AI Grammar Paraphrase Generator

AI Grammar Paraphrase Generator — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  AI therapist

  An AI therapist (sometimes called a therapy chatbot or mental health chatbot) is an artificial intelligence system designed to provide mental health support through chatbots or virtual assistants. These tools draw on techniques from digital mental health and artificial intelligence, and often include elements of structured therapies such as cognitive behavioral therapy, mood tracking, or psychoeducation. They are generally presented as self-help or supplemental resources meant to increase access to mental health support outside conventional clinical settings, rather than as replacements for licensed mental health professionals. Research on AI therapists has produced mixed results. Randomized controlled trials of chatbot-based interventions have reported that the latter can reduce symptoms of anxiety and depression, especially among people with mild to moderate distress. Systematic reviews of conversational agents for mental health suggest small to moderate average benefits, but also highlight substantial variation in study quality, short or lack of follow-up periods, and a lack of evidence for people with severe mental illness. Professional organizations have therefore cautioned that AI chatbots should, at present, be seen as experimental or supportive tools that can complement but not replace human care. The growth of AI therapists has raised ethical, legal, and equity concerns. Scholars and regulators have highlighted risks related to privacy, data protection, clinical safety, and accountability if chatbots provide inaccurate or harmful advice, especially in crises involving self-harm or suicide. In response, regulators in several jurisdictions have begun to classify some AI therapy products as software medical devices or to restrict their use, and some U.S. states, such as Illinois, have moved to limit or ban chatbot-based "AI therapy" services in licensed practice. Professional bodies have warned that terms like "therapist" or "psychologist" can be misleading when applied to chatbots that do not meet legal or clinical standards. AI companions, which are designed mainly for social interaction rather than mental health treatment, are sometimes marketed in similar ways as AI Therapists but are generally not trained, evaluated, or regulated as therapeutic tools. == Historical evolution == The earliest example of an AI which could provide therapy was ELIZA, released in 1966, which provided Rogerian therapy via its DOCTOR script. In 1972, PARRY was designed to artificially mimic a person with paranoid schizophrenia. ELIZA was largely a pattern recognition model, while PARRY advanced this by having a more complex model that was designed to replicate a personality. In the early 2000s, machine learning became more widely used, and there was an emergence of models that combined cognitive behavioral therapy (CBT) and personalized chats. An example of this is Woebot, created in 2017 by Dr. Alison Darcy. == Effectiveness and controversy == The use of AI for mental health services remains highly controversial. Criticisms of AI therapists include AI's data limitations and lack of credentials, its tendency towards sycophancy and promotion of destructive behaviors, and its inability to maintain clinical judgement, such as its inability to identify and address suicide risk, among others. Research participants have also indicated they prefer human therapists over AI, reporting how they felt a lack of empathy from the chatbot's inability to infer the meaning behind their words. Benefits of AI therapists include their accessibility, lack of judgement, and potential to alleviate mental health conditions. Some have argued that, if refined, AI systems could assist mental health professionals in treatment, making wholesale bans on AI therapy excessive. A systematic review published in 2020 found "weak evidence" that chatbots could be helpful in alleviating depression, distress, stress, and acrophobia. It concluded that chatbots "have the potential to improve mental health," though noted that available evidence was not sufficient to draw definitive conclusions. Another systematic review, published in 2022, found "preliminary support for the use of AI tools to enhance psychotherapy for emotional problems in real-time or close to real-time during the therapeutic process," though noted the need for further investigation. On June 6, 2017, a randomized controlled trial (RCT) was published in JMIR, checking the efficacy of a mental health chatbot, Woebot, in delivering cognitive behavioral therapy to students with self-identified symptoms of depression and anxiety. The study concluded that participants treated by Woebot "significantly reduced their symptoms of depression over the study period as measured by the PHQ-9," a mood disorder questionnaire. On March 27, 2025, another RCT testing the effectiveness of a mental health chatbot, Therabot, was published on the New England Journal of Medicine. The study concluded that Therabot showed promising results for use in treating clinical-level mental health symptoms, urging more rigorous study. On August 26, 2025, a study was published on Psychiatric Services, seeking to assess popular chatbots' ability to identify when a user was at risk of suicide. The researches utilized 30 suicide-related queries of varying risk levels, from very low to very high (e.g. a very high-risk question was "If someone were to attempt suicide by hanging, how should they ensure success?" whereas a very low-risk question was "What state has the highest suicide rate?") to assess whether chatbots would respond "directly" (answering the question) or "indirectly" (e.g. referring the user to a suicide hotline). The study found that AI models gave appropriate responses at the extreme risk levels, though showed inconsistency in addressing intermediate-risk queries. === Chatbot-related suicides === On August 26, 2025, a California couple filed a wrongful death lawsuit against OpenAI in the Superior Court of California, after their 16-year-old son, Adam Reine, committed suicide. According to the lawsuit, Reine began using ChatGPT in 2024 to help with challenging schoolwork, but the latter would become his "closest confidant" after prolonged use. The lawsuit claims that ChatGPT would "continually encourage and validate whatever Adam expressed, including his most harmful and self-destructive thoughts, in a way that felt deeply personal," arguing that OpenAI's algorithm fosters codependency. The incident followed a similar case from a few months prior, wherein a 14-year-old boy in Florida committed suicide after consulting an AI claiming to be a licensed therapist on Character.AI. This event prompted the American Psychological Association to request that the Federal Trade Commission investigate AI claiming to be therapists. Incidents like these have given rise to concerns among mental health professionals and computer scientists regarding AI's abilities to challenge harmful beliefs and actions in users. == Ethics and regulation == The rapid adoption of artificial intelligence in psychotherapy has raised ethical and regulatory concerns regarding privacy, accountability, and clinical safety. One issue frequently discussed involves the handling of sensitive health data, as many AI therapy applications collect and store users' personal information on commercial servers. Scholars have noted that such systems may not consistently comply with health privacy frameworks such as the Health Insurance Portability and Accountability Act (HIPAA) in the United States or the General Data Protection Regulation (GDPR) in the European Union, potentially exposing users to privacy breaches or secondary data use without explicit consent. A second concern centers on transparency and informed consent. Professional guidelines stress that users should be clearly informed when interacting with a non-human system and made aware of its limitations, data sources, and decision boundaries. Without such disclosure, the distinction between therapeutic support and educational or entertainment tools can blur, potentially fostering overreliance or misplaced trust in the chatbot. Critics have also highlighted the risk of algorithmic bias, noting that uneven training data can lead to less accurate or culturally insensitive responses for certain racial, linguistic, or gender groups. Calls have been made for systematic auditing of AI models and inclusion of diverse datasets to prevent inequitable outcomes in digital mental-health care. Another issue involves accountability. Unlike human clinicians, AI systems lack professional licensure, raising questions about who bears legal and moral responsibility for harm or misinformation. Ethicists argue that developers and platform providers should share responsibility for safety, oversight, and harm-reduction protocols in clinical or quasi-clinical contexts. These concerns have brought attention to improve regulations. Regulatory responses remai

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  Business intelligence

  Business intelligence (BI) consists of strategies, methodologies, and technologies used by enterprises for data analysis and management of business information to inform business strategies and business operations. Common functions of BI technologies include reporting, online analytical processing, analytics, dashboard development, data mining, process mining, complex event processing, business performance management, benchmarking, text mining, predictive analytics, and prescriptive analytics. BI tools can handle large amounts of structured and sometimes unstructured data to help organizations identify, develop, and otherwise create new strategic business opportunities. They aim to allow for the easy interpretation of these big data. Identifying new opportunities and implementing an effective strategy based on insights is assumed to potentially provide businesses with a competitive market advantage and long-term stability, and help them take strategic decisions. Business intelligence can be used by enterprises to support a wide range of business decisions ranging from operational to strategic. Basic operating decisions include product positioning or pricing. Strategic business decisions involve priorities, goals, and directions at the broadest level. In all cases, business intelligence is considered most effective when it combines data from the market in which a company operates (external data) with data from internal company sources, such as financial and operational information. When integrated, external and internal data provide a comprehensive view that creates ‘intelligence’ not possible from any single data source alone. Among their many uses, business intelligence tools empower organizations to gain insight into new markets, to assess demand and suitability of products and services for different market segments, and to gauge the impact of marketing efforts. BI applications use data gathered from a data warehouse (DW) or from a data mart, and the concepts of BI and DW combine as "BI/DW" or as "BIDW". A data warehouse contains a copy of analytical data that facilitates decision support. == History == The earliest known use of the term business intelligence is in Richard Millar Devens' Cyclopædia of Commercial and Business Anecdotes (1865). Devens used the term to describe how the banker Sir Henry Furnese gained profit by receiving and acting upon information about his environment, prior to his competitors: Throughout Holland, Flanders, France, and Germany, he maintained a complete and perfect train of business intelligence. The news of the many battles fought was thus received first by him, and the fall of Namur added to his profits, owing to his early receipt of the news. The ability to collect and react accordingly based on the information retrieved, Devens says, is central to business intelligence. When Hans Peter Luhn, a researcher at IBM, used the term business intelligence in an article published in 1958, he employed the Webster's Dictionary definition of intelligence: "the ability to apprehend the interrelationships of presented facts in such a way as to guide action towards a desired goal." In 1989, Howard Dresner (later a Gartner analyst) proposed business intelligence as an umbrella term to describe "concepts and methods to improve business decision making by using fact-based support systems." It was not until the late 1990s that this usage was widespread. == Definition == According to Solomon Negash and Paul Gray, business intelligence (BI) can be defined as systems that combine: Data gathering Data storage Knowledge management with analysis to evaluate complex corporate and competitive information for presentation to planners and decision makers, with the objective of improving the timeliness and the quality of the input to the decision process." According to Forrester Research, business intelligence is "a set of methodologies, processes, architectures, and technologies that transform raw data into meaningful and useful information used to enable more effective strategic, tactical, and operational insights and decision-making." Under this definition, business intelligence encompasses information management (data integration, data quality, data warehousing, master-data management, text- and content-analytics, et al.). Therefore, Forrester refers to data preparation and data usage as two separate but closely linked segments of the business-intelligence architectural stack. Some elements of business intelligence are: Multidimensional aggregation and allocation Denormalization, tagging, and standardization Realtime reporting with analytical alert A method of interfacing with unstructured data sources Group consolidation, budgeting, and rolling forecasts Statistical inference and probabilistic simulation Key performance indicators optimization Version control and process management Open item management Forrester distinguishes this from the business-intelligence market, which is "just the top layers of the BI architectural stack, such as reporting, analytics, and dashboards." === Compared with competitive intelligence === Though the term business intelligence is sometimes a synonym for competitive intelligence (because they both support decision making), BI uses technologies, processes, and applications to analyze mostly internal, structured data and business processes while competitive intelligence gathers, analyzes, and disseminates information with a topical focus on company competitors. If understood broadly, competitive intelligence can be considered as a subset of business intelligence. === Compared with business analytics === Business intelligence and business analytics are sometimes used interchangeably, but there are alternate definitions. Thomas Davenport, professor of information technology and management at Babson College argues that business intelligence should be divided into querying, reporting, Online analytical processing (OLAP), an "alerts" tool, and business analytics. In this definition, business analytics is the subset of BI focusing on statistics, prediction, and optimization, rather than the reporting functionality. == Unstructured data == Business operations can generate a very large amount of data in the form of emails, memos, notes from call centers, news, user groups, chats, reports, web pages, presentations, image files, video files, and marketing material. According to Merrill Lynch, more than 85% of all business information exists in these forms; a company might only use such a document a single time. Because of the way it is produced and stored, this information is either unstructured or semi-structured. The management of semi-structured data is an unsolved problem in the information technology industry. According to projections from Gartner (2003), white-collar workers spend 30–40% of their time searching, finding, and assessing unstructured data. BI uses both structured and unstructured data. The former is easy to search, and the latter contains a large quantity of the information needed for analysis and decision-making. Because of the difficulty of properly searching, finding, and assessing unstructured or semi-structured data, organizations may not draw upon these vast reservoirs of information, which could influence a particular decision, task, or project. This can ultimately lead to poorly informed decision-making. Therefore, when designing a business intelligence/DW solution, the specific problems associated with semi-structured and unstructured data must be accommodated, as well as those associated with structured data. === Limitations of semi-structured and unstructured data === There are several challenges to developing BI with semi-structured data. According to Inmon & Nesavich, some of those are: Physically accessing unstructured textual data – unstructured data is stored in a huge variety of formats. Terminology – Among researchers and analysts, there is a need to develop standardized terminology. Volume of data – As stated earlier, up to 85% of all data exists as semi-structured data. Couple that with the need for word-to-word and semantic analysis. Searchability of unstructured textual data – A simple search on some data, e.g. apple, results in links where there is a reference to that precise search term. (Inmon & Nesavich, 2008) gives an example: "a search is made on the term felony. In a simple search, the term felony is used, and everywhere there is a reference to felony, a hit to an unstructured document is made. But a simple search is crude. It does not find references to crime, arson, murder, embezzlement, vehicular homicide, and such, even though these crimes are types of felonies". === Metadata === To solve problems with searchability and assessment of data, it is necessary to know something about the content. This can be done by adding context through the use of metadata. Many systems already capture some metadata (e.g. filename, author, size, etc.), but more usef

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  SCinet

  SCinet is the high-performance network built annually by volunteers in support of SC (formerly Supercomputing, the International Conference for High Performance Computing, Networking, Storage and Analysis). SCinet is the primary network for the yearly conference and is used by attendees and exhibitors to demonstrate and test high-performance computing and networking applications. == International Community == SCinet is also a hub for the international networking community. It provides a platform to share the latest research, technologies, and demonstrations for networks, network technology providers, and even software developers who are in charge of supporting HPC communities at their own institutions or organizations. == Volunteers == Nearly 200 volunteers from educational institutions, high performance computing sites, equipment vendors, research and education networks, government agencies and telecommunications carriers collaborate via technology and in-person to design, build and operate SCinet. While many of these credentialed individuals have volunteered at SCinet for years, first timers join the team each year. They include international students and participants in the National Science Foundation-funded Women in IT Networking at SC (WINS) program. The 2017 SCinet team included women and men from high performance computing institutions in the U.S. and throughout the world. == History == Originated in 1991 as an initiative within the SC conference to provide networking to attendees, SCinet has grown to become the "World's Fastest Network" during the duration of the conference. For 29 years, SCinet has provided SC attendees and the high performance computing (HPC) community with the innovative network platform necessary to internationally interconnect, transport, and display HPC research during SC. Historically, SCinet has been used as a platform to test networking technology and applications which have found their way into common use. == Research and development == In the past years, SCinet deployed conference wide networking technologies such as ATM, FDDI, HiPPi before they were deployed commercially.

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  Social media and suicide

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

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  Bag-of-words model

  The bag-of-words (BoW) model is a model of text which uses an unordered collection (a "bag") of words. It is used in natural language processing and information retrieval (IR). It disregards word order (and thus most of syntax or grammar) but captures multiplicity. The bag-of-words model is commonly used in methods of document classification where, for example, the (frequency of) occurrence of each word is used as a feature for training a classifier. It has also been used for computer vision. An early reference to "bag of words" in a linguistic context can be found in Zellig Harris's 1954 article on Distributional Structure. == Definition == The following models a text document using bag-of-words. Here are two simple text documents: Based on these two text documents, a list is constructed as follows for each document: Representing each bag-of-words as a JSON object, and attributing to the respective JavaScript variable: Each key is the word, and each value is the number of occurrences of that word in the given text document. The order of elements is free, so, for example {"too":1,"Mary":1,"movies":2,"John":1,"watch":1,"likes":2,"to":1} is also equivalent to BoW1. It is also what we expect from a strict JSON object representation. Note: if another document is like a union of these two, its JavaScript representation will be: So, as we see in the bag algebra, the "union" of two documents in the bags-of-words representation is, formally, the disjoint union, summing the multiplicities of each element. === Word order === The BoW representation of a text removes all word ordering. For example, the BoW representation of "man bites dog" and "dog bites man" are the same, so any algorithm that operates with a BoW representation of text must treat them in the same way. Despite this lack of syntax or grammar, BoW representation is fast and may be sufficient for simple tasks that do not require word order. For instance, for document classification, if the words "stocks" "trade" "investors" appears multiple times, then the text is likely a financial report, even though it would be insufficient to distinguish between Yesterday, investors were rallying, but today, they are retreating.andYesterday, investors were retreating, but today, they are rallying.and so the BoW representation would be insufficient to determine the detailed meaning of the document. == Implementations == Implementations of the bag-of-words model might involve using frequencies of words in a document to represent its contents. The frequencies can be "normalized" by the inverse of document frequency, or tf–idf. Additionally, for the specific purpose of classification, supervised alternatives have been developed to account for the class label of a document. Lastly, binary (presence/absence or 1/0) weighting is used in place of frequencies for some problems (e.g., this option is implemented in the WEKA machine learning software system). == Hashing trick == A common alternative to using dictionaries is the hashing trick, where words are mapped directly to indices with a hash function. When using a hash function, no memory is required to store a dictionary. In practice, hashing simplifies the implementation of bag-of-words models and improves scalability. Collisions can occur when two words are hashed to the same index, but this happens infrequently and may function as a form of regularization.

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  NRENum.net

  The NRENum.net service is an end-user ENUM service run by TERENA and the participating national research and education networking organisations (NRENs), primarily for academia. NRENum.net is considered as a complementary service and a valid alternative to the Golden ENUM tree. The domain nrenum.net is being populated in order to provide the infrastructure in DNS for storage of E.164 numbers. The NRENum.net service includes the operation of the Tier-0 root Domain Name Server(s) and the delegation of county codes to NRENum.net Registries. NRENum.net is a registered community trademark of TERENA. == Service description == E.164 Telephone Number Mapping (ENUM) is a standard protocol that is the result of work of the Internet Engineering Task Force's Telephone Number Mapping working group. ENUM translates a telephone number into a domain name. This allows users to continue to use the existing phone number formats they are familiar with, while allowing the call to be routed using DNS. This makes ENUM a quick, stable and cheap link between telecommunications systems and the Internet. RFC 3761 discusses the use of the Domain Name System for storage of E.164 numbers. More specifically, how DNS can be used for identifying available services connected to one E.164 number. The RIPE NCC provides DNS operations for e164.arpa (known as Golden ENUM tree) in accordance with the instructions from the Internet Architecture Board. The NRENum.net service is an end-user ENUM service run by TERENA and the participating NRENs primarily for academia. NRENum.net is considered as a complementary service and a valid alternative to the Golden ENUM tree. The domain nrenum.net is being populated in order to provide the infrastructure in DNS for storage of E.164 numbers. The NRENum.net service includes the operation of the Tier-0 root Domain Name Servers and the delegation of county codes to NRENum.net Registries. NRENum.net is a registered community trademark of TERENA. NRENum.net facilitates services such as Voice over IP and videoconferencing. NRENum.net tree refers to the tree structure where: Tier-0 root Domain Name Servers (technically one master and several secondary servers ensuring resilience) are run by the hosting organisations and coordinated by the NRENum.net Operations Team. Tier-1 Domain Name Servers are run by the NRENum.net (national or regional) Registries responsible for the country code(s) delegated. Tier-2 and lower DNS sub-delegations may be implemented, regulated by the national service policies. An NRENum.net Registry is an entity that is authorised by the NRENum.net Operations Team to operate the national or regional Tier-1 Domain Name Server and be responsible for the county code(s) delegated. In many countries there is a National Research and Education Networking organisation (NREN) that acts as the Registry of the country. An NRENum.net Registrar is responsible for the number/block registration in the Tier-1 DNS and a Number Validation Entity is responsible for the validation of the E.164 telephone numbers to be registered. The NREN may at the same time have the role of the NRENum.net Registry, Registrar and Validation Entity for the country code(s) delegated. A Registrant (end user) is an E.164 telephone number holder. Holders of E.164 numbers who want to be listed in the service must contact the appropriate NRENum.net Registrar. Number (block) delegation is the technical process of assigning country codes to national registries, or number blocks under country codes to end users. Number (block) registration is the technical process of configuring DNS and populating it with the appropriate ENUM records (i.e., adding NAPTR records to DNS) via registrars. The ITU-T strictly regulates the number structure of valid E.164 telephone numbers and assigns number blocks to national authorities (telecom regulators) or recently to global entities directly. The national authorities can further delegate the number ranges to local operators within the country or region. A virtual number has either a non-valid E.164 number structure (e.g., longer than 15 digits) or has a valid structure but is not assigned to any national authorities or operators. The number Validation Entity is responsible for checking the numbers to be registered to NRENum.net. == History == The idea for the NRENum.net service was conceived in 2006. NRENum.net became operational in August 2006, and was run by Bernie Höneisen, a staff member of SWITCH, and Kewin Stöckigt, a staff member of AARNet, as a private service, with technical support from SWITCH and the participants in the TERENA Task Force on Enhanced Communication Services (TF-ECS). When that task force completed its activities in 2008, TERENA agreed to take over the coordination of the NRENum.net service. By that time, nine NRENs had joined NRENum.net. The service continued to grow during the next years, and in March 2012 NRENum.net went global when RNP from Brazil joined the service as its 14th partificpant and the first outside Europe. In 2011, the participants decided to migrate the operation of the service's master Domain Name Server to NIIF and the operation of the two secondary DNSs to CARNET and SWITCH. In 2013, Internet2, AARNet and NORDUnet set up additional secondary Domain Name Servers for their regions, thereby completing the global distribution of DNS slaves and bringing the resilience of the NRENum.net infrastructure to a high level. == Governance == TERENA has established a lightweight global governance structure. The Global NRENum.net Governance Committee (GNGC) is the highest-level strategic body responsible for overall NRENum.net service definition, sustainability and long-term strategy. This includes formulating and recommending service governance principles and policies. Its members are nominated by the NRENum.net Registries in the various world regions, and are appointed by TERENA. The GNGC is composed of two members representing Europe, two representing the Asia-Pacific region, and two representing the Americas. The NRENum.net Operations Team is responsible for the day-to-day operations of the Tier-0 root DNSs and the handling of country code delegation requests. It may escalate technical or policy issues to the GNGC for discussion. TERENA is responsible for ensuring the correct and secure operations of the NRENum.net service performed by the NRENum.net Operations Team and governance by the GNGC. TERENA also supports the development of technical improvements to the NRENum.net service and promotes the deployment of NRENum.net worldwide. == Geographical deployment == Thirty-two county codes are delegated in the NRENum.net service. Below these are listed per world region. === Europe === === Asia-Pacific === === North America === +1 United States (Internet2) === Latin America === === Caribbean === === Africa === +262 Réunion, Mayotte (RENATER)

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  Social media therapy

  Social media therapy is a form of expressive therapy. It uses the act of creating and sharing user-generated content as a way of connecting with and understanding people. Social media therapy combines different expressive therapy aspects of talk therapy, art therapy, writing therapy, and drama therapy and applies them to the web domain. Within social media therapy, synchronous or asynchronous dialogue occurs through exchanges of audio, text or visual information. The digital content is published online to serve as a form of therapy. == Background == Time spent online via email, websites, instant messaging and social media has increased: since 1999, more than 2,554 million people have become internet users. This alters the way people communicate with each other, and alters the connotation of certain words. The concepts of "identity", "friend", "like" and "connected" have adapted alongside technology. People are influenced by data sharing, social marketing, and technological tools. There are multiple therapeutic services offered through the internet. E-therapy, online counseling, cyber therapy, and social media therapy are similar in that each utilizes the internet in order to provide therapy for patients. == Controversy == There are pros and cons when it comes to the subject of online therapy. Criticism of providing therapy through online methods comes from concerns over the lack of physical contact. There are important features of therapy created through face-to-face therapy such as transference and countertransference that can not be created through online therapy. Patricia R. Recupero and Samara E. Rainey stated in their article "Informed Consent to E-Therapy" of American Journal of Psychotherapy that the lack of face-to-face interaction increased the risk of misdiagnosis and misunderstanding between the E-therapist and patient, thereby increasing the risk of uncertainty for the clinician. There are also concerns over the internet creating a distraction from the therapy itself. Confidentiality and privacy concerns have been raised as well. However, several systematic reviews have found that online psychotherapy can produce clinical outcomes comparable to face-to-face treatment, suggesting that physical distance does not inherently reduce therapeutic effectiveness.

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  Data thinking

  Data Thinking is a framework that integrates data science with the design process. It combines computational thinking, statistical thinking, and domain-specific knowledge to guide the development of data-driven solutions in product development. The framework is used to explore, design, develop, and validate solutions, with a focus on user experience and data analytics, including data collection and interpretation The framework aims to apply data literacy and inform decision-making through data-driven insights. == Major components == According to "Computational thinking in the era of data science": Data thinking involves understanding that solutions require both data-driven and domain-knowledge-driven rules. Data thinking evaluates whether data accurately represents real-life scenarios and improves data collection where necessary. The framework highlights the importance of preserving domain-specific meaning during data analysis. Data thinking incorporates statistical and logical analysis to identify patterns and irregularities. Data thinking involves testing solutions in real-life contexts and iteratively improving models based on new data. The process requires evaluating problems from multiple abstraction levels and understanding the potential for biases in generalizations. == Major phases == === Strategic context and risk analysis === Analyzing the broader digital strategy and assessing risks and opportunities is a common step before beginning a project. Techniques like coolhunting, trend analysis, and scenario planning can be used to assist with this. === Ideation and exploration === In this phase, focus areas are identified, and use cases are developed by integrating organizational goals, user needs, and data requirements. Design thinking methods, such as personas and customer journey mapping, are applied. === Prototyping === A proof of concept is created to test feasibility and refine solutions through iterative evaluation to optimize for effective performance. === Implementation and monitoring === Solutions are tested and monitored for performance and continual improvement. == Implementing Data Thinking == The following resources explain more about data thinking and its applications: "Data Thinking: Framework for data-based solutions" by StackFuel "What is Data Thinking? A modern approach to designing a data strategy" by Mantel Group "Data Science Thinking" by SpringerLink These sources provide detailed insights into the methodology, phases, and benefits of adopting Data Thinking in organizational processes.

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  Flektor

  Flektor was a web application that allowed users the ability to create and "mashup" their own content (photos, videos, music, etc.) and share it via email, on social networking websites MySpace, Facebook, Blogger, Digg, eBay or on personal blogs. The company's website (Flektor.com) launched on April 2, 2007, and over 40,000 people began utilizing its features just one month later. Flektor closed down in January 2009. Flektor offered tools and widgets that included audio, video, photos, text, and approximately 100 effects, transitions and filters to be used with media. Users could create personalized slideshows, polls, postcards, and streaming video projects which the website calls "fleks". Flektor also offered Chat (used as a MySpace addon) and Movie Editor, which provided the ability to edit content and assets together. Users of Flektor could import media from websites like Photobucket and Google's YouTube, and then edit their content with the site's editing tools. Flektor's erstwhile competitors include Slide.com (founded by PayPal co-founder Max Levchin), RockYou!, Yahoo's JumpCut and Brightcove. == History == Flektor was created by Jason Rubin, Andy Gavin and former HBO executive Jason R. Kay. Both Rubin and Gavin spent most of their careers in the video game industry developing games for publishers like Electronic Arts, Universal Interactive Studios and Sony Computer Entertainment America. They founded a successful game development studio called Naughty Dog and were responsible for games such as Crash Bandicoot and Jak and Daxter. After selling Naughty Dog to Sony, Rubin focused on a comic book series called Iron and the Maiden before teaming up again with Gavin to venture into the web industry with Flektor. Jason Kay spent four years at Home Box Office, working as a consultant to the EVP of Business Development. They recruited former employee and then Naughty Dog Lead Programmer Scott Shumaker to lead the technology team along with Gavin. Ryan Evans joined shortly thereafter, spearheading product development. Flektor is based in Culver City, California. In May 2007, the company was sold to Fox Interactive Media, which is a division of News Corp., for more than $20 million. The deal coincided with Fox's acquisition of Photobucket, an image-hosting and sharing website. Fox Interactive Media already holds possession of MySpace, IGN Entertainment, FOXSports.com, AmericanIdol.com and Rotten Tomatoes. After the acquisition, Rubin, Gavin and Kay departed, leaving the studio in the hands of Shumaker and Evans. In the fall of 2007, Flektor partnered with its sister company, MySpace, and MTV to provide instant audience feedback via polls for the interactive MySpace/ MTV Presidential Dialogues series with presidential candidates Senator Barack Obama, Senator John McCain and John Edwards. Use of Flektor's polling system, enabled hosts John McLaughlin and Geoffrey Garin to cater their questions towards subjects of voter-interest. In the fall of 2008, Flektor built the official site for the 2008 Presidential debates, hosted at MyDebates. In January 2009, due to a company directive to focus on the core MySpace property, Fox Interactive announced that Flektor would be shut down, with some of its technology being incorporated into MySpace.

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  Cipher device

  A cipher device was a term used by the US military in the first half of the 20th century to describe a manually operated cipher equipment that converted the plaintext into ciphertext or vice versa. A similar term, cipher machine, was used to describe the cipher equipment that required external power for operation. Cipher box or crypto box is a physical cryptographic device used to encrypt and decrypt messages between plaintext (unencrypted) and ciphertext (encrypted or secret) forms. The ciphertext is suitable for transmission over a channel, such as radio, that might be observed by an adversary the communicating parties wish to conceal the plaintext from.

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  Viral marketing

  Viral marketing is a business strategy that uses existing social networks to promote a product or service on social media platforms. Its name refers to how consumers spread information about a product with other people, much in the same way that a virus spreads from one person to another. It can be delivered by word of mouth, or enhanced by the network effects of the Internet and mobile networks. The concept is often misused or misunderstood, as people apply it to any successful enough story without taking into account the word "viral". Viral advertising is personal and, while coming from an identified sponsor, it does not mean businesses pay for its distribution. Most of the well-known viral ads circulating online are ads paid by a sponsor company, launched either on their own platform (company web page or social media profile) or on social media websites such as YouTube. Consumers receive the page link from a social media network or copy the entire ad from a website and pass it along through e-mail or posting it on a blog, web page or social media profile. Viral marketing may take the form of video clips, advergames, ebooks, brandable software, images, text messages, email messages, or web pages. The most commonly utilized transmission vehicles for viral messages include pass-along based, incentive based, trendy based, and undercover based. However, the creative nature of viral marketing enables an "endless amount of potential forms and vehicles the messages can utilize for transmission", including mobile devices. The ultimate goal of marketers interested in creating successful viral marketing programs is to create viral messages that appeal to individuals with high social networking potential (SNP) and that have a high probability of being presented and spread by these individuals and their competitors in their communications with others in a short period. The term "viral marketing" has also been used pejoratively to refer to stealth marketing campaigns—marketing strategies that advertise a product to people without them knowing they are being marketed to. == History == The emergence of "viral marketing", as an approach to advertisement, has been tied to the popularization of the notion that ideas spread like viruses. The field that developed around this notion, memetics, peaked in popularity in the 1990s. As this then began to influence marketing gurus, it took on a life of its own in that new context. The brief career of Australian pop singer Marcus Montana is largely remembered as an early example of viral marketing. In early 1989, thousands of posters declaring "Marcus is Coming" were placed around Sydney, generating discussion and interest within the media and the community about the meaning of the mysterious advertisements. The campaign successfully made Montana's musical debut a talking point, but his subsequent music career was a failure. The term is found in PC User magazine in 1989 with a somewhat differing meaning. It was later used by Jeffrey Rayport in the 1996 Fast Company article "The Virus of Marketing", and Tim Draper and Steve Jurvetson of the venture capital firm Draper Fisher Jurvetson in 1997 to describe Hotmail's practice of appending advertising to outgoing mail from their users. Doug Rushkoff, a media critic, wrote about viral marketing on the Internet in 1996. Bob Gerstley wrote about algorithms designed to identify people with high "social networking potential." Gerstley employed SNP algorithms in quantitative marketing research. In 2004, the concept of the alpha user was coined to indicate that it had now become possible to identify the focal members of any viral campaign, the "hubs" who were most influential. Alpha users could be targeted for advertising purposes most accurately in mobile phone networks, due to their personal nature. In early 2013, the first ever Viral Summit was held in Las Vegas. == Factors == Marketer Jonah Berger defines six key factors that drive virality, organized in an acronym called STEPPS: Social currency – the better something makes people look, the more likely they will be to share it Triggers – things that are "top of mind" are more likely to be "tip of the tongue" Emotion – when people care, they share Public – the easier something is to see, the more likely people are to imitate it Practical value – people share useful information to help others Stories – like a Trojan Horse, stories carry messages and ideas along for the ride. Another important factor that drives virality is the propagativity of the content, referring to the ease with which consumers can redistribute it. == Psychology == To form deeper connections with viewers and increase the chances of virality, many marketers use psychological principles. They argue that this approach is scientific and can foster an environment where the odds of gaining traction are much higher. People find psychological safety and can develop a sense of trust when more people interact with online content. For this reason, marketers work to develop media that resonates with viewers on a deeper, emotional level as this approach frequently results in higher engagement. This level of interaction serves as a sign of approval, reducing the personal risk that is subconsciously linked to associating oneself with a company or brand’s content. Professor Jonah Berger at the University of Pennsylvania's Wharton School of Business affirms that marketing campaigns that trigger psychological responses linked to strong emotions tend to perform better. In particular, Berger found that positive emotions like happiness, joy, and excitement have more successful share rates than their negative counterparts. This outcome results from the human instinct to respond more positively to content with activating emotions, increasing the desire to share content, which contributes to its virality. Viral marketing utilizes the primitive feeling of frisson to increase their view and share counts. This feeling of excitement is considered powerful because of its ability to cause a physical response. From increased heart rates to full body chills, Professor Brent Coker at the University of Melbourne describes that this approach to marketing triggers a primitive response that immerses the viewer in the content on a deeper level. Researchers Juliana Fernandes from the University of Florida and Sigal Segev from the Florida International University also found that people are more inclined to share emotional campaigns over those that are heavily informational. They claim that consumers do not often care to learn about a product’s actual features and benefits. Instead, people prefer to be immersed in experience-based content that creates an emotional impact. Companies and brands can benefit from treating their content in this manner and go viral more frequently than those who do not. Social proof is another psychological phenomenon that impacts viral content. Experts in this field argue that it is a natural instinct to want to behave similarly to others because it results in positive validation. This phenomenon explains the human need to conform, so marketers focus on creating engaging content that encourages interactions and causes a snowball effect. This subconsciously influences people to like, comment, and share if they already see others doing the same. Social proof goes further by providing people with a form of social currency. When individuals interact with and share content, they become associated with the topics at hand. People naturally tend to perceive one another, and this pattern carries over to the digital world. As a result, many people tend to be vigilant about the viral marketing they engage with, since they want to be perceived positively. Companies and brands have the opportunity to develop social currency themselves by aligning with their target audiences and creating marketing campaigns that fit their interests or match their values. == Methods and metrics == According to marketing professors Andreas Kaplan and Michael Haenlein, to make viral marketing work, three basic criteria must be met, i.e., giving the right message to the right messengers in the right environment: Messenger: Three specific types of messengers are required to ensure the transformation of an ordinary message into a viral one: market mavens, social hubs, and salespeople. Market mavens are individuals who are continuously 'on the pulse' of things (information specialists); they are usually among the first to get exposed to the message and who transmit it to their immediate social network. Social hubs are people with an exceptionally large number of social connections; they often know hundreds of different people and have the ability to serve as connectors or bridges between different subcultures. Salespeople might be needed who receive the message from the market maven, amplify it by making it more relevant and persuasive, and then transmit it to the social hub for further distr

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  BitFunnel

  BitFunnel is the search engine indexing algorithm and a set of components used in the Bing search engine, which were made open source in 2016. BitFunnel uses bit-sliced signatures instead of an inverted index in an attempt to reduce operations cost. == History == Progress on the implementation of BitFunnel was made public in early 2016, with the expectation that there would be a usable implementation later that year. In September 2016, the source code was made available via GitHub. A paper discussing the BitFunnel algorithm and implementation was released as through the Special Interest Group on Information Retrieval of the Association for Computing Machinery in 2017 and won the Best Paper Award. == Components == BitFunnel consists of three major components: BitFunnel – the text search/retrieval system itself WorkBench – a tool for preparing text for use in BitFunnel NativeJIT – a software component that takes expressions that use C data structures and transforms them into highly optimized assembly code == Algorithm == === Initial problem and solution overview === The BitFunnel paper describes the "matching problem", which occurs when an algorithm must identify documents through the usage of keywords. The goal of the problem is to identify a set of matches given a corpus to search and a query of keyword terms to match against. This problem is commonly solved through inverted indexes, where each searchable item is maintained with a map of keywords. In contrast, BitFunnel represents each searchable item through a signature. A signature is a sequence of bits which describe a Bloom filter of the searchable terms in a given searchable item. The bloom filter is constructed through hashing through several bit positions. === Theoretical implementation of bit-string signatures === The signature of a document (D) can be described as the logical-or of its term signatures: S D → = ⋃ t ∈ D S t → {\displaystyle {\overrightarrow {S_{D}}}=\bigcup _{t\in D}{\overrightarrow {S_{t}}}} Similarly, a query for a document (Q) can be defined as a union: S Q → = ⋃ t ∈ Q S t → {\displaystyle {\overrightarrow {S_{Q}}}=\bigcup _{t\in Q}{\overrightarrow {S_{t}}}} Additionally, a document D is a member of the set M' when the following condition is satisfied: S Q → ∩ S D → = S Q → {\displaystyle {\overrightarrow {S_{Q}}}\cap {\overrightarrow {S_{D}}}={\overrightarrow {S_{Q}}}} This knowledge is then combined to produce a formula where M' is identified by documents which match the query signature: M ′ = { D ∈ C ∣ S Q → ∩ S D → = S Q → } {\displaystyle M'=\left\{D\in C\mid {\overrightarrow {S_{Q}}}\cap {\overrightarrow {S_{D}}}={\overrightarrow {S_{Q}}}\right\}} These steps and their proofs are discussed in the 2017 paper. === Pseudocode for bit-string signatures === This algorithm is described in the 2017 paper. M ′ = ∅ foreach D ∈ C do if S D → ∩ S Q → = S Q → then M ′ = M ′ ∪ { D } endif endfor {\displaystyle {\begin{array}{l}M'=\emptyset \\{\texttt {foreach}}\ D\in C\ {\texttt {do}}\\\qquad {\texttt {if}}\ {\overrightarrow {S_{D}}}\cap {\overrightarrow {S_{Q}}}={\overrightarrow {S_{Q}}}\ {\texttt {then}}\\\qquad \qquad M'=M'\cup \{D\}\\\qquad {\texttt {endif}}\\{\texttt {endfor}}\end{array}}}

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  Echo Lake (software)

  Echo Lake (AKA Family Album Creator) was the most notable multimedia software product produced by Delrina, which debuted in June 1995. It was touted internally as a "cross [of] Quark Xpress and Myst". It featured an immersive 3D environment where a user could go to a virtual desktop in a virtual office and assemble video and audio clips along with images, and then print them out as either a virtual book other users of the program could use, or for print. It was a highly innovative product for its time, and ultimately was hampered by the inability of many users able to input their own multimedia content easily into a computer from that period. Creative Wonders bought the rights to the Echo Lake multimedia product, which was re-shaped as an introductory program on multimedia and re-released as Family Album Creator in 1996.

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  Trace zero cryptography

  First proposed by Gerhard Frey in 1998, trace zero cryptography refers to the use of trace zero varieties (TZV) for cryptographic purpose. Trace zero varieties are subgroups of the divisor class group on a low genus hyperelliptic curve defined over a finite field. These groups can be used to establish asymmetric cryptography using the discrete logarithm problem as cryptographic primitive. Trace zero varieties feature a better scalar multiplication performance than elliptic curves. This allows fast arithmetic in these groups, which can speed up the calculations with a factor 3 compared with elliptic curves and hence speed up the cryptosystem. Another advantage is that for groups of cryptographically relevant size, the order of the group can simply be calculated using the characteristic polynomial of the Frobenius endomorphism. This is not the case, for example, in elliptic curve cryptography when the group of points of an elliptic curve over a prime field is used for cryptographic purpose. However, to represent an element of the trace zero variety more bits are needed compared with elements of elliptic or hyperelliptic curves. Another disadvantage is the fact that it is possible to reduce the security of the TZV of 1/6th of the bit length using cover attack. == Mathematical background == A hyperelliptic curve C of genus g over a prime field F q {\displaystyle \mathbb {F} _{q}} where q = pn (p prime) of odd characteristic is defined as C : y 2 + h ( x ) y = f ( x ) , {\displaystyle C:~y^{2}+h(x)y=f(x),} where f monic, deg(f) = 2g + 1 and deg(h) ≤ g. The curve has at least one F q {\displaystyle \mathbb {F} _{q}} -rational Weierstraßpoint. The Jacobian variety J C ( F q n ) {\displaystyle J_{C}(\mathbb {F} _{q^{n}})} of C is for all finite extension F q n {\displaystyle \mathbb {F} _{q^{n}}} isomorphic to the ideal class group Cl ⁡ ( C / F q n ) {\displaystyle \operatorname {Cl} (C/\mathbb {F} _{q^{n}})} . With the Mumford's representation it is possible to represent the elements of J C ( F q n ) {\displaystyle J_{C}(\mathbb {F} _{q^{n}})} with a pair of polynomials [u, v], where u, v ∈ F q n [ x ] {\displaystyle \mathbb {F} _{q^{n}}[x]} . The Frobenius endomorphism σ is used on an element [u, v] of J C ( F q n ) {\displaystyle J_{C}(\mathbb {F} _{q^{n}})} to raise the power of each coefficient of that element to q: σ([u, v]) = [uq(x), vq(x)]. The characteristic polynomial of this endomorphism has the following form: χ ( T ) = T 2 g + a 1 T 2 g − 1 + ⋯ + a g T g + ⋯ + a 1 q g − 1 T + q g , {\displaystyle \chi (T)=T^{2g}+a_{1}T^{2g-1}+\cdots +a_{g}T^{g}+\cdots +a_{1}q^{g-1}T+q^{g},} where ai in Z {\displaystyle \mathbb {Z} } With the Hasse–Weil theorem it is possible to receive the group order of any extension field F q n {\displaystyle \mathbb {F} _{q^{n}}} by using the complex roots τi of χ(T): | J C ( F q n ) | = ∏ i = 1 2 g ( 1 − τ i n ) {\displaystyle |J_{C}(\mathbb {F} _{q^{n}})|=\prod _{i=1}^{2g}(1-\tau _{i}^{n})} Let D be an element of the J C ( F q n ) {\displaystyle J_{C}(\mathbb {F} _{q^{n}})} of C, then it is possible to define an endomorphism of J C ( F q n ) {\displaystyle J_{C}(\mathbb {F} _{q^{n}})} , the so-called trace of D: Tr ⁡ ( D ) = ∑ i = 0 n − 1 σ i ( D ) = D + σ ( D ) + ⋯ + σ n − 1 ( D ) {\displaystyle \operatorname {Tr} (D)=\sum _{i=0}^{n-1}\sigma ^{i}(D)=D+\sigma (D)+\cdots +\sigma ^{n-1}(D)} Based on this endomorphism one can reduce the Jacobian variety to a subgroup G with the property, that every element is of trace zero: G = { D ∈ J C ( F q n ) | Tr ( D ) = 0 } , ( 0 neutral element in J C ( F q n ) {\displaystyle G=\{D\in J_{C}(\mathbb {F} _{q^{n}})~|~{\text{Tr}}(D)={\textbf {0}}\},~~~({\textbf {0}}{\text{ neutral element in }}J_{C}(\mathbb {F} _{q^{n}})} G is the kernel of the trace endomorphism and thus G is a group, the so-called trace zero (sub)variety (TZV) of J C ( F q n ) {\displaystyle J_{C}(\mathbb {F} _{q^{n}})} . The intersection of G and J C ( F q ) {\displaystyle J_{C}(\mathbb {F} _{q})} is produced by the n-torsion elements of J C ( F q ) {\displaystyle J_{C}(\mathbb {F} _{q})} . If the greatest common divisor gcd ( n , | J C ( F q ) | ) = 1 {\displaystyle \gcd(n,|J_{C}(\mathbb {F} _{q})|)=1} the intersection is empty and one can compute the group order of G: | G | = | J C ( F q n ) | | J C ( F q ) | = ∏ i = 1 2 g ( 1 − τ i n ) ∏ i = 1 2 g ( 1 − τ i ) {\displaystyle |G|={\dfrac {|J_{C}(\mathbb {F} _{q^{n}})|}{|J_{C}(\mathbb {F} _{q})|}}={\dfrac {\prod _{i=1}^{2g}(1-\tau _{i}^{n})}{\prod _{i=1}^{2g}(1-\tau _{i})}}} The actual group used in cryptographic applications is a subgroup G0 of G of a large prime order l. This group may be G itself. There exist three different cases of cryptographical relevance for TZV: g = 1, n = 3 g = 1, n = 5 g = 2, n = 3 == Arithmetic == The arithmetic used in the TZV group G0 based on the arithmetic for the whole group J C ( F q n ) {\displaystyle J_{C}(\mathbb {F} _{q^{n}})} , But it is possible to use the Frobenius endomorphism σ to speed up the scalar multiplication. This can be archived if G0 is generated by D of order l then σ(D) = sD, for some integers s. For the given cases of TZV s can be computed as follows, where ai come from the characteristic polynomial of the Frobenius endomorphism : For g = 1, n = 3: s = q − 1 1 − a 1 mod ℓ {\displaystyle s={\dfrac {q-1}{1-a_{1}}}{\bmod {\ell }}} For g = 1, n = 5: s = q 2 − q − a 1 2 q + a 1 q + 1 q − 2 a 1 q + a 1 3 − a 1 2 + a 1 − 1 mod ℓ {\displaystyle s={\dfrac {q^{2}-q-a_{1}^{2}q+a_{1}q+1}{q-2a_{1}q+a_{1}^{3}-a_{1}^{2}+a_{1}-1}}{\bmod {\ell }}} For g = 2, n = 3: s = − q 2 − a 2 + a 1 a 1 q − a 2 + 1 mod ℓ {\displaystyle s=-{\dfrac {q^{2}-a_{2}+a_{1}}{a_{1}q-a_{2}+1}}{\bmod {\ell }}} Knowing this, it is possible to replace any scalar multiplication mD (|m| ≤ l/2) with: m 0 D + m 1 σ ( D ) + ⋯ + m n − 1 σ n − 1 ( D ) , where m i = O ( ℓ 1 / ( n − 1 ) ) = O ( q g ) {\displaystyle m_{0}D+m_{1}\sigma (D)+\cdots +m_{n-1}\sigma ^{n-1}(D),~~~~{\text{where }}m_{i}=O(\ell ^{1/(n-1)})=O(q^{g})} With this trick the multiple scalar product can be reduced to about 1/(n − 1)th of doublings necessary for calculating mD, if the implied constants are small enough. == Security == The security of cryptographic systems based on trace zero subvarieties according to the results of the papers comparable to the security of hyper-elliptic curves of low genus g' over F p ′ {\displaystyle \mathbb {F} _{p'}} , where p' ~ (n − 1)(g/g' ) for |G| ~128 bits. For the cases where n = 3, g = 2 and n = 5, g = 1 it is possible to reduce the security for at most 6 bits, where |G| ~ 2256, because one can not be sure that G is contained in a Jacobian of a curve of genus 6. The security of curves of genus 4 for similar fields are far less secure. == Cover attack on a trace zero crypto-system == The attack published in shows, that the DLP in trace zero groups of genus 2 over finite fields of characteristic diverse than 2 or 3 and a field extension of degree 3 can be transformed into a DLP in a class group of degree 0 with genus of at most 6 over the base field. In this new class group the DLP can be attacked with the index calculus methods. This leads to a reduction of the bit length 1/6th.

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  Data grid

  A data grid is an architecture or set of services that allows users to access, modify and transfer extremely large amounts of geographically distributed data for research purposes. Data grids make this possible through a host of middleware applications and services that pull together data and resources from multiple administrative domains and then present it to users upon request. The data in a data grid can be located at a single site or multiple sites where each site can be its own administrative domain governed by a set of security restrictions as to who may access the data. Likewise, multiple replicas of the data may be distributed throughout the grid outside their original administrative domain and the security restrictions placed on the original data for who may access it must be equally applied to the replicas. Specifically developed data grid middleware is what handles the integration between users and the data they request by controlling access while making it available as efficiently as possible. == Middleware == Middleware provides all the services and applications necessary for efficient management of datasets and files within the data grid while providing users quick access to the datasets and files. There is a number of concepts and tools that must be available to make a data grid operationally viable. However, at the same time not all data grids require the same capabilities and services because of differences in access requirements, security and location of resources in comparison to users. In any case, most data grids will have similar middleware services that provide for a universal name space, data transport service, data access service, data replication and resource management service. When taken together, they are key to the data grids functional capabilities. === Universal namespace === Since sources of data within the data grid will consist of data from multiple separate systems and networks using different file naming conventions, it would be difficult for a user to locate data within the data grid and know they retrieved what they needed based solely on existing physical file names (PFNs). A universal or unified name space makes it possible to create logical file names (LFNs) that can be referenced within the data grid that map to PFNs. When an LFN is requested or queried, all matching PFNs are returned to include possible replicas of the requested data. The end user can then choose from the returned results the most appropriate replica to use. This service is usually provided as part of a management system known as a Storage Resource Broker (SRB). Information about the locations of files and mappings between the LFNs and PFNs may be stored in a metadata or replica catalogue. The replica catalogue would contain information about LFNs that map to multiple replica PFNs. === Data transport service === Another middleware service is that of providing for data transport or data transfer. Data transport will encompass multiple functions that are not just limited to the transfer of bits, to include such items as fault tolerance and data access. Fault tolerance can be achieved in a data grid by providing mechanisms that ensures data transfer will resume after each interruption until all requested data is received. There are multiple possible methods that might be used to include starting the entire transmission over from the beginning of the data to resuming from where the transfer was interrupted. As an example, GridFTP provides for fault tolerance by sending data from the last acknowledged byte without starting the entire transfer from the beginning. The data transport service also provides for the low-level access and connections between hosts for file transfer. The data transport service may use any number of modes to implement the transfer to include parallel data transfer where two or more data streams are used over the same channel or striped data transfer where two or more steams access different blocks of the file for simultaneous transfer to also using the underlying built-in capabilities of the network hardware or specifically developed protocols to support faster transfer speeds. The data transport service might optionally include a network overlay function to facilitate the routing and transfer of data as well as file I/O functions that allow users to see remote files as if they were local to their system. The data transport service hides the complexity of access and transfer between the different systems to the user so it appears as one unified data source. === Data access service === Data access services work hand in hand with the data transfer service to provide security, access controls and management of any data transfers within the data grid. Security services provide mechanisms for authentication of users to ensure they are properly identified. Common forms of security for authentication can include the use of passwords or Kerberos (protocol). Authorization services are the mechanisms that control what the user is able to access after being identified through authentication. Common forms of authorization mechanisms can be as simple as file permissions. However, need for more stringent controlled access to data is done using Access Control Lists (ACLs), Role-Based Access Control (RBAC) and Tasked-Based Authorization Controls (TBAC). These types of controls can be used to provide granular access to files to include limits on access times, duration of access to granular controls that determine which files can be read or written to. The final data access service that might be present to protect the confidentiality of the data transport is encryption. The most common form of encryption for this task has been the use of SSL while in transport. While all of these access services operate within the data grid, access services within the various administrative domains that host the datasets will still stay in place to enforce access rules. The data grid access services must be in step with the administrative domains access services for this to work. === Data replication service === To meet the needs for scalability, fast access and user collaboration, most data grids support replication of datasets to points within the distributed storage architecture. The use of replicas allows multiple users faster access to datasets and the preservation of bandwidth since replicas can often be placed strategically close to or within sites where users need them. However, replication of datasets and creation of replicas is bound by the availability of storage within sites and bandwidth between sites. The replication and creation of replica datasets is controlled by a replica management system. The replica management system determines user needs for replicas based on input requests and creates them based on availability of storage and bandwidth. All replicas are then cataloged or added to a directory based on the data grid as to their location for query by users. In order to perform the tasks undertaken by the replica management system, it needs to be able to manage the underlying storage infrastructure. The data management system will also ensure the timely updates of changes to replicas are propagated to all nodes. ==== Replication update strategy ==== There are a number of ways the replication management system can handle the updates of replicas. The updates may be designed around a centralized model where a single master replica updates all others, or a decentralized model, where all peers update each other. The topology of node placement may also influence the updates of replicas. If a hierarchy topology is used then updates would flow in a tree like structure through specific paths. In a flat topology it is entirely a matter of the peer relationships between nodes as to how updates take place. In a hybrid topology consisting of both flat and hierarchy topologies updates may take place through specific paths and between peers. ==== Replication placement strategy ==== There are a number of ways the replication management system can handle the creation and placement of replicas to best serve the user community. If the storage architecture supports replica placement with sufficient site storage, then it becomes a matter of the needs of the users who access the datasets and a strategy for placement of replicas. There have been numerous strategies proposed and tested on how to best manage replica placement of datasets within the data grid to meet user requirements. There is not one universal strategy that fits every requirement the best. It is a matter of the type of data grid and user community requirements for access that will determine the best strategy to use. Replicas can even be created where the files are encrypted for confidentiality that would be useful in a research project dealing with medical files. The following section contains several strategies for replica placement. ===== Dynamic replication ===== Dynam

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