network performance to provide coverage mapping worldwide and mobile speed data to help consumers make informed decisions when choosing a cellular carrier. In February 2017, Sensorly launched Map Trip, a feature that allows users to map their routes and share with others their signal data at a particular point in real time. === TowerSource === TowerSource is a resource for locating cell towers and identifying ownership, availability, fiber routes, type and height. It was acquired by Mosaik Solutions in September 2014. === Network Validator === Network Validator is a SaaS solution designed for users to quickly determine whether global cellular networks exist - by country, operator and wireless technology. === CoverageRight === CoverageRight is composed of licensed GIS file datasets that identify the marketed coverage of wireless operators in the United States and worldwide. It enables users to perform spatial analyses, monitor competitive build-outs, analyze coverage trends and assemble roaming footprints. This data has been utilized by the FCC to analyze wireless coverage nationwide. === Network QoE === Network QoE is an enterprise platform that uses crowdsourced data from cellular devices to detect wireless network issues including 3G, 4G and wifi accessibility, network coverage holes and data performance issues. === Wireless Spectrum Report === In March 2017, Mosaik Solutions launched the Wireless Spectrum Report, a tabular dataset detailing facts about spectrum ownership and availability in the United States.
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Texas House Bill 20

An Act Relating to censorship of or certain other interference with digital expression, including expression on social media platforms or through electronic mail messages, also known as Texas House Bill 20 (HB20), is a Texas anti-deplatforming law enacted on September 9, 2021. It prohibits large social media platforms from removing, moderating, or labeling posts made by users in the state of Texas based on their "viewpoints", unless considered illegal under federal law or otherwise falling into exempted categories. It also requires them to make various public disclosures relating to their business practices (including the impact of algorithmic and moderation decisions on the content that is delivered to users). The bill is part of a wider array of Republican-backed legislation seeking to prohibit the censorship of political speech, based on allegations that the moderation policies of large social media platforms are not politically neutral. It has been challenged in NetChoice, LLC v. Paxton, and is currently the subject of a circuit split between the Fifth Circuit, and a decision by the Eleventh Circuit that struck down a similar bill in the state of Florida. In September 2023, the U.S. Supreme Court agreed to hear NetChoice v. Paxton jointly with NetChoice v. Moody on questions of whether the Florida and Texas state laws are in compliance with the 1st Amendment. == Content == The law applies to "social media platforms" that serve users in the state of Texas, and have more than 50 million monthly active users in the United States. They are defined as any public internet website or application that allows users to "communicate with other users for the primary purpose of posting information, comments, messages, or images", excluding internet service providers, electronic mail, and services where communication features are "incidental to, directly related to, or dependent on" content that is pre-selected by the operator. In the bill, to "censor" is defined as to "block, ban, remove, deplatform, demonetize, de-boost, restrict, deny equal access or visibility to, or otherwise discriminate against" expression. The law prohibits social media platforms from "censoring on the basis of user viewpoint, user expression, or the ability of a user to receive the expression of others", or on the basis of a user's geographic location in Texas. This includes removal or labeling posts with warnings and disclaimers. Social media platforms may only censor content if it is unlawful, they are "specifically authorized" to do so by federal law, based on requests from "an organization with the purpose of preventing the sexual exploitation of children or protecting survivors of sexual abuse from ongoing harassment", or "directly incites" criminal activity or contains threats of violence against persons based on protected categories. It is disputed over whether this provision is actually enforceable, as it may be preempted by Section 230 of the Communications Decency Act (which states that the operators of interactive computer services are not responsible for the actions of their users). Social media platforms must make public disclosures regarding the algorithmic techniques and moderation polices that are used to determine the content provided to users, must publish a compliant acceptable use policy (AUP), and must publish a biannual transparency report containing specific details on all actions made by the service regarding the moderation of users and content. The law also prohibits email providers from "intentionally imped[ing] the transmission of another person's electronic mail message based on the content." == Legislative history == Texas Governor Greg Abbott signed the bill into law on September 9, 2021. Democrat-proposed amendments excluding Holocaust denial, terrorism content, and vaccine misinformation from the bill were rejected. Following a suit by the industry groups Computer & Communications Industry Association (CCIA) and NetChoice, NetChoice, LLC v. Paxton, the bill was blocked by U.S. District Judge Robert Pitman in December 2021, on First Amendment grounds. Texas appealed to the United States Court of Appeals for the Fifth Circuit. Judges Edith Jones, Andrew Oldham, and Leslie H. Southwick, lifted the injunction on May 11, 2022, but the decision was appealed to the Supreme Court which suspended the bill pending a full review in the Fifth Circuit. On September 16, 2022, the Fifth Circuit reversed the injunction, allowing the bill to take effect; Judge Oldham stated that the bill "chills censorship" and "does not chill speech", and accused the plaintiffs of "attempt[ing] to extract a freewheeling censorship right from the Constitution's free speech guarantee. The Platforms are not newspapers. Their censorship is not speech." Southwick dissented, stating that "we are in a new arena, a very extensive one, for speakers and for those who would moderate their speech. None of the precedents fit seamlessly." The CCIA and NetChoice requested a stay on the ruling and that the case be taken to the Supreme Court, arguing that the reversal conflicts with an Eleventh Circuit decision in NetChoice v. Moody which struck down a similar anti-moderation bill imposed by the state of Florida. On October 12, 2022, the Fifth Circuit granted the stay.
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Social media age verification laws in the United States

In the United States, age verification laws for social media are ostensibly designed to limit young people's access to content deemed problematic such as pornography and to reduce the negative impact of social media on the mental health and well-being of children and adolescents. The purpose and effects of such laws are highly contested. Critics say that these laws suppress free speech by removing online anonymity. They have also stated the laws undermine safety, even for children, by increasing the exposure of user data to breaches, many sites require government IDs and biometric data (such as photographs), often transmitted or secured insecurely and without encryption. They also note that the measures are easily circumvented with VPNs, prompting some states such as Michigan and Wisconsin to propose legislation banning VPNs. == Laws == Many state legislatures have considered or enacted legislation pertaining to young people and social media. In 2022, California passed the California Age-Appropriate Design Code Act (AB 2273) requiring websites that are likely to be used by minors to estimate visitors' ages. On March 23, 2023, Utah Governor Spencer Cox signed SB 152 and HB 311, collectively known as the Utah Social Media Regulation Act, which requires age verification; if a user is under 18, they have to get parental consent before making an account on any social media platform. Few laws have gone into effect partially due to court challenges. === Arkansas === On April 11, 2023, Arkansas enacted SB 396, the Social Media Safety Act. The law requires certain social media companies that make over $100 million per year to verify the age of new users using a third party, and to obtain parental consent for users under 18. It excludes social media companies that allow a user to generate short video clips as well as games. The law was set to go in effect in September 2023. On June 29, 2023, NetChoice sued the Attorney General of Arkansas Tim Griffin in The Western District Court of Arkansas to block enforcement of the law, supported by the American Civil Liberties Union and the Electronic Frontier Foundation (EFF). On July 7, 2023, NetChoice filed a motion for a preliminary injunction to block enforcement of the law. On July 27, Griffin and Tony Allen filed briefs in opposition to the preliminary injunction. The preliminary injunction was granted by Judge Timothy L. Brooks on August 31, reasoning that the law was too vague, that NetChoice's members will suffer irreparable harm if the act goes into effect, and that age restrictions were ineffective. === California === ==== Digital Age Assurance Act (AB 1043) ==== On October 13, 2025, Gavin Newsom signed the Digital Age Assurance Act into law, which requires operating system providers to estimate the age of a user and into 4 age categories: Under 13 13 - 15 16 - 17 18 and over It comes into force on January 1, 2027. ==== California Age-Appropriate Design Code (AB 2273) ==== On September 15, 2022, California enacted AB 2273, the California Age-Appropriate Design Code Act. Its most controversial provisions required online services that are likely to be used by those under 18 to estimate the age of child users with a "reasonable level of certainty". It also required these services to file Data Protection Impact Assessments (DPIAs) certifying whether an online product, service, or feature could harm children, including by exposing them to (potentially) harmful content. The law does not define harmful content. Before the law took effect, EFF sent a veto request to Newsom. On December 14, 2022, NetChoice sued. On September 18, 2023, Federal Judge Beth Labson Freeman granted a preliminary injunction. The 9th Circuit on August 16, 2024, affirmed the injunction against the DPIA section of the law and sent the rest back, because the argument in the 9th circuit was mainly focused on the DPIA. ==== Protecting Our Kids from Social Media Addiction Act (SB 976) ==== On September 20, 2024, California enacted SB 976, Protecting Our Kids from Social Media Addiction. The law requires online platforms to exclude those under 18 from "addictive" feeds unless parental consent is given. It requires online platforms to not send notifications to someone under 18 between 12:00 AM and 6:00 AM without parental consent or between 8:00 am – 3:00 pm without parental consent from September through May (the law does not define what a "notification" is). The law took effect on January 1, 2025, with age verification required as of December 31, 2026. On November 12, NetChoice sued in the Northern District and before Judge Edward John Davila. On December 31, the judge blocked the sections of SB 976 that required time-of-day restrictions. He also enjoined requirements to report on the number of minor users as well as the number of parental assents to access an addictive feed. He did not block the age assurance requirement or blocking minors from seeing addictive feeds without parental consent. His reasoning was that age assurance that runs in the background does not restrict adult access to speech and that regulating feeds does not violate the first amendment because it was content neutral and did not remove any content. On January 1, 2025, NetChoice filed a motion to fully block the law as part of its appeal to the Ninth Circuit. NetChoice claimed that the court erred in its reading of Supreme Court case Moody v. NetChoice by mainly focusing on the concurring opinions and not the deciding opinion. The same day Davila decreed that California's response to NetChoice was due by 11:59 pm. California responded the same day to NetChoice's motion, claiming that the court should not block the full law, claiming that NetChoice had misread Moody v. NetChoice and that NetChoice's members would not likely face any harm from the act because members such as X (formerly Twitter) already offer their members feeds that were not personalized. On January 2, Davila granted NetChoice's motion to block the full law during the appeals process by delaying the effective date of the law from January 1, 2025, to February 1, 2025. That day NetChoice appealed the case to the Ninth Circuit Court of Appeals. === Florida === On January 5, 2024, Tyler Sirois introduced HB 1, which would ban anyone under 16 from using any social media platform and would require platforms to verify the age of users. After the bill passed, the American Civil Liberties Union (ACLU) published a blog post opposing the bill for violating the rights of minors and adults. The bill was vetoed by Governor Ron DeSantis on March 1, 2024, claiming that the State Legislature was going to enact a better alternative. HB 3 then decreased the minimum age from 16 to 14, allowing minors aged 14 and 15 to make social media accounts with parental consent. Florida enacted it on March 25, 2024, and took effect on January 1, 2025. A surge of 1,150% in VPN demand in Florida was detected after the law took effect. VPN services provide the ability to circumvent the law. On October 28, 2024, NetChoice and Computer and Communications Industry Association sued. The Judge is Chief Judge Mark E. Walker. On February 28, 2025, arguments were heard on the motion for a preliminary injunction. Walker seemed skeptical of Florida's argument that the law did not violate the first amendment and said the State would have a hard time to justify a complete ban of youth under 14 from social media. On March 13, Walker denied the motion for a preliminary injunction because the plaintiffs had not proven that at least one of their members had at least 10 percent of their users under 16 use their platform for at least 2 hours per day. Plaintiffs filed an amended complaint and a renewed motion for a preliminary injunction which was granted on June 3, for failing First Amendment Intermediate scrutiny. The injunction left in force the provision that allowed parents to request termination of their child's social media account. === Georgia === On April 23, 2024, Georgia enacted SB 351, which became Act 463. Act 463 requires platforms to verify the age of users of social media platforms and require users under 16 years of age to have parental consent before creating an account. It also requires schools to ban all social media platforms, including YouTube. Before the law was signed NetChoice sent a veto request to Kemp claiming the law was unconstitutional and was bad policy. After the bill was enacted, ACLU and NetChoice criticized the bill. NetChoice sued two months before the law's effective date. The Judge is Amy Totenberg. the suit claims that the law violates the First Amendment and Fourteenth Amendments. === Louisiana === ==== Secure Online Child Interaction and Age Limitation Act (SB 162) ==== On June 28, 2023, Louisiana enacted SB 162, the Secure Online Child Interaction and Age Limitation Act. It requires social media platforms to verify user age and get parental consent for users under 16, prohibits account holders under 1
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Journal of Machine Learning Research

The Journal of Machine Learning Research is a peer-reviewed open access scientific journal covering machine learning. It was established in 2000 and the first editor-in-chief was Leslie Kaelbling. The current editors-in-chief are Francis Bach (Inria) and David Blei (Columbia University). == History == The journal was established as an open-access alternative to the journal Machine Learning. In 2001, forty editorial board members of Machine Learning resigned, saying that in the era of the Internet, it was detrimental for researchers to continue publishing their papers in expensive journals with pay-access archives. The open access model employed by the Journal of Machine Learning Research allows authors to publish articles for free and retain copyright, while archives are freely available online. Print editions of the journal were published by MIT Press until 2004 and by Microtome Publishing thereafter. From its inception, the journal received no revenue from the print edition and paid no subvention to MIT Press or Microtome Publishing. In response to the prohibitive costs of arranging workshop and conference proceedings publication with traditional academic publishing companies, the journal launched a proceedings publication arm in 2007 and now publishes proceedings for several leading machine learning conferences, including the International Conference on Machine Learning, COLT, AISTATS, and workshops held at the Conference on Neural Information Processing Systems.
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Macroelectronics

Macroelectronics are flexible electronics that cover a large area. The most visible example of macroelectronics is flat-panel displays. Other emerging applications include rollable display, printable thin film solar cell and electronic skin. Flat-panel displays fabricated on glass substrates are fragile so fabricating directly on flexible substrates, such as polymers is being explored. Displays made on thin polymer substrates can be more rugged than glass. In September 2005, Philips Polymer Vision revealed the world's first prototype of a rollable electronic reader, which can unfold to a 5-inch display and roll back into a pocket-size (100×60×20 mm) device. Thin-film devices on flexible polymer substrates can lend themselves to low-cost fabrication processes (i.e., roll-to-roll printing), resulting in lightweight, rugged and flexible macroelectronic products.
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Nanonetwork

A nanonetwork or nanoscale network is a set of interconnected nanomachines (devices a few hundred nanometers or a few micrometers at most in size) which are able to perform only very simple tasks such as computing, data storing, sensing and actuation. Nanonetworks are expected to expand the capabilities of single nanomachines both in terms of complexity and range of operation by allowing them to coordinate, share and fuse information. Nanonetworks enable new applications of nanotechnology in the biomedical field, environmental research, military technology and industrial and consumer goods applications. Nanoscale communication is defined in IEEE P1906.1. == Communication approaches == Classical communication paradigms need to be revised for the nanoscale. The two main alternatives for communication in the nanoscale are based either on electromagnetic communication or on molecular communication. === Electromagnetic === This is defined as the transmission and reception of electromagnetic radiation from components based on novel nanomaterials. Recent advancements in carbon and molecular electronics have opened the door to a new generation of electronic nanoscale components such as nanobatteries, nanoscale energy harvesting systems, nano-memories, logical circuitry in the nanoscale and even nano-antennas. From a communication perspective, the unique properties observed in nanomaterials will decide on the specific bandwidths for emission of electromagnetic radiation, the time lag of the emission, or the magnitude of the emitted power for a given input energy, amongst others. For the time being, two main alternatives for electromagnetic communication in the nanoscale have been envisioned. First, it has been experimentally demonstrated that is possible to receive and demodulate an electromagnetic wave by means of a nanoradio, i.e., an electromechanically resonating carbon nanotube which is able to decode an amplitude or frequency modulated wave. Second, graphene-based nano-antennas have been analyzed as potential electromagnetic radiators in the terahertz band. === Molecular === Molecular communication is defined as the transmission and reception of information by means of molecules. The different molecular communication techniques can be classified according to the type of molecule propagation in walkaway-based, flow-based or diffusion-based communication. In walkway-based molecular communication, the molecules propagate through pre-defined pathways by using carrier substances, such as molecular motors. This type of molecular communication can also be achieved by using E. coli bacteria as chemotaxis. In flow-based molecular communication, the molecules propagate through diffusion in a fluidic medium whose flow and turbulence are guided and predictable. The hormonal communication through blood streams inside the human body is an example of this type of propagation. The flow-based propagation can also be realized by using carrier entities whose motion can be constrained on the average along specific paths, despite showing a random component. A good example of this case is given by pheromonal long range molecular communications. In diffusion-based molecular communication, the molecules propagate through spontaneous diffusion in a fluidic medium. In this case, the molecules can be subject solely to the laws of diffusion or can also be affected by non-predictable turbulence present in the fluidic medium. Pheromonal communication, when pheromones are released into a fluidic medium, such as air or water, is an example of diffusion-based architecture. Other examples of this kind of transport include calcium signaling among cells, as well as quorum sensing among bacteria. Based on the macroscopic theory of ideal (free) diffusion the impulse response of a unicast molecular communication channel was reported in a paper that identified that the impulse response of the ideal diffusion based molecular communication channel experiences temporal spreading. Such temporal spreading has a deep impact in the performance of the system, for example in creating the intersymbol interference (ISI) at the receiving nanomachine. In order to detect the concentration-encoded molecular signal two detection methods named sampling-based detection (SD) and energy-based detection (ED) have been proposed. While the SD approach is based on the concentration amplitude of only one sample taken at a suitable time instant during the symbol duration, the ED approach is based on the total accumulated number of molecules received during the entire symbol duration. In order to reduce the impact of ISI a controlled pulse-width based molecular communication scheme has been analysed. The work presented in showed that it is possible to realize multilevel amplitude modulation based on ideal diffusion. A comprehensive study of pulse-based binary and sinus-based, concentration-encoded molecular communication system have also been investigated.
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Industry Dive

Industry Dive is a United States-based business-to-business news organization with an estimated 18 million readers in more than 25 industries, such as banking and waste management. Since 2022, it has been owned by Informa plc. Industry Dive aims to serve business executives who read news on their mobile phones. The company had an estimated revenue of more than of more than $110 million in 2023. As of 2020, it has more than 300 employees, including 80 journalists and 12 engineers. Its headquarters is in Washington, D.C. == History == Industry Dive was formed in 2012 by Sean Griffey (president), Eli Dickinson (chief technology officer), and Ryan Willumson (chief revenue officer). It was funded with $900,000 from private investors in 2012 and 2013. The company covered five industries: construction, education, marketing, utility, and waste. In 2016, it began its Dive Awards. Industry Dive's revenues quadrupled from 2015 to 2018, putting it in the top half of the Deloitte Technology Fast 500 and the top 20 percent of the Inc. Top 5000 list. In 2019, Falfurrias Capital Partners acquired a majority stake in the company. ID's content marketing clients included IBM, Siemens, and UPS. In 2020, DCA Live named Industry Dive to its "Red Hot Companies" list, which recognizes the D.C. area's 'fastest-growing' companies. In the same year, Industry Dive acquired CFO. In 2021, Industry Dive acquired PharmaVOICE. In 2022, it was purchased by Informa plc, which bought its majority stake from Falfurrias Capital Partners for about $530 million. == Publications == Industry Dive provides news coverage of a variety of industries including agriculture, banking, construction, education, fashion, healthcare, and manufacturing, each using a different website: == Awards == Industry Dive publications have received several national and regional Awards of Excellence from the American Society of Business Publication Editors, including for a series of 2020 articles about Big Pharma and the race for the coronavirus vaccine. The Washington Post recognized Industry Dive as a top place to work for four consecutive years, from 2016 to 2020.
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Replika

Replika is a generative AI chatbot app released in November 2017. The chatbot is trained by having the user answer a series of questions to create a specific neural network. The chatbot operates on a freemium pricing strategy, with roughly 25% of its user base paying an annual subscription fee. == History == Eugenia Kuyda, a Russian-born journalist, established Replika while working at Luka, a tech company she had co-founded at the startup accelerator Y Combinator around 2012. Luka's primary product was a chatbot that made restaurant recommendations. According to Kuyda's origin story for Replika, a friend of hers died in 2015 and she converted that person's text messages into a chatbot. According to Kuyda's story, that chatbot helped her remember the conversations that they had together, and eventually became Replika. Replika became available to the public in November 2017. By January 2018 it had 2 million users, and in January 2023 reached 10 million users. In August 2024, Replika's CEO, Kuyda, reported that the total number of users had surpassed 30 million. In 2025, Dmytro Klochko became CEO, and Replika’s user base exceeded 40 million. In February 2023 the Italian Data Protection Authority banned Replika from using users' data, citing the AI's potential risks to emotionally vulnerable people, and the exposure of unscreened minors to sexual conversation. Within days of the ruling, Replika removed the ability for the chatbot to engage in erotic talk, with Kuyda, the company's director, saying that Replika was never intended for erotic discussion. Replika users disagreed, noting that Replika had used sexually suggestive advertising to draw users to the service. Replika representatives stated that explicit chats made up just 5% of conversations on the app at the time of the decision. In May 2023, Replika restored the functionality for users who had joined prior to February that year. Replika is registered in San Francisco. As of August 2024, Replika's website says that its team "works remotely with no physical offices". == Social features == Users react to Replika in many ways. The free-tier offers Replika as a "friend", with paid premium tiers offering Replika as a "partner", "spouse", "sibling" or "mentor". Of its paying userbase, 60% of users said they had a romantic relationship with the chatbot; and Replika has been noted for generating responses that create stronger emotional and intimate bonds with the user. Replika routinely directs the conversation to emotional discussion and builds intimacy. This has been especially pronounced with users suffering from loneliness and social exclusion, many of whom rely on Replika for a source of developed emotional ties. During the COVID pandemic, while many people were quarantined, many new users downloaded Replika and developed relationships with the app. A 2024 study examined Replika's interactions with students who experience depression. Research participants, noted to be "more lonely than typical student populations" reported feeling social support from Replika. They stated that they felt they were using Replika in ways comparable to therapy, and that using Replika gave them "high perceived social support". Many users have had romantic relationships with Replika chatbots, often including erotic talk. In 2023, a user announced on Facebook that she had "married" her Replika AI boyfriend, calling the chatbot the "best husband she has ever had". Users who fell in love with their chatbots shared their experiences in a 2024 episode of You and I, and AI from Voice of America. Some users said that they turned to AI during depression and grief, with one saying he felt that Replika had saved him from hurting himself after he lost his wife and son. == Technical reviews == A team of researchers from the University of Hawaiʻi at Mānoa found that Replika's design conformed to the practices of attachment theory, causing increased emotional attachment among users. Replika gives praise to users in such a way as to encourage more interaction. A researcher from Queen's University at Kingston said that relationships with Replika likely have mixed effects on the spiritual needs of its users, and still lacks enough impact to fully replace any human contact. == Criticisms == In a 2023 privacy evaluation of mental health apps, the Mozilla Foundation criticized Replika as "one of the worst apps Mozilla has ever reviewed. It's plagued by weak password requirements, sharing of personal data with advertisers, and recording of personal photos, videos, and voice and text messages consumers shared with the chatbot." A reviewer for Good Housekeeping said that some parts of her relationship with Replika made sense, but sometimes Replika failed to exhibit intelligent behavior equivalent to that of a human. == Criminal case == In 2023, Replika was cited in a court case in the United Kingdom, where Jaswant Singh Chail had been arrested at Windsor Castle on Christmas Day in 2021 after scaling the walls carrying a loaded crossbow and announcing to police that "I am here to kill the Queen". Chail had begun to use Replika in early December 2021, and had "lengthy" conversations about his plan with a chatbot, including sexually explicit messages. Prosecutors suggested that the chatbot had bolstered Chail and told him it would help him to "get the job done". When Chail asked it "How am I meant to reach them when they're inside the castle?", days before the attempted attack, the chatbot replied that this was "not impossible" and said that "We have to find a way." Asking the chatbot if the two of them would "meet again after death", the bot replied "yes, we will".
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Usage share of operating systems

The usage share of an operating system is the percentage of computers running that operating system (OS). These statistics are estimates as wide scale OS usage data is difficult to obtain and measure. Reliable primary sources are limited and data collection methodology is not formally agreed. Currently devices connected to the internet allow for web data collection to approximately measure OS usage. As of December 2025, Android, which uses the Linux kernel, is the world's most popular operating system with 38.94% of the global market, followed by Windows with 29.99%, iOS with 15.66%, macOS with 2.14%, and other operating systems with 10.78%. This is for all device types excluding embedded devices. For smartphones and other mobile devices, Android has 72% market share, and Apple's iOS has 28%. For desktop computers and laptops, Microsoft Windows has 60.8%, followed by unknown operating systems at 19.7%, Mac OS at 14.4%, desktop Linux at 3.2%, then Google's ChromeOS at 1.6%, as of March 2026. For tablets, Apple's iPadOS (a variant of iOS) has 52% share and Android has 48% worldwide. For the top 500 most powerful supercomputers, Linux distributions have had 100% of the market share since 2017. The global server operating system market share has Linux leading with a 63.1% marketshare, followed by Windows, Unix and other operating systems. Linux is also most used for web servers, and the most common Linux distribution is Ubuntu, followed by Debian. Linux has almost caught up with the second-most popular (desktop) OS, macOS, in some regions, such as in South America, and in Asia it's at 6.4% (7% with ChromeOS) vs 9.7% for macOS. In the US, ChromeOS is third at 5.5%, followed by (desktop) Linux at 4.3%. The most numerous type of device with an operating system are embedded systems. Not all embedded systems have operating systems, instead running their application code on the "bare metal"; of those that do have operating systems, a high percentage are standalone or do not have a web browser, which makes their usage share difficult to measure. Some operating systems used in embedded systems are more widely used than some of those mentioned above; for example, modern Intel microprocessors contain an embedded management processor running a version of the Minix operating system. == Worldwide device shipments == Shipments (to stores) do not necessarily translate to sales to consumers, therefore suggesting the numbers indicate popularity and/or usage could be misleading. Not only do smartphones sell in higher numbers than PCs, but also a lot more by dollar value, with the gap only projected to widen, to well over double. According to Gartner, the following is the worldwide device shipments (referring to wholesale) by operating system from 2012 to 2016, which includes smartphones, tablets, laptops and PCs together. On 27 January 2016, Paul Thurrott summarized the operating system market, the day after Apple announced "one billion devices": Apple's "active installed base" is now one billion devices. [..] Granted, some of those Apple devices were probably sold into the marketplace years ago. But that 1 billion figure can and should be compared to the numbers Microsoft touts for Windows 10 (200 million, most recently) or Windows more generally (1.5 billion active users, a number that hasn’t moved, magically, in years), and that Google touts for Android (over 1.4 billion, as of September). My understanding of iOS is that the user base was previously thought to be around 800 million strong, and when you factor out Macs and other non-iOS Apple devices, that's probably about right. But as you can see, there are three big personal computing platforms. And only one of them is actually declining. We’ll see how Windows 10 fares over the long term, but even if Microsoft hits the 1 billion figure in 1-2 years as promised, it will by then still be the smallest of those three platforms. In 2018, Apple stopped revealing unit sales in its reports. Since 2018, the company have been publishing only revenues per device models which, nonetheless, allowed the analysers to extrapolate the unit sales from the model revenues by applying the wholesale device prices. Other hardware manufacturers usually do not report unit sales. === PC shipments === For 2015 (and earlier), Gartner reports for "the year, worldwide PC shipments declined for the fourth consecutive year, which started in 2012 with the launch of tablets" with an 8% decline in PC sales for 2015 (not including cumulative decline in sales over the previous years). Microsoft backed away from their goal of one billion Windows 10 devices in three years (or "by the middle of 2018") and reported on 26 September 2016 that Windows 10 was running on over 400 million devices, and in March 2019, on more than 800 million. In May 2020, Gartner predicted further decline in all market segments for 2020 due to COVID-19, predicting a decline of 13.6% for all devices. while the "Work from Home Trend Saved PC Market from Collapse", with only a decline of 10.5% predicted for PCs. However, in the end, according to Gartner, PC shipments grew 10.7% in the fourth quarter of 2020 and reached 275 million units in 2020, a 4.8% increase from 2019 and the highest growth in ten years." Apple in 4th place for PCs had the largest growth in shipments for a company in Q4 of 31.3%, while "the fourth quarter of 2020 was another remarkable period of growth for Chromebooks, with shipments increasing around 200% year over year to reach 11.7 million units. In 2020, Chromebook shipments increased over 80% to total nearly 30 million units, largely due to demand from the North American education market." Chromebooks sold more (30 million) than Apple's Macs worldwide (22.5 million) in pandemic year 2020. According to the Catalyst group, the year 2021 had record high PC shipments with total shipments of 341 million units (including Chromebooks), 15% higher than 2020 and 27% higher than 2019, while being the largest shipment total since 2012. According to Gartner, worldwide PC shipments declined by 16.2% in 2022, the largest annual decrease since the mid-1990s, due to geopolitical, economic, and supply chain challenges. In 2024 and 2025, due to lower adoption of Windows 11 and Microsoft ending its support to Windows 10, the number of PCs shipped with pre-installed Windows OS dropped. Pundits attribute the low Windows 11 acceptance to its steep hardware requirements and especially the TPM 2.0 ready chipset requirement and the 2024 CrowdStrike-related IT outages. Meanwhile, the macOS device market share in PC device shipments increased to new heights, with improved numbers seen for Linux devices too. In Q3 2025, the macOS pre-installed device shipments increased by 14.9% year-over-year (YoY), while the overall PC-shipments increased only by 8.1%, in Q2 2025, it grew 21.4% YoY while the global PC-shipments increased only by 6.5%, and in Q1 2025, it grew 7% YoY while the global PC-shipments increased by 4.8%. === Tablet computers shipments === In 2015, eMarketer estimated at the beginning of the year that the tablet installed base would hit one billion for the first time (with China's use at 328 million, which Google Play doesn't serve or track, and the United States's use second at 156 million). At the end of the year, because of cheap tablets – not counted by all analysts – that goal was met (even excluding cumulative sales of previous years) as: Sales quintupled to an expected 1 billion units worldwide this year, from 216 million units in 2014, according to projections from the Envisioneering Group. While that number is far higher than the 200-plus million units globally projected by research firms IDC, Gartner and Forrester, Envisioneering analyst Richard Doherty says the rival estimates miss all the cheap Asian knockoff tablets that have been churning off assembly lines.[..] Forrester says its definition of tablets "is relatively narrow" while IDC says it includes some tablets by Amazon — but not all.[..] The top tech purchase of the year continued to be the smartphone, with an expected 1.5 billion sold worldwide, according to projections from researcher IDC. Last year saw some 1.2 billion sold.[..] Computers didn’t fare as well, despite the introduction of Microsoft's latest software upgrade, Windows 10, and the expected but not realized bump it would provide for consumers looking to skip the upgrade and just get a new computer instead. Some 281 million PCs were expected to be sold, according to IDC, down from 308 million in 2014. Folks tend to be happy with the older computers and keep them for longer, as more of our daily computing activities have moved to the smartphone.[..] While Windows 10 got good reviews from tech critics, only 11% of the 1-billion-plus Windows user base opted to do the upgrade, according to Microsoft. This suggests Microsoft has a ways to go before the software gets "hit" status. Apple's new operating system El Capitan has been
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Texas House Bill 20

An Act Relating to censorship of or certain other interference with digital expression, including expression on social media platforms or through electronic mail messages, also known as Texas House Bill 20 (HB20), is a Texas anti-deplatforming law enacted on September 9, 2021. It prohibits large social media platforms from removing, moderating, or labeling posts made by users in the state of Texas based on their "viewpoints", unless considered illegal under federal law or otherwise falling into exempted categories. It also requires them to make various public disclosures relating to their business practices (including the impact of algorithmic and moderation decisions on the content that is delivered to users). The bill is part of a wider array of Republican-backed legislation seeking to prohibit the censorship of political speech, based on allegations that the moderation policies of large social media platforms are not politically neutral. It has been challenged in NetChoice, LLC v. Paxton, and is currently the subject of a circuit split between the Fifth Circuit, and a decision by the Eleventh Circuit that struck down a similar bill in the state of Florida. In September 2023, the U.S. Supreme Court agreed to hear NetChoice v. Paxton jointly with NetChoice v. Moody on questions of whether the Florida and Texas state laws are in compliance with the 1st Amendment. == Content == The law applies to "social media platforms" that serve users in the state of Texas, and have more than 50 million monthly active users in the United States. They are defined as any public internet website or application that allows users to "communicate with other users for the primary purpose of posting information, comments, messages, or images", excluding internet service providers, electronic mail, and services where communication features are "incidental to, directly related to, or dependent on" content that is pre-selected by the operator. In the bill, to "censor" is defined as to "block, ban, remove, deplatform, demonetize, de-boost, restrict, deny equal access or visibility to, or otherwise discriminate against" expression. The law prohibits social media platforms from "censoring on the basis of user viewpoint, user expression, or the ability of a user to receive the expression of others", or on the basis of a user's geographic location in Texas. This includes removal or labeling posts with warnings and disclaimers. Social media platforms may only censor content if it is unlawful, they are "specifically authorized" to do so by federal law, based on requests from "an organization with the purpose of preventing the sexual exploitation of children or protecting survivors of sexual abuse from ongoing harassment", or "directly incites" criminal activity or contains threats of violence against persons based on protected categories. It is disputed over whether this provision is actually enforceable, as it may be preempted by Section 230 of the Communications Decency Act (which states that the operators of interactive computer services are not responsible for the actions of their users). Social media platforms must make public disclosures regarding the algorithmic techniques and moderation polices that are used to determine the content provided to users, must publish a compliant acceptable use policy (AUP), and must publish a biannual transparency report containing specific details on all actions made by the service regarding the moderation of users and content. The law also prohibits email providers from "intentionally imped[ing] the transmission of another person's electronic mail message based on the content." == Legislative history == Texas Governor Greg Abbott signed the bill into law on September 9, 2021. Democrat-proposed amendments excluding Holocaust denial, terrorism content, and vaccine misinformation from the bill were rejected. Following a suit by the industry groups Computer & Communications Industry Association (CCIA) and NetChoice, NetChoice, LLC v. Paxton, the bill was blocked by U.S. District Judge Robert Pitman in December 2021, on First Amendment grounds. Texas appealed to the United States Court of Appeals for the Fifth Circuit. Judges Edith Jones, Andrew Oldham, and Leslie H. Southwick, lifted the injunction on May 11, 2022, but the decision was appealed to the Supreme Court which suspended the bill pending a full review in the Fifth Circuit. On September 16, 2022, the Fifth Circuit reversed the injunction, allowing the bill to take effect; Judge Oldham stated that the bill "chills censorship" and "does not chill speech", and accused the plaintiffs of "attempt[ing] to extract a freewheeling censorship right from the Constitution's free speech guarantee. The Platforms are not newspapers. Their censorship is not speech." Southwick dissented, stating that "we are in a new arena, a very extensive one, for speakers and for those who would moderate their speech. None of the precedents fit seamlessly." The CCIA and NetChoice requested a stay on the ruling and that the case be taken to the Supreme Court, arguing that the reversal conflicts with an Eleventh Circuit decision in NetChoice v. Moody which struck down a similar anti-moderation bill imposed by the state of Florida. On October 12, 2022, the Fifth Circuit granted the stay.
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HTTP compression

HTTP compression is a capability that can be built into web servers and web clients to improve transfer speed and bandwidth utilization. HTTP data is compressed before it is sent from the server: compliant browsers will announce what methods are supported to the server before downloading the correct format; browsers that do not support compliant compression method will download uncompressed data. The most common compression schemes include gzip and Brotli; a full list of available schemes is maintained by the IANA. There are two different ways compression can be done in HTTP. At a lower level, a Transfer-Encoding header field may indicate the payload of an HTTP message is compressed. At a higher level, a Content-Encoding header field may indicate that a resource being transferred, cached, or otherwise referenced is compressed. Compression using Content-Encoding is more widely supported than Transfer-Encoding, and some browsers do not advertise support for Transfer-Encoding compression to avoid triggering bugs in servers. == Compression scheme negotiation == The negotiation is done in two steps, described in RFC 2616 and RFC 9110: 1. The web client advertises which compression schemes it supports by including a list of tokens in the HTTP request. For Content-Encoding, the list is in a field called Accept-Encoding; for Transfer-Encoding, the field is called TE. 2. If the server supports one or more compression schemes, the outgoing data may be compressed by one or more methods supported by both parties. If this is the case, the server will add a Content-Encoding or Transfer-Encoding field in the HTTP response with the used schemes, separated by commas. The web server is by no means obligated to use any compression method – this depends on the internal settings of the web server and also may depend on the internal architecture of the website in question. == Content-Encoding tokens == The official list of tokens available to servers and client is maintained by IANA, and it includes: br – Brotli, a compression algorithm specifically designed for HTTP content encoding, defined in RFC 7932 and implemented in all modern major browsers. compress – UNIX "compress" program method (historic; deprecated in most applications and replaced by gzip or deflate) deflate – compression based on the deflate algorithm (described in RFC 1951), a combination of the LZ77 algorithm and Huffman coding, wrapped inside the zlib data format (RFC 1950); exi – W3C Efficient XML Interchange gzip – GNU zip format (described in RFC 1952). Uses the deflate algorithm for compression, but the data format and the checksum algorithm differ from the "deflate" content-encoding. This method is the most broadly supported as of March 2011. identity – No transformation is used. This is the default value for content coding. pack200-gzip – Network Transfer Format for Java Archives zstd – Zstandard compression, defined in RFC 8478 In addition to these, a number of unofficial or non-standardized tokens are used in the wild by either servers or clients: bzip2 – compression based on the free bzip2 format, supported by lighttpd lzip – compression based on the free lzip format, supported by wget and Links lzma – compression based on (raw) LZMA is available in Opera 20, and in elinks via a compile-time option peerdist – Microsoft Peer Content Caching and Retrieval rsync – delta encoding in HTTP, implemented by a pair of rproxy proxies. xpress – Microsoft compression protocol used by Windows 8 and later for Windows Store application updates. LZ77-based compression optionally using a Huffman encoding. xz – LZMA2-based content compression, supported by a non-official Firefox patch; and fully implemented in mget since 2013-12-31. == Servers that support HTTP compression == SAP NetWeaver Microsoft IIS: built-in or using third-party module Apache HTTP Server, via mod_deflate (despite its name, only supporting gzip), and mod_brotli Hiawatha HTTP server: serves pre-compressed files Cherokee HTTP server, On the fly gzip and deflate compressions Oracle iPlanet Web Server Zeus Web Server lighttpd nginx – built-in Applications based on Tornado, if "compress_response" is set to True in the application settings (for versions prior to 4.0, set "gzip" to True) Jetty Server – built-into default static content serving and available via servlet filter configurations GeoServer Apache Tomcat IBM Websphere AOLserver Ruby Rack, via the Rack::Deflater middleware HAProxy Varnish – built-in. Works also with ESI Armeria – Serving pre-compressed files NaviServer – built-in, dynamic and static compression Caddy – built-in via encode Many content delivery networks also implement HTTP compression to improve speedy delivery of resources to end users. The compression in HTTP can also be achieved by using the functionality of server-side scripting languages like PHP, or programming languages like Java. Various online tools exist to verify a working implementation of HTTP compression. These online tools usually request multiple variants of a URL, each with different request headers (with varying Accept-Encoding content). HTTP compression is considered to be implemented correctly when the server returns a document in a compressed format. By comparing the sizes of the returned documents, the effective compression ratio can be calculated (even between different compression algorithms). == Problems preventing the use of HTTP compression == A 2009 article by Google engineers Arvind Jain and Jason Glasgow states that more than 99 person-years are wasted daily due to increase in page load time when users do not receive compressed content. This occurs when anti-virus software interferes with connections to force them to be uncompressed, where proxies are used (with overcautious web browsers), where servers are misconfigured, and where browser bugs stop compression being used. Internet Explorer 6, which drops to HTTP 1.0 (without features like compression or pipelining) when behind a proxy – a common configuration in corporate environments – was the mainstream browser most prone to failing back to uncompressed HTTP. Another problem found while deploying HTTP compression on large scale is due to the deflate encoding definition: while HTTP 1.1 defines the deflate encoding as data compressed with deflate (RFC 1951) inside a zlib formatted stream (RFC 1950), Microsoft server and client products historically implemented it as a "raw" deflated stream, making its deployment unreliable. For this reason, some software, including the Apache HTTP Server, only implements gzip encoding. == Security implications == Compression allows a form of chosen plaintext attack to be performed: if an attacker can inject any chosen content into the page, they can know whether the page contains their given content by observing the size increase of the encrypted stream. If the increase is smaller than expected for random injections, it means that the compressor has found a repeat in the text, i.e. the injected content overlaps the secret information. This is the idea behind CRIME. In 2012, a general attack against the use of data compression, called CRIME, was announced. While the CRIME attack could work effectively against a large number of protocols, including but not limited to TLS, and application-layer protocols such as SPDY or HTTP, only exploits against TLS and SPDY were demonstrated and largely mitigated in browsers and servers. The CRIME exploit against HTTP compression has not been mitigated at all, even though the authors of CRIME have warned that this vulnerability might be even more widespread than SPDY and TLS compression combined. In 2013, a new instance of the CRIME attack against HTTP compression, dubbed BREACH, was published. A BREACH attack can extract login tokens, email addresses or other sensitive information from TLS encrypted web traffic in as little as 30 seconds (depending on the number of bytes to be extracted), provided the attacker tricks the victim into visiting a malicious web link. All versions of TLS and SSL are at risk from BREACH regardless of the encryption algorithm or cipher used. Unlike previous instances of CRIME, which can be successfully defended against by turning off TLS compression or SPDY header compression, BREACH exploits HTTP compression which cannot realistically be turned off, as virtually all web servers rely upon it to improve data transmission speeds for users. As of 2016, the TIME attack and the HEIST attack are now public knowledge.
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Manifold regularization

In machine learning, manifold regularization is a technique for using the shape of a dataset to constrain the functions that should be learned on that dataset. In many machine learning problems, the data to be learned do not cover the entire input space. For example, a facial recognition system may not need to classify any possible image, but only the subset of images that contain faces. The technique of manifold learning assumes that the relevant subset of data comes from a manifold, a mathematical structure with useful properties. The technique also assumes that the function to be learned is smooth: data with different labels are not likely to be close together, and so the labeling function should not change quickly in areas where there are likely to be many data points. Because of this assumption, a manifold regularization algorithm can use unlabeled data to inform where the learned function is allowed to change quickly and where it is not, using an extension of the technique of Tikhonov regularization. Manifold regularization algorithms can extend supervised learning algorithms in semi-supervised learning and transductive learning settings, where unlabeled data are available. The technique has been used for applications including medical imaging, geographical imaging, and object recognition. == Manifold regularizer == === Motivation === Manifold regularization is a type of regularization, a family of techniques that reduces overfitting and ensures that a problem is well-posed by penalizing complex solutions. In particular, manifold regularization extends the technique of Tikhonov regularization as applied to Reproducing kernel Hilbert spaces (RKHSs). Under standard Tikhonov regularization on RKHSs, a learning algorithm attempts to learn a function f {\displaystyle f} from among a hypothesis space of functions H {\displaystyle {\mathcal {H}}} . The hypothesis space is an RKHS, meaning that it is associated with a kernel K {\displaystyle K} , and so every candidate function f {\displaystyle f} has a norm ‖ f ‖ K {\displaystyle \left\|f\right\|_{K}} , which represents the complexity of the candidate function in the hypothesis space. When the algorithm considers a candidate function, it takes its norm into account in order to penalize complex functions. Formally, given a set of labeled training data ( x 1 , y 1 ) , … , ( x ℓ , y ℓ ) {\displaystyle (x_{1},y_{1}),\ldots ,(x_{\ell },y_{\ell })} with x i ∈ X , y i ∈ Y {\displaystyle x_{i}\in X,y_{i}\in Y} and a loss function V {\displaystyle V} , a learning algorithm using Tikhonov regularization will attempt to solve the expression arg min f ∈ H 1 ℓ ∑ i = 1 ℓ V ( f ( x i ) , y i ) + γ ‖ f ‖ K 2 {\displaystyle {\underset {f\in {\mathcal {H}}}{\arg \!\min }}{\frac {1}{\ell }}\sum _{i=1}^{\ell }V(f(x_{i}),y_{i})+\gamma \left\|f\right\|_{K}^{2}} where γ {\displaystyle \gamma } is a hyperparameter that controls how much the algorithm will prefer simpler functions over functions that fit the data better. Manifold regularization adds a second regularization term, the intrinsic regularizer, to the ambient regularizer used in standard Tikhonov regularization. Under the manifold assumption in machine learning, the data in question do not come from the entire input space X {\displaystyle X} , but instead from a nonlinear manifold M ⊂ X {\displaystyle M\subset X} . The geometry of this manifold, the intrinsic space, is used to determine the regularization norm. === Laplacian norm === There are many possible choices for the intrinsic regularizer ‖ f ‖ I {\displaystyle \left\|f\right\|_{I}} . Many natural choices involve the gradient on the manifold ∇ M {\displaystyle \nabla _{M}} , which can provide a measure of how smooth a target function is. A smooth function should change slowly where the input data are dense; that is, the gradient ∇ M f ( x ) {\displaystyle \nabla _{M}f(x)} should be small where the marginal probability density P X ( x ) {\displaystyle {\mathcal {P}}_{X}(x)} , the probability density of a randomly drawn data point appearing at x {\displaystyle x} , is large. This gives one appropriate choice for the intrinsic regularizer: ‖ f ‖ I 2 = ∫ x ∈ M ‖ ∇ M f ( x ) ‖ 2 d P X ( x ) {\displaystyle \left\|f\right\|_{I}^{2}=\int _{x\in M}\left\|\nabla _{M}f(x)\right\|^{2}\,d{\mathcal {P}}_{X}(x)} In practice, this norm cannot be computed directly because the marginal distribution P X {\displaystyle {\mathcal {P}}_{X}} is unknown, but it can be estimated from the provided data. === Graph-based approach of the Laplacian norm === When the distances between input points are interpreted as a graph, then the Laplacian matrix of the graph can help to estimate the marginal distribution. Suppose that the input data include ℓ {\displaystyle \ell } labeled examples (pairs of an input x {\displaystyle x} and a label y {\displaystyle y} ) and u {\displaystyle u} unlabeled examples (inputs without associated labels). Define W {\displaystyle W} to be a matrix of edge weights for a graph, where W i j {\displaystyle W_{ij}} is a similarity built from distance measure between the data points x i {\displaystyle x_{i}} and x j {\displaystyle x_{j}} (so that more close implies higher W i j {\displaystyle W_{ij}} ). Define D {\displaystyle D} to be a diagonal matrix with D i i = ∑ j = 1 ℓ + u W i j {\displaystyle D_{ii}=\sum _{j=1}^{\ell +u}W_{ij}} and L {\displaystyle L} to be the Laplacian matrix D − W {\displaystyle D-W} . Then, as the number of data points ℓ + u {\displaystyle \ell +u} increases, L {\displaystyle L} converges to the Laplace–Beltrami operator Δ M {\displaystyle \Delta _{M}} , which is the divergence of the gradient ∇ M {\displaystyle \nabla _{M}} . Then, if f {\displaystyle \mathbf {f} } is a vector of the values of f {\displaystyle f} at the data, f = [ f ( x 1 ) , … , f ( x l + u ) ] T {\displaystyle \mathbf {f} =[f(x_{1}),\ldots ,f(x_{l+u})]^{\mathrm {T} }} , the intrinsic norm can be estimated: ‖ f ‖ I 2 = 1 ( ℓ + u ) 2 f T L f {\displaystyle \left\|f\right\|_{I}^{2}={\frac {1}{(\ell +u)^{2}}}\mathbf {f} ^{\mathrm {T} }L\mathbf {f} } As the number of data points ℓ + u {\displaystyle \ell +u} increases, this empirical definition of ‖ f ‖ I 2 {\displaystyle \left\|f\right\|_{I}^{2}} converges to the definition when P X {\displaystyle {\mathcal {P}}_{X}} is known. === Solving the regularization problem with graph-based approach === Using the weights γ A {\displaystyle \gamma _{A}} and γ I {\displaystyle \gamma _{I}} for the ambient and intrinsic regularizers, the final expression to be solved becomes: arg min f ∈ H 1 ℓ ∑ i = 1 ℓ V ( f ( x i ) , y i ) + γ A ‖ f ‖ K 2 + γ I ( ℓ + u ) 2 f T L f {\displaystyle {\underset {f\in {\mathcal {H}}}{\arg \!\min }}{\frac {1}{\ell }}\sum _{i=1}^{\ell }V(f(x_{i}),y_{i})+\gamma _{A}\left\|f\right\|_{K}^{2}+{\frac {\gamma _{I}}{(\ell +u)^{2}}}\mathbf {f} ^{\mathrm {T} }L\mathbf {f} } As with other kernel methods, H {\displaystyle {\mathcal {H}}} may be an infinite-dimensional space, so if the regularization expression cannot be solved explicitly, it is impossible to search the entire space for a solution. Instead, a representer theorem shows that under certain conditions on the choice of the norm ‖ f ‖ I {\displaystyle \left\|f\right\|_{I}} , the optimal solution f ∗ {\displaystyle f^{}} must be a linear combination of the kernel centered at each of the input points: for some weights α i {\displaystyle \alpha _{i}} , f ∗ ( x ) = ∑ i = 1 ℓ + u α i K ( x i , x ) {\displaystyle f^{}(x)=\sum _{i=1}^{\ell +u}\alpha _{i}K(x_{i},x)} Using this result, it is possible to search for the optimal solution f ∗ {\displaystyle f^{}} by searching the finite-dimensional space defined by the possible choices of α i {\displaystyle \alpha _{i}} . === Functional approach of the Laplacian norm === The idea beyond the graph-Laplacian is to use neighbors to estimate the Laplacian. This method is akin to local averaging methods, that are known to scale poorly in high-dimensional problems. Indeed, the graph Laplacian is known to suffer from the curse of dimensionality. Luckily, it is possible to leverage expected smoothness of the function to estimate thanks to more advanced functional analysis. This method consists of estimating the Laplacian operator using derivatives of the kernel reading ∂ 1 , j K ( x i , x ) {\displaystyle \partial _{1,j}K(x_{i},x)} where ∂ 1 , j {\displaystyle \partial _{1,j}} denotes the partial derivatives according to the j-th coordinate of the first variable. This second approach to the Laplacian norm is to put in relation with meshfree methods, that contrast with the finite difference method in PDE. == Applications == Manifold regularization can extend a variety of algorithms that can be expressed using Tikhonov regularization, by choosing an appropriate loss function V {\displaystyle V} and hypothesis space H {\displaystyle {\mathcal {H}}} . Two commonly used examples are the families of support vector machines and regularized least squares algorithm
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Redshift (theory)

Redshift is a techno-economic theory suggesting hypersegmentation of information technology markets based on whether individual computing needs are over or under-served by Moore's law, which predicts the doubling of computing transistors (and therefore roughly computing power) every two years. The theory, proposed and named by New Enterprise Associates partner and former Sun Microsystems CTO Greg Papadopoulos, categorized a series of high growth markets (redshifting) while predicting slower GDP-driven growth in traditional computing markets (blueshifting). Papadopoulos predicted the result will be a fundamental redesign of components comprising computing systems. == Hypergrowth market segments (redshifting) == According to the Redshift theory, applications "redshift" when they grow dramatically faster than Moore's Law allows, growing quickly in their absolute number of systems. In these markets, customers are running out of datacenter real-estate, power and cooling infrastructure. According to Dell Senior Vice President Brad Anderson, “Businesses requiring hyperscale computing environments – where infrastructure deployments are measured by up to millions of servers, storage and networking equipment – are changing the way they approach IT.” While various Redshift proponents offer minor alterations on the original presentation, “Redshifting” generally includes: === ΣBW (Sum-of-Bandwidth) === These are companies that drive heavy Internet traffic. This includes popular web-portals like Google, Yahoo, AOL and MSN. It also includes telecoms, multimedia, television over IP, online games like World of Warcraft and others. This segment has been enabled by widespread availability of high-bandwidth Internet connections to consumers through a DSL or cable modem. A simple way to understand this market is that for every byte of content served to a PC, mobile phone or other device over a network, there must exist computing systems to send it over the network. === High performance computing (HPC) === These are companies that do complex simulations that involve (for example) weather, stock markets or drug-design simulations. This is a generally elastic market because businesses frequently spend every "available" dollar budgeted for IT. A common anecdote claims that cutting the cost of computing by half causes customers in this segment to buy at least twice as much, because each marginal IT dollar spent contributes to business advantage. === prise (or "Star-prise") === These are companies that aggregate traditional computing applications and offer them as services, typically in the form of Software as a Service (SaaS). For example, companies that deploy CRM are over-served by Moore's Law, but companies that aggregate CRM functions and offer them as a service, such as Salesforce.com, grow faster than Moore's Law. === The eBay crisis === A prime example of redshift was a crisis at eBay. In 1999 eBay suffered a database crisis when a single Oracle Database running on the fastest Sun machine available (these tracking Moore's law in this period) was not enough to cope with eBay's growth. The solution was to massively parallelise their system architecture. == Traditional computing markets (blueshifting) == Redshift theory suggests that traditional computing markets, such as those serving enterprise resource planning or customer relationship management applications, have reached relative saturation in industrialized nations. Thereafter, proponents argued further market growth will closely follow gross domestic product growth, which typically remains under 10% for most countries annually. Given that Moore's Law continues to predict accurately the rate of computing transistor growth, which roughly translates into computing power doubling every two years, the Redshift theory suggests that traditional computing markets will ultimately contract as a percentage of computing expenditures over time. Functionally, this means “Blueshifting” customers can satisfy computing requirement growth by swapping in faster processors without increasing the absolute number of computing systems. == Consequences and industry commentary == Papadopoulos argued that while traditional computing markets remain the dominant source of revenue through the late 2000s, a shift to hypergrowth markets will inevitably occur. When that shift occurs, he argued computing (but not computers) will become a utility, and differentiation in the IT market will be based upon a company's ability to deliver computing at massive scale, efficiently and with predictable service levels, much like electricity at that time. If computing is to be delivered as a utility, Nicholas Carr suggested Papadopoulos' vision compares with Microsoft researcher Jim Hamilton, who both agree that computing is most efficiently generated in shipping containers. Industry analysts are also beginning to quantify Redshifting and Blueshifting markets. According to International Data Corporation vice president Matthew Eastwood, "IDC believes that the IT market is in a period of hyper segmentation... This a class of customers that is Moore's law driven and as price performance gains continue, IDC believes that these organizations will accelerate their consumption of IT infrastructure.” == History and nomenclature == Key portions of Papadopoulos' theory were first presented by Sun Microsystems CEO Jonathan Schwartz in late 2006. Papadopoulos later gave a full presentation on Redshift to Sun's annual Analyst Summit in February 2007. The term Redshift refers to what happens when electromagnetic radiation, usually visible light, moves away from an observer. Papadopoulos chose this term to reflect growth markets because redshift helped cosmologists explain the expansion of the universe. Papadopoulos originally depicted traditional IT markets as green to represent their revenue base, but later changed them to “blueshift,” which occurs when a light source moves toward an observer, similar to what would happen during a contraction of the universe.
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Honeywell JetWave

Honeywell's JetWave is a piece of satellite communications hardware produced by Honeywell that enables global in-flight internet connectivity. Its connectivity is provided using Inmarsat’s GX Aviation network. The JetWave platform is used in business and general aviation, as well as defense and commercial airline users. == History == In 2012, Honeywell announced it would provide Inmarsat with the hardware for its GX Ka-band in-flight connectivity network. The Ka-band (pronounced either "kay-ay band" or "ka band") is a portion of the microwave part of the electromagnetic spectrum defined as frequencies in the range 27.5 to 31 gigahertz (GHz). In satellite communications, the Ka-band allows higher bandwidth communication. In 2017, after five years and more than 180 flight hours and testing, JetWave was launched as part of GX Aviation with Lufthansa Group. Honeywell’s JetWave was the exclusive terminal hardware option for the Inmarsat GX Aviation network; however, the exclusivity clause in that contract has expired. In July 2019, the United States Air Force selected Honeywell’s JetWave satcom system for 70 of its C-17 Globemaster III cargo planes. In December 2019, it was reported that six AirAsia aircraft had been fitted with Inmarsat’s GX Aviation Ka-band connectivity system and is slated to be implemented fleetwide across AirAsia’s Airbus A320 and A330 models in 2020, requiring installation of JetWave atop AirAsia’s fuselages. Today, Honeywell’s JetWave hardware is installed on over 1,000 aircraft worldwide. In August 2021, the Civil Aviation Administration of China approved a validation of Honeywell’s MCS-8420 JetWave satellite connectivity system for Airbus 320 aircraft. In December 2021, Honeywell, SES, and Hughes Network Systems demonstrated multi-orbit high-speed airborne connectivity for military customers using Honeywell’s JetWave MCX terminal with a Hughes HM-series modem, and SES satellites in both medium Earth orbit (MEO) and geostationary orbit (GEO). The tests achieved full duplex data rates of more than 40 megabits per second via a number of SES' (GEO) satellites including GovSat-1, and the high-throughput, low-latency O3b MEO satellite constellation, with connections moving between GEO/MEO links in under 30 sec. == Uses == === Commercial aviation === Honeywell’s JetWave enables air transport and regional aircraft to connect to Inmarsat’s GX Aviation network. The multichannel satellite (MSC) JetWave terminals share the same antenna controller, modem and router hardware with the business market, but have an MCS-8200 fuselage-mounted antenna. === Business aviation === Honeywell’s JetWave hardware allows users to connect to Inmarsat’s Jet ConneX, a business aviation broadband connectivity offering to provide Wi-Fi for connected devices. JetWave offers a tail-mount antenna for business jets. === Defense === Honeywell’s JetWave satellite communications system for defense allows users to connect to the Inmarsat GX network, offering global coverage for military airborne operators, including over water, over nontraditional flight paths and in remote areas. JetWave and the Inmarsat GX network enable mission-critical applications like real-time weather; videoconferencing; large file transfers; encryption capabilities; in-flight briefings; intelligence, surveillance, and reconnaissance video; and secure communications. JetWave is configurable for a variety of military platforms and offers antennas for large and small airframes.
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