AI Coding Platforms

AI Coding Platforms — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  NeoPaint

  NeoPaint is a raster graphics editor for Windows and MS-DOS. It supports several file formats including JPEG, GIF, BMP, PNG, and TIFF. The developer, NeoSoft, advertises NeoPaint as "being simple enough for use by children while remaining powerful enough for the purposes of advanced image editing". The first version, NeoPaint 1.0, was released in 1992 on floppy disks. It supported video modes ranging from 640x350 to 1024x768 and multiple fonts. NeoPaint 2.2 came out for MS-DOS 3.1 in 1993, with support of for 2, 16, or 256 color images in Hercules, EGA, VGA, and Super VGA modes. NeoPaint 3.1 was released in 1995 supporting 24-bit images and formats like PCX, TIFF and BMP. NeoPaint 3.2 was released in 1996. An updated version, NeoPaint 3.2a, supported the GIF file format. NeoPaint 3.2d was released in 1998. A Windows 95 version named NeoPaint for Windows v4.0 was released in 1999 supporting the PNG file format. On September 1, 2018 the program was rebranded as PixelNEO, becoming one of the VisualNEO software products. Formats such as JPEG 2000, ICO, CUR, PSD and RAW are supported.

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  Social search

  Social search is a behavior of retrieving and searching on a social searching engine that mainly searches user-generated content such as news, videos and images related search queries on social media like Facebook, LinkedIn, Twitter, Instagram and Flickr. It is an enhanced version of web search that combines traditional algorithms. The idea behind social search is that instead of ranking search results purely based on semantic relevance between a query and the results, a social search system also takes into account social relationships between the results and the searcher. The social relationships could be in various forms. For example, in LinkedIn people search engine, the social relationships include social connections between searcher and each result, whether or not they are in the same industries, work for the same companies, belong the same social groups, and go the same schools, etc. Social search may not be demonstrably better than algorithm-driven search. In the algorithmic ranking model that search engines used in the past, relevance of a site is determined after analyzing the text and content on the page and link structure of the document. In contrast, search results with social search highlight content that was created or touched by other users who are in the Social Graph of the person conducting a search. It is a personalized search technology with online community filtering to produce highly personalized results. Social search takes many forms, ranging from simple shared bookmarks or tagging of content with descriptive labels to more sophisticated approaches that combine human intelligence with computer algorithms. Depending on the feature-set of a particular search engine, these results may then be saved and added to community search results, further improving the relevance of results for future searches of that keyword. The principle behind social search is that human network oriented results would be more meaningful and relevant for the user, instead of computer algorithms deciding the results for specific queries. == Research and implementations == Over the years, there have been different studies, researches and some implementations of Social Search. In 2008, there were a few startup companies that focused on ranking search results according to one's social graph on social networks. Companies in the social search space include Sproose, Mahalo, Jumper 2.0, Scour, Wink, Eurekster, and Delver. Former efforts include Wikia Search. In 2008, a story on TechCrunch showed Google potentially adding in a voting mechanism to search results similar to Digg's methodology. This suggests growing interest in how social groups can influence and potentially enhance the ability of algorithms to find meaningful data for end users. There are also other services like Sentiment that turn search personal by searching within the users' social circles. In 2009, a startup project called HeyStaks (www.heystaks.com) developed a web browser plugin "HayStaks". HeyStaks applies social search through collaboration in web search as a way that leads to better search results. The main motivation for HeyStaks to work on this idea is to provide the user with features that search engines didn't provide at that time. For instance, different searches have indicated that about 70% of the time when user search for something, a friend or a coworker have found it already. Also, studies have shown that approximately, 30% of people who use online search, search for something that they have found before. The startup believe that they help avoid these kind of issues by providing a shared and rich search experience through a list of recommendations that get generated based on search results. In October 2009, Google rolled out its "Social Search"; after a time in beta, the feature was expanded to multiple languages in May 2011. Before the expansion however in 2010 Bing and Google were already taking into account re-tweets and Likes when providing search results. However, after a search deal with Twitter ended without renewal, Google began to retool its Social Search. In January 2012, Google released "Search plus Your World", a further development of Social Search. The feature, which is integrated into Google's regular search as an opt-out feature, pulls references to results from Google+ profiles. The goal was to deliver better, more relevant and personalized search results with this integration. This integration however had some problems in which Google+ still is not wildly adopted or has much usage among many users. Later on, Google was criticized by Twitter for the perceived potential impact of "Search plus Your World" upon web publishers, describing the feature's release to the public as a "bad day for the web", while Google replied that Twitter refused to allow deep search crawling by Google of Twitter's content. By Google integrating Google+, the company was encouraging users to switch to Google's social networking site in order to improve search results. One famous example occurred when Google showed a link to Mark Zuckerberg's dormant Google+ account rather than the active Facebook profile. In November 2014 these accusations started to die down because Google's Knowledge Graph started to finally show links to Facebook, Twitter, and other social media sites. In December 2008, Twitter had re-introduced their people search feature. While the interface had since changed significantly, it allows you to search either full names or usernames in a straight-forward search engine. In January 2013, Facebook announced a new search engine called Graph Search still in the beta stages. The goal was to allow users to prioritize results that were popular with their social circle over the general internet. Facebook's Graph search utilized Facebook's user generated content to target users. Although there have been different researches and studies in social search, social media networks have not vested enough interest in working with search engines. LinkedIn for example has taken steps to improve its own individual search functions in order to stray users from external search engines. Even Microsoft started working with Twitter in order to integrate some tweets into Bing's search results in November 2013. Yet Twitter has its own search engine which points out how much value their data has and why they would like to keep it in house. In the end though social search will never be truly comprehensive of the subjects that matter to people unless users opt to be completely public with their information. == Social discovery == Social discovery is the use of social preferences and personal information to predict what content will be desirable to the user. Technology is used to discover new people and sometimes new experiences shopping, meeting friends or even traveling. The discovery of new people is often in real-time, enabled by mobile apps. However, social discovery is not limited to meeting people in real-time, it also leads to sales and revenue for companies via social media. An example of retail would be the addition of social sharing with music, through the iTunes music store. There is a social component to discovering new music Social discovery is at the basis of Facebook's profitability, generating ad revenue by targeting the ads to users using the social connections to enhance the commercial appeal. == Social search engines == A social search engine in an aspect can be thought of as a search engine that provides an answer for a question from another answer by identifying a person in the answer. That can happen by retrieving a user submitted query and determining that the query is related to the question; and provides an answer, including the link to the resource, as part of search results that are responsive to the query. Few social search engines depend only on online communities. Depending on the feature-set of a particular search engine, these results may then be saved and added to community search results, further improving the relevance of results for future searches of that keyword. Social search engines are considered a part of Web 2.0 because they use the collective filtering of online communities to elevate particularly interesting or relevant content using tagging. These descriptive tags add to the meta data embedded in Web pages, theoretically improving the results for particular keywords over time. A user will generally see suggested tags for a particular search term, indicating tags that have previously been added. An implementation of a social search engine is Aardvark. Aardvark is a social search engine that is based on the "village paradigm" which is about connecting the user who has a question with friends or friends of friends whom can answer his or her question. In Aadvark, a user ask a question in different ways that mostly involves online ways such as instant messaging, email, web input or other non-online ways such as text message or voice. The Aar

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  List of cryptography journals

  List of cryptography journals includes notable peer-reviewed academic journals that focus on cryptography, cryptanalysis, information security, and related areas in computer science and mathematics. == Notable journals == Cryptologia Designs, Codes and Cryptography IEEE Transactions on Information Theory International Journal of Information Security Journal of Cryptology Journal of Computer Security ACM Transactions on Privacy and Security Information Processing Letters Information and Computation

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  Intranet

  An intranet is a computer network for sharing information, easier communication, collaboration tools, operational systems, and other computing services within an organization, usually to the exclusion of access by outsiders. The term is used in contrast to public networks, such as the Internet, but uses the same technology based on the Internet protocol suite. An organization-wide intranet can constitute a focal point of internal communication and collaboration, and provide a single starting point to access internal and external resources. In its simplest form, an intranet is established with the technologies for local area networks (LANs) and wide area networks (WANs). Many modern intranets have search engines, user profiles, blogs, mobile apps with notifications, and events planning within their infrastructure. An intranet is sometimes contrasted to an extranet. While an intranet is generally restricted to employees of the organization, extranets may also be accessed by customers, suppliers, or other approved parties. Extranets extend a private network onto the Internet with special provisions for authentication, authorization and accounting (AAA protocol). == Uses == Intranets are increasingly being used to deliver tools, such as for collaboration (to facilitate working in groups and teleconferencing) or corporate directories, sales and customer relationship management, or project management. Intranets are also used as corporate culture-change platforms. For example, a large number of employees using an intranet forum application to host a discussion about key issues could come up with new ideas related to management, productivity, quality, and other corporate issues. In large intranets, website traffic is often similar to public website traffic and can be better understood by using web metrics software to track overall activity. User surveys also improve intranet website effectiveness. Larger businesses allow users within their intranet to access public internet through firewall servers. They have the ability to screen incoming and outgoing messages, keeping security intact. When part of an intranet is made accessible to customers and others outside the business, it becomes part of an extranet. Businesses can send private messages through the public network using special encryption/decryption and other security safeguards to connect one part of their intranet to another. Intranet user-experience, editorial, and technology teams work together to produce in-house sites. Most commonly, intranets are managed by the communications, HR or CIO departments of large organizations, or some combination of these. Because of the scope and variety of content and the number of system interfaces, the intranets of many organizations are much more complex than their respective public websites. Intranets and the use of intranets are growing rapidly. According to the Intranet Design Annual 2007 from Nielsen Norman Group, the number of pages on participants' intranets averaged 200,000 over the years 2001 to 2003 and has grown to an average of 6 million pages over 2005–2007. == Benefits == Intranets can help users locate and view information faster and use applications relevant to their roles and responsibilities. With a web browser interface, users can access data held in any database the organization wants to make available at any time and — subject to security provisions — from anywhere within company workstations, increasing employees' ability to perform their jobs faster, more accurately, and with confidence that they have the right information. It also helps improve services provided to users. Using hypermedia and Web technology, Web publishing allows for the maintenance of and easy access to cumbersome corporate knowledge, such as employee manuals, benefits documents, company policies, business standards, news feeds, and even training, all of which can be accessed throughout a company using common Internet standards (Acrobat files, Flash files, CGI applications). Because each business unit can update the online copy of a document, the most recent version is usually available to employees using the intranet. Intranets are also used as a platform for developing and deploying applications to support business operations and decisions across the internetworked enterprise. Information is easily accessible to all authorised users, enabling collaboration. Being able to communicate in real-time through integrated third-party tools, such as an instant messenger, promotes the sharing of ideas and removes blockages to communication to help boost a business's productivity. Intranets can serve as powerful tools for communicating (such as through chat, email and/or blogs) within a given organization about vertically strategic initiatives that have a global reach throughout said organization. The type of information that can easily be conveyed is the purpose of the initiative and what it is aiming to achieve, who is driving it, results achieved to date, and whom to speak to for more information. By providing this information on the intranet, staff can keep up-to-date with the strategic focus of their organization. For example, when Nestlé had a number of food processing plants in Scandinavia, their central support system had to deal with a number of queries every day. When Nestlé decided to invest in an intranet, they quickly realized the savings. Gerry McGovern says that the savings from the reduction in query calls was substantially greater than the investment in the intranet. Users can view information and data via a web browser rather than maintaining physical documents such as procedure manuals, internal phone list and requisition forms. This can potentially save the business money on printing, duplicating documents, and the environment, as well as document maintenance overhead. For example, the HRM company PeopleSoft "derived significant cost savings by shifting HR processes to the intranet". McGovern goes on to say the manual cost of enrolling in benefits was found to be US$109.48 per enrollment. "Shifting this process to the intranet reduced the cost per enrollment to $21.79; a saving of 80 percent". Another company that saved money on expense reports was Cisco. "In 1996, Cisco processed 54,000 reports and the amount of dollars processed was USD19 million". Many companies dictate computer specifications which, in turn, may allow Intranet developers to write applications that only have to work on one browser such that there are no cross-browser compatibility issues. Being able to specifically address one's "viewer" is a great advantage. Since intranets are user-specific (requiring database/network authentication prior to access), users know exactly who they are interfacing with and can personalize their intranet based on role (job title, department) or individual ("Congratulations Jane, on your 3rd year with our company!"). Since "involvement in decision making" is one of the main drivers of employee engagement, offering tools (like forums or surveys) that foster peer-to-peer collaboration and employee participation can make employees feel more valued and involved. == Planning and creation == Most organizations devote considerable resources into the planning and implementation of their intranet as it is of strategic importance to the organization's success. Some of the planning would include topics such as determining the purpose and goals of the intranet, identifying persons or departments responsible for implementation and management and devising functional plans, page layouts and designs. The appropriate staff would also ensure that implementation schedules and phase-out of existing systems were organized, while defining and implementing security of the intranet and ensuring it lies within legal boundaries and other constraints. In order to produce a high-value end product, systems planners should determine the level of interactivity (e.g. wikis, on-line forms) desired. Planners may also consider whether the input of new data and updating of existing data is to be centrally controlled or devolve. These decisions sit alongside to the hardware and software considerations (like content management systems), participation issues (like good taste, harassment, confidentiality), and features to be supported. Intranets are often static sites; they are a shared drive, serving up centrally stored documents alongside internal articles or communications (often one-way communication). By leveraging firms which specialise in 'social' intranets, organisations are beginning to think of how their intranets can become a 'communication hub' for their entire team. The actual implementation would include steps such as securing senior management support and funding, conducting a business requirement analysis and identifying users' information needs. From the technical perspective, there would need to be a coordinated installation of the web server and user access netw

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  Cloud robotics

  Cloud robotics is a field of robotics that attempts to invoke cloud technologies such as cloud computing, cloud storage, and other Internet technologies centered on the benefits of converged infrastructure and shared services for robotics. When connected to the cloud, robots can benefit from the powerful computation, storage, and communication resources of a modern data center in the cloud, which can process and share information from various robots or agents (other machines, smart objects, humans, etc.). Humans can also delegate tasks to robots remotely through networks. Cloud computing technologies enable robot systems to be gain capability whilst reducing costs through cloud technologies. Thus, it is possible to build lightweight, low-cost, smarter robots with an intelligent "brain" in the cloud. The "brain" consists of data center, knowledge base, task planners, deep learning, information processing, environment models, communication support, etc. == Components == A cloud for robots potentially has at least six significant components: Building a "cloud brain" for robots, the main object of cloud robotics; Offering a global library of images, maps, and object data, often with geometry and mechanical properties, expert system, knowledge base (i.e. semantic web, data centres); Massively-parallel computation on demand for sample-based statistical modelling and motion planning, task planning, multi-robot collaboration, scheduling and coordination of system; Robot sharing of outcomes, trajectories, and dynamic control policies and robot learning support; Human sharing of open-source code, data, and designs for programming, experimentation, and hardware construction; On-demand human guidance and assistance for evaluation, learning, and error recovery; Augmented human–robot interaction through various ways (semantics knowledge base, Apple SIRI like service, etc.). == Applications == Autonomous mobile robots Google's self-driving cars are cloud robots. The cars use the network to access Google's enormous database of maps and satellite and environment model (like Streetview) and combines it with streaming data from GPS, cameras, and 3D sensors to monitor its own position within centimetres, and with past and current traffic patterns to avoid collisions. Each car can learn something about environments, roads, or driving, or conditions, and it sends the information to the Google cloud, where it can be used to improve the performance of other cars. Cloud medical robots a medical cloud (also called a healthcare cluster) consists of various services such as a disease archive, electronic medical records, a patient health management system, practice services, analytics services, clinic solutions, expert systems, etc. A robot can connect to the cloud to provide clinical service to patients, as well as deliver assistance to doctors (e.g. a co-surgery robot). Moreover, it also provides a collaboration service by sharing information between doctors and care givers about clinical treatment. Assistive robots A domestic robot can be employed for healthcare and life monitoring for elderly people. The system collects the health status of users and exchange information with cloud expert system or doctors to facilitate elderly peoples life, especially for those with chronic diseases. For example, the robots are able to provide support to prevent the elderly from falling down, emergency healthy support such as heart disease, blooding disease. Care givers of elderly people can also get notification when in emergency from the robot through network. Industrial robots As highlighted by the German government's Industry 4.0 Plan, "Industry is on the threshold of the fourth industrial revolution. Driven by the Internet, the real and virtual worlds are growing closer and closer together to form the Internet of Things. Industrial production of the future will be characterised by the strong individualisation of products under the conditions of highly flexible (large series) production, the extensive integration of customers and business partners in business and value-added processes, and the linking of production and high-quality services leading to so-called hybrid products." In manufacturing, such cloud based robot systems could learn to handle tasks such as threading wires or cables, or aligning gaskets from a professional knowledge base. A group of robots can share information for some collaborative tasks. Even more, a consumer is able to place customised product orders to manufacturing robots directly with online ordering systems. Another potential paradigm is shopping-delivery robot systems. Once an order is placed, a warehouse robot dispatches the item to an autonomous car or autonomous drone to deliver it to its recipient. == Research == RoboEarth was funded by the European Union's Seventh Framework Programme for research, technological development projects, specifically to explore the field of cloud robotics. The goal of RoboEarth is to allow robotic systems to benefit from the experience of other robots, paving the way for rapid advances in machine cognition and behaviour, and ultimately, for more subtle and sophisticated human-machine interaction. RoboEarth offers a Cloud Robotics infrastructure. RoboEarth's World-Wide-Web style database stores knowledge generated by humans – and robots – in a machine-readable format. Data stored in the RoboEarth knowledge base include software components, maps for navigation (e.g., object locations, world models), task knowledge (e.g., action recipes, manipulation strategies), and object recognition models (e.g., images, object models). The RoboEarth Cloud Engine includes support for mobile robots, autonomous vehicles, and drones, which require much computation for navigation. Rapyuta is an open source cloud robotics framework based on RoboEarth Engine developed by the robotics researcher at ETHZ. Within the framework, each robot connected to Rapyuta can have a secured computing environment (rectangular boxes) giving them the ability to move their heavy computation into the cloud. In addition, the computing environments are tightly interconnected with each other and have a high bandwidth connection to the RoboEarth knowledge repository. FogROS2 is an open-source extension to the Robot Operating System 2 (ROS 2) developed by researchers at UC Berkeley. It enables robots to offload computationally intensive tasks—such as SLAM, grasp planning, and motion planning—to cloud resources, thereby enhancing performance and reducing onboard computational requirements. FogROS2 automates the provisioning of cloud instances, deployment of ROS 2 nodes, and secure communication between robots and cloud services. The platform is designed to be compatible with existing ROS 2 applications without requiring code modifications. Further advancements include FogROS2-SGC, which facilitates secure global connectivity across different networks and locations, and FogROS2-FT, which introduces fault tolerance by replicating services across multiple cloud providers to ensure robustness against failures. KnowRob is an extensional project of RoboEarth. It is a knowledge processing system that combines knowledge representation and reasoning methods with techniques for acquiring knowledge and for grounding the knowledge in a physical system and can serve as a common semantic framework for integrating information from different sources. RoboBrain is a large-scale computational system that learns from publicly available Internet resources, computer simulations, and real-life robot trials. It accumulates everything robotics into a comprehensive and interconnected knowledge base. Applications include prototyping for robotics research, household robots, and self-driving cars. The goal is as direct as the project's name—to create a centralised, always-online brain for robots to tap into. The project is dominated by Stanford University and Cornell University. And the project is supported by the National Science Foundation, the Office of Naval Research, the Army Research Office, Google, Microsoft, Qualcomm, the Alfred P. Sloan Foundation and the National Robotics Initiative, whose goal is to advance robotics to help make the United States more competitive in the world economy. MyRobots is a service for connecting robots and intelligent devices to the Internet. It can be regarded as a social network for robots and smart objects (i.e. Facebook for robots). With socialising, collaborating and sharing, robots can benefit from those interactions too by sharing their sensor information giving insight on their perspective of their current state. COALAS is funded by the INTERREG IVA France (Channel) – England European cross-border co-operation programme. The project aims to develop new technologies for disabled people through social and technological innovation and through the users' social and psychological integrity. The objective is to produce a cognitive ambient

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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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  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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  Completeness (cryptography)

  In cryptography, a boolean function is said to be complete if the value of each output bit depends on all input bits. This is a desirable property to have in an encryption cipher, so that if one bit of the input (plaintext) is changed, every bit of the output (ciphertext) has an average of 50% probability of changing. The easiest way to show why this is good is the following: consider that if we changed our 8-byte plaintext's last byte, it would only have any effect on the 8th byte of the ciphertext. This would mean that if the attacker guessed 256 different plaintext-ciphertext pairs, he would always know the last byte of every 8byte sequence we send (effectively 12.5% of all our data). Finding out 256 plaintext-ciphertext pairs is not hard at all in the internet world, given that standard protocols are used, and standard protocols have standard headers and commands (e.g. "get", "put", "mail from:", etc.) which the attacker can safely guess. On the other hand, if our cipher has this property (and is generally secure in other ways, too), the attacker would need to collect 264 (~1020) plaintext-ciphertext pairs to crack the cipher in this way.

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  Random feature

  Random features (RF) are a technique used in machine learning to approximate kernel methods, introduced by Ali Rahimi and Ben Recht in their 2007 paper "Random Features for Large-Scale Kernel Machines", and extended by. RF uses a Monte Carlo approximation to kernel functions by randomly sampled feature maps. It is used for datasets that are too large for traditional kernel methods like support vector machine, kernel ridge regression, and gaussian process. == Mathematics == === Kernel method === Given a feature map ϕ : R d → V {\textstyle \phi :\mathbb {R} ^{d}\to V} , where V {\textstyle V} is a Hilbert space (more specifically, a reproducing kernel Hilbert space), the kernel trick replaces inner products in feature space ⟨ ϕ ( x i ) , ϕ ( x j ) ⟩ V {\displaystyle \langle \phi (x_{i}),\phi (x_{j})\rangle _{V}} by a kernel function k ( x i , x j ) : R d × R d → R {\displaystyle k(x_{i},x_{j}):\mathbb {R} ^{d}\times \mathbb {R} ^{d}\to \mathbb {R} } Kernel methods replaces linear operations in high-dimensional space by operations on the kernel matrix: K X := [ k ( x i , x j ) ] i , j ∈ 1 : N {\displaystyle K_{X}:=[k(x_{i},x_{j})]_{i,j\in 1:N}} where N {\textstyle N} is the number of data points. === Random kernel method === The problem with kernel methods is that the kernel matrix K X {\textstyle K_{X}} has size N × N {\textstyle N\times N} . This becomes computationally infeasible when N {\textstyle N} reaches the order of a million. The random kernel method replaces the kernel function k {\textstyle k} by an inner product in low-dimensional feature space R D {\textstyle \mathbb {R} ^{D}} : k ( x , y ) ≈ ⟨ z ( x ) , z ( y ) ⟩ {\displaystyle k(x,y)\approx \langle z(x),z(y)\rangle } where z {\textstyle z} is a randomly sampled feature map z : R d → R D {\textstyle z:\mathbb {R} ^{d}\to \mathbb {R} ^{D}} . This converts kernel linear regression into linear regression in feature space, kernel SVM into SVM in feature space, etc. Since we have K X ≈ Z X T Z X {\displaystyle K_{X}\approx Z_{X}^{T}Z_{X}} where Z X = [ z ( x 1 ) , … , z ( x N ) ] {\displaystyle Z_{X}=[z(x_{1}),\dots ,z(x_{N})]} , these methods no longer involve matrices of size O ( N 2 ) {\textstyle O(N^{2})} , but only random feature matrices of size O ( D N ) {\textstyle O(DN)} . == Random Fourier feature == === Radial basis function kernel === The radial basis function (RBF) kernel on two samples x i , x j ∈ R d {\displaystyle x_{i},x_{j}\in \mathbb {R} ^{d}} is defined as k ( x i , x j ) = exp ⁡ ( − ‖ x i − x j ‖ 2 2 σ 2 ) {\displaystyle k(x_{i},x_{j})=\exp \left(-{\frac {\|x_{i}-x_{j}\|^{2}}{2\sigma ^{2}}}\right)} where ‖ x i − x j ‖ 2 {\displaystyle \|x_{i}-x_{j}\|^{2}} is the squared Euclidean distance and σ {\displaystyle \sigma } is a free parameter defining the shape of the kernel. It can be approximated by a random Fourier feature map z : R d → R 2 D {\displaystyle z:\mathbb {R} ^{d}\to \mathbb {R} ^{2D}} : z ( x ) := 1 D [ cos ⁡ ⟨ ω 1 , x ⟩ , sin ⁡ ⟨ ω 1 , x ⟩ , … , cos ⁡ ⟨ ω D , x ⟩ , sin ⁡ ⟨ ω D , x ⟩ ] T {\displaystyle z(x):={\frac {1}{\sqrt {D}}}[\cos \langle \omega _{1},x\rangle ,\sin \langle \omega _{1},x\rangle ,\ldots ,\cos \langle \omega _{D},x\rangle ,\sin \langle \omega _{D},x\rangle ]^{T}} where ω 1 , . . . , ω D {\displaystyle \omega _{1},...,\omega _{D}} are IID samples from the multidimensional normal distribution N ( 0 , σ − 2 I ) {\displaystyle N(0,\sigma ^{-2}I)} . Since cos , sin {\displaystyle \cos ,\sin } are bounded, there is a stronger convergence guarantee by Hoeffding's inequality. === Random Fourier features === By Bochner's theorem, the above construction can be generalized to arbitrary positive definite shift-invariant kernel k ( x , y ) = k ( x − y ) {\displaystyle k(x,y)=k(x-y)} . Define its Fourier transform p ( ω ) = 1 2 π ∫ R d e − j ⟨ ω , Δ ⟩ k ( Δ ) d Δ {\displaystyle p(\omega )={\frac {1}{2\pi }}\int _{\mathbb {R} ^{d}}e^{-j\langle \omega ,\Delta \rangle }k(\Delta )d\Delta } then ω 1 , . . . , ω D {\displaystyle \omega _{1},...,\omega _{D}} are sampled IID from the probability distribution with probability density p {\displaystyle p} . This applies for other kernels like the Laplace kernel and the Cauchy kernel. === Neural network interpretation === Given a random Fourier feature map z {\displaystyle z} , training the feature on a dataset by featurized linear regression is equivalent to fitting complex parameters θ 1 , … , θ D ∈ C {\displaystyle \theta _{1},\dots ,\theta _{D}\in \mathbb {C} } such that f θ ( x ) = R e ( ∑ k θ k e i ⟨ ω k , x ⟩ ) {\displaystyle f_{\theta }(x)=\mathrm {Re} \left(\sum _{k}\theta _{k}e^{i\langle \omega _{k},x\rangle }\right)} which is a neural network with a single hidden layer, with activation function t ↦ e i t {\displaystyle t\mapsto e^{it}} , zero bias, and the parameters in the first layer frozen. In the overparameterized case, when 2 D ≥ N {\displaystyle 2D\geq N} , the network linearly interpolates the dataset { ( x i , y i ) } i ∈ 1 : N {\displaystyle \{(x_{i},y_{i})\}_{i\in 1:N}} , and the network parameters is the least-norm solution: θ ^ = arg ⁡ min θ ∈ C D , f θ ( x k ) = y k ∀ k ∈ 1 : N ‖ θ ‖ {\displaystyle {\hat {\theta }}=\arg \min _{\theta \in \mathbb {C} ^{D},f_{\theta }(x_{k})=y_{k}\forall k\in 1:N}\|\theta \|} At the limit of D → ∞ {\displaystyle D\to \infty } , the L2 norm ‖ θ ^ ‖ → ‖ f K ‖ H {\displaystyle \|{\hat {\theta }}\|\to \|f_{K}\|_{H}} where f K {\displaystyle f_{K}} is the interpolating function obtained by the kernel regression with the original kernel, and ‖ ⋅ ‖ H {\displaystyle \|\cdot \|_{H}} is the norm in the reproducing kernel Hilbert space for the kernel. == Other examples == === Random binning features === A random binning features map partitions the input space using randomly shifted grids at randomly chosen resolutions and assigns to an input point a binary bit string that corresponds to the bins in which it falls. The grids are constructed so that the probability that two points x i , x j ∈ R d {\displaystyle x_{i},x_{j}\in \mathbb {R} ^{d}} are assigned to the same bin is proportional to K ( x i , x j ) {\displaystyle K(x_{i},x_{j})} . The inner product between a pair of transformed points is proportional to the number of times the two points are binned together, and is therefore an unbiased estimate of K ( x i , x j ) {\displaystyle K(x_{i},x_{j})} . Since this mapping is not smooth and uses the proximity between input points, Random Binning Features works well for approximating kernels that depend only on the L 1 {\displaystyle L_{1}} distance between datapoints. === Orthogonal random features === Orthogonal random features uses a random orthogonal matrix instead of a random Fourier matrix. == Historical context == In NIPS 2006, deep learning had just become competitive with linear models like PCA and linear SVMs for large datasets, and people speculated about whether it could compete with kernel SVMs. However, there was no way to train kernel SVM on large datasets. The two authors developed the random feature method to train those. It was then found that the O ( 1 / D ) {\displaystyle O(1/D)} variance bound did not match practice: the variance bound predicts that approximation to within 0.01 {\displaystyle 0.01} requires D ∼ 10 4 {\displaystyle D\sim 10^{4}} , but in practice required only ∼ 10 2 {\displaystyle \sim 10^{2}} . Attempting to discover what caused this led to the subsequent two papers.

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  ACTS Gigabit Satellite Network

  The ACTS Gigabit Satellite Network was a pioneering, high-speed communications satellite network in the years 1993-2004, created as a prototype system to explore high-speed networking of digital endpoints. The system was jointly sponsored by NASA and ARPA, implemented by BBN Technologies and Motorola, and was inducted into the Space Technology Hall of Fame in April 1997. The Advanced Communications Technology Satellite (ACTS) network was designed to provide fiber-compatible SONET service to remote nodes and networks through a wideband satellite system, and provided long-haul, point-to-point and point-to-multipoint full-duplex SONET services, at rates up to 622 Mbit/s, over NASA's Advanced Communication Technology Satellite (ACTS). The Advanced Communications Technology Satellite itself, built and operated by Lockheed Martin, was launched on STS-51 on September 12, 1993, by the Space Shuttle Discovery, and occupied a geostationary orbit at 100° west longitude. It was the first communication satellite to operate in the 20–30 GHz frequency band (Ka band), with 30 GHz uplink and 20 GHz downlink signals. The satellite incorporated advanced on-board switching and multiple dynamically-hopping spot-beam antennas for selected areas of the United States including Hawaii. Up to 3 uplink and 3 downlink antenna beams could be active simultaneously. The ACTS network ground terminals were transportable Gigabit Earth Stations (GES) with fiber-optic SONET interfaces (OC-3 and OC-12), which also supported the Asynchronous Transfer Mode (ATM) protocol suite. The network control and management functions are distributed in the various Gigabit Earth Stations, with the operator's interface being centralized in a Network Management Terminal (NMT), which could be collocated at a GES, or anywhere in the Internet. The system was operational and used for experiments for 127 months, instead of the originally planned 24–48 months. In all, 53 terminals were built and used by more than 100 experimenters to test ACTS abilities. In Nov. 1997 a record data rate of 520 Mbit/s TCP/IP throughput was achieved using ATM between several ground stations via ACTS. On May 31, 2000 the ACTS experiments program officially came to a close, but the system continued to support experiments until it was deactivated on April 28, 2004.

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  Cover (telecommunications)

  In telecommunications and tradecraft, cover is the technique of concealing or altering the characteristics of communications patterns for the purpose of denying an unauthorized receiver information that would be of value. The purpose of cover is not to make the communication secure, but to make it look like noise, rendering it uninteresting and not worth analysis. Even if an attacker recognizes the communication as interesting, cover makes traffic analysis more difficult since he must crack the cover before he can find out to whom it is addressed. Usually, the covered communication is also encrypted. In this way, enemies have no idea you sent a message; friends know you sent a message, but don't know what you said; the intended recipient knows what you said. Technically, cover sometimes refers to the specific process of modulo two additions of a pseudorandom bit stream generated by a cryptographic device with bits from the control message. Source: from Federal Standard 1037C and from MIL-STD-188

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  Kruskal count

  The Kruskal count (also known as Kruskal's principle, Dynkin–Kruskal count, Dynkin's counting trick, Dynkin's card trick, coupling card trick or shift coupling) is a probabilistic concept originally demonstrated by the Russian mathematician Evgenii Borisovich Dynkin in the 1950s or 1960s discussing coupling effects and rediscovered as a card trick by the American mathematician Martin David Kruskal in the early 1970s as a side-product while working on another problem. It was published by Kruskal's friend Martin Gardner and magician Karl Fulves in 1975. This is related to a similar trick published by magician Alexander F. Kraus in 1957 as Sum total and later called Kraus principle. Besides uses as a card trick, the underlying phenomenon has applications in cryptography, code breaking, software tamper protection, code self-synchronization, control-flow resynchronization, design of variable-length codes and variable-length instruction sets, web navigation, object alignment, and others. == Card trick == The trick is performed with cards, but is more a magical-looking effect than a conventional magic trick. The magician has no access to the cards, which are manipulated by members of the audience. Thus sleight of hand is not possible. Rather the effect is based on the mathematical fact that the output of a Markov chain, under certain conditions, is typically independent of the input. A simplified version using the hands of a clock performed by David Copperfield is as follows. A volunteer picks a number from one to twelve and does not reveal it to the magician. The volunteer is instructed to start from 12 on the clock and move clockwise by a number of spaces equal to the number of letters that the chosen number has when spelled out. This is then repeated, moving by the number of letters in the new number. The output after three or more moves does not depend on the initially chosen number and therefore the magician can predict it.

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  Multi-armed bandit

  In probability theory and machine learning, the multi-armed bandit problem (sometimes called the K- or N-armed bandit problem) is named from imagining a gambler at a row of slot machines (sometimes known as "one-armed bandits"), who has to decide which machines to play, how many times to play each machine and in which order to play them, and whether to continue with the current machine or try a different machine. More generally, it is a problem in which a decision maker iteratively selects one of multiple fixed choices (i.e., arms or actions) when the properties of each choice are only partially known at the time of allocation, and may become better understood as time passes. A fundamental aspect of bandit problems is that choosing an arm does not affect the properties of the arm or other arms. Instances of the multi-armed bandit problem include the task of iteratively allocating a fixed, limited set of resources between competing (alternative) choices in a way that minimizes the regret. A notable alternative setup for the multi-armed bandit problem includes the "best arm identification (BAI)" problem where the goal is instead to identify the best choice by the end of a finite number of rounds. The multi-armed bandit problem is a classic reinforcement learning problem that exemplifies the exploration–exploitation tradeoff dilemma. In contrast to general reinforcement learning, the selected actions in bandit problems do not affect the reward distribution of the arms. The multi-armed bandit problem also falls into the broad category of stochastic scheduling. In the problem, each machine provides a random reward from a probability distribution specific to that machine, that is not known a priori. The objective of the gambler is to maximize the sum of rewards earned through a sequence of lever pulls. The crucial tradeoff the gambler faces at each trial is between "exploitation" of the machine that has the highest expected payoff and "exploration" to get more information about the expected payoffs of the other machines. The trade-off between exploration and exploitation is also faced in machine learning. In practice, multi-armed bandits have been used to model problems such as managing research projects in a large organization, like a science foundation or a pharmaceutical company. In early versions of the problem, the gambler begins with no initial knowledge about the machines. Herbert Robbins in 1952, realizing the importance of the problem, constructed convergent population selection strategies in "some aspects of the sequential design of experiments". A theorem, the Gittins index, first published by John C. Gittins, gives an optimal policy for maximizing the expected discounted reward. == Empirical motivation == The multi-armed bandit problem models an agent that simultaneously attempts to acquire new knowledge (called "exploration") and optimize their decisions based on existing knowledge (called "exploitation"). The agent attempts to balance these competing tasks in order to maximize their total value over the period of time considered. There are many practical applications of the bandit model, for example: clinical trials investigating the effects of different experimental treatments while minimizing patient losses, adaptive routing efforts for minimizing delays in a network, financial portfolio design In these practical examples, the problem requires balancing reward maximization based on the knowledge already acquired with attempting new actions to further increase knowledge. This is known as the exploitation vs. exploration tradeoff in machine learning. The model has also been used to control dynamic allocation of resources to different projects, answering the question of which project to work on, given uncertainty about the difficulty and payoff of each possibility. Originally considered by Allied scientists in World War II, it proved so intractable that, according to Peter Whittle, the problem was proposed to be dropped over Germany so that German scientists could also waste their time on it. The version of the problem now commonly analyzed was formulated by Herbert Robbins in 1952. == The multi-armed bandit model == The multi-armed bandit (short: bandit or MAB) can be seen as a set of real distributions B = { R 1 , … , R K } {\displaystyle B=\{R_{1},\dots ,R_{K}\}} , each distribution being associated with the rewards delivered by one of the K ∈ N + {\displaystyle K\in \mathbb {N} ^{+}} levers. Let μ 1 , … , μ K {\displaystyle \mu _{1},\dots ,\mu _{K}} be the mean values associated with these reward distributions. The gambler iteratively plays one lever per round and observes the associated reward. The objective is to maximize the sum of the collected rewards. The horizon H {\displaystyle H} is the number of rounds that remain to be played. The bandit problem is formally equivalent to a one-state Markov decision process. The regret ρ {\displaystyle \rho } after T {\displaystyle T} rounds is defined as the expected difference between the reward sum associated with an optimal strategy and the sum of the collected rewards: ρ = T μ ∗ − ∑ t = 1 T r ^ t {\displaystyle \rho =T\mu ^{}-\sum _{t=1}^{T}{\widehat {r}}_{t}} , where μ ∗ {\displaystyle \mu ^{}} is the maximal reward mean, μ ∗ = max k { μ k } {\displaystyle \mu ^{}=\max _{k}\{\mu _{k}\}} , and r ^ t {\displaystyle {\widehat {r}}_{t}} is the reward in round t {\displaystyle t} . A zero-regret strategy is a strategy whose average regret per round ρ / T {\displaystyle \rho /T} tends to zero with probability 1 when the number of played rounds tends to infinity. Intuitively, zero-regret strategies are guaranteed to converge to a (not necessarily unique) optimal strategy if enough rounds are played. == Variations == A common formulation is the Binary multi-armed bandit or Bernoulli multi-armed bandit, which issues a reward of one with probability p {\displaystyle p} , and otherwise a reward of zero. Another formulation of the multi-armed bandit has each arm representing an independent Markov machine. Each time a particular arm is played, the state of that machine advances to a new one, chosen according to the Markov state evolution probabilities. There is a reward depending on the current state of the machine. In a generalization called the "restless bandit problem", the states of non-played arms can also evolve over time. There has also been discussion of systems where the number of choices (about which arm to play) increases over time. Computer science researchers have studied multi-armed bandits under worst-case assumptions, obtaining algorithms to minimize regret in both finite and infinite (asymptotic) time horizons for both stochastic and non-stochastic arm payoffs. === Best arm identification === An important variation of the classical regret minimization problem in multi-armed bandits is best arm identification (BAI), also known as pure exploration. This problem is crucial in various applications, including clinical trials, adaptive routing, recommendation systems, and A/B testing. In BAI, the objective is to identify the arm having the highest expected reward. An algorithm in this setting is characterized by a sampling rule, a decision rule, and a stopping rule, described as follows: Sampling rule: ( a t ) t ≥ 1 {\displaystyle (a_{t})_{t\geq 1}} is a sequence of actions at each time step Stopping rule: τ {\displaystyle \tau } is a (random) stopping time which suggests when to stop collecting samples Decision rule: a ^ τ {\displaystyle {\hat {a}}_{\tau }} is a guess on the best arm based on the data collected up to time τ {\displaystyle \tau } There are two predominant settings in BAI: Fixed budget setting: Given a time horizon T ≥ 1 {\displaystyle T\geq 1} , the objective is to identify the arm with the highest expected reward a ⋆ ∈ arg ⁡ max k μ k {\displaystyle a^{\star }\in \arg \max _{k}\mu _{k}} minimizing probability of error δ {\displaystyle \delta } . Fixed confidence setting: Given a confidence level δ ∈ ( 0 , 1 ) {\displaystyle \delta \in (0,1)} , the objective is to identify the arm with the highest expected reward a ⋆ ∈ arg ⁡ max k μ k {\displaystyle a^{\star }\in \arg \max _{k}\mu _{k}} with the least possible amount of trials and with probability of error P ( a ^ τ ≠ a ⋆ ) ≤ δ {\displaystyle \mathbb {P} ({\hat {a}}_{\tau }\neq a^{\star })\leq \delta } . For example using a decision rule, we could use m 1 {\displaystyle m_{1}} where m {\displaystyle m} is the machine no.1 (you can use a different variable respectively) and 1 {\displaystyle 1} is the amount for each time an attempt is made at pulling the lever, where ∫ ∑ m 1 , m 2 , ( . . . ) = M {\displaystyle \int \sum m_{1},m_{2},(...)=M} , identify M {\displaystyle M} as the sum of each attempts m 1 + m 2 {\displaystyle m_{1}+m_{2}} , (...) as needed, and from there you can get a ratio, sum or mean as quantitative probability and sample your formulation for each slots. You can also do ∫ ∑ k ∝ i N − (

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  Cryptographic multilinear map

  A cryptographic n {\displaystyle n} -multilinear map is a kind of multilinear map, that is, a function e : G 1 × ⋯ × G n → G T {\displaystyle e:G_{1}\times \cdots \times G_{n}\rightarrow G_{T}} such that for any integers a 1 , … , a n {\displaystyle a_{1},\ldots ,a_{n}} and elements g i ∈ G i {\displaystyle g_{i}\in G_{i}} , e ( g 1 a 1 , … , g n a n ) = e ( g 1 , … , g n ) ∏ i = 1 n a i {\displaystyle e(g_{1}^{a_{1}},\ldots ,g_{n}^{a_{n}})=e(g_{1},\ldots ,g_{n})^{\prod _{i=1}^{n}a_{i}}} , and which in addition is efficiently computable and satisfies some security properties. It has several applications on cryptography, as key exchange protocols, identity-based encryption, and broadcast encryption. There exist constructions of cryptographic 2-multilinear maps, known as bilinear maps, however, the problem of constructing such multilinear maps for n > 2 {\displaystyle n>2} seems much more difficult and the security of the proposed candidates is still unclear. == Definition == === For n = 2 === In this case, multilinear maps are mostly known as bilinear maps or pairings, and they are usually defined as follows: Let G 1 , G 2 {\displaystyle G_{1},G_{2}} be two additive cyclic groups of prime order q {\displaystyle q} , and G T {\displaystyle G_{T}} another cyclic group of order q {\displaystyle q} written multiplicatively. A pairing is a map: e : G 1 × G 2 → G T {\displaystyle e:G_{1}\times G_{2}\rightarrow G_{T}} , which satisfies the following properties: Bilinearity ∀ a , b ∈ F q ∗ , ∀ P ∈ G 1 , Q ∈ G 2 : e ( a P , b Q ) = e ( P , Q ) a b {\displaystyle \forall a,b\in F_{q}^{},\ \forall P\in G_{1},Q\in G_{2}:\ e(aP,bQ)=e(P,Q)^{ab}} Non-degeneracy If g 1 {\displaystyle g_{1}} and g 2 {\displaystyle g_{2}} are generators of G 1 {\displaystyle G_{1}} and G 2 {\displaystyle G_{2}} , respectively, then e ( g 1 , g 2 ) {\displaystyle e(g_{1},g_{2})} is a generator of G T {\displaystyle G_{T}} . Computability There exists an efficient algorithm to compute e {\displaystyle e} . In addition, for security purposes, the discrete logarithm problem is required to be hard in both G 1 {\displaystyle G_{1}} and G 2 {\displaystyle G_{2}} . === General case (for any n) === We say that a map e : G 1 × ⋯ × G n → G T {\displaystyle e:G_{1}\times \cdots \times G_{n}\rightarrow G_{T}} is an n {\displaystyle n} -multilinear map if it satisfies the following properties: All G i {\displaystyle G_{i}} (for 1 ≤ i ≤ n {\displaystyle 1\leq i\leq n} ) and G T {\displaystyle G_{T}} are groups of same order; if a 1 , … , a n ∈ Z {\displaystyle a_{1},\ldots ,a_{n}\in \mathbb {Z} } and ( g 1 , … , g n ) ∈ G 1 × ⋯ × G n {\displaystyle (g_{1},\ldots ,g_{n})\in G_{1}\times \cdots \times G_{n}} , then e ( g 1 a 1 , … , g n a n ) = e ( g 1 , … , g n ) ∏ i = 1 n a i {\displaystyle e(g_{1}^{a_{1}},\ldots ,g_{n}^{a_{n}})=e(g_{1},\ldots ,g_{n})^{\prod _{i=1}^{n}a_{i}}} ; the map is non-degenerate in the sense that if g 1 , … , g n {\displaystyle g_{1},\ldots ,g_{n}} are generators of G 1 , … , G n {\displaystyle G_{1},\ldots ,G_{n}} , respectively, then e ( g 1 , … , g n ) {\displaystyle e(g_{1},\ldots ,g_{n})} is a generator of G T {\displaystyle G_{T}} There exists an efficient algorithm to compute e {\displaystyle e} . In addition, for security purposes, the discrete logarithm problem is required to be hard in G 1 , … , G n {\displaystyle G_{1},\ldots ,G_{n}} . === Candidates === All the candidates multilinear maps are actually slightly generalizations of multilinear maps known as graded-encoding systems, since they allow the map e {\displaystyle e} to be applied partially: instead of being applied in all the n {\displaystyle n} values at once, which would produce a value in the target set G T {\displaystyle G_{T}} , it is possible to apply e {\displaystyle e} to some values, which generates values in intermediate target sets. For example, for n = 3 {\displaystyle n=3} , it is possible to do y = e ( g 2 , g 3 ) ∈ G T 2 {\displaystyle y=e(g_{2},g_{3})\in G_{T_{2}}} then e ( g 1 , y ) ∈ G T {\displaystyle e(g_{1},y)\in G_{T}} . The three main candidates are GGH13, which is based on ideals of polynomial rings; CLT13, which is based approximate GCD problem and works over integers, hence, it is supposed to be easier to understand than GGH13 multilinear map; and GGH15, which is based on graphs.

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  MIME Object Security Services

  MIME Object Security Services (MOSS) is a protocol that uses the multipart/signed and multipart/encrypted framework to apply digital signature and encryption services to MIME objects. == Details == The services are offered through the use of end-to-end cryptography between an originator and a recipient at the application layer. Asymmetric (public key) cryptography is used in support of the digital signature service and encryption key management. Symmetric (secret key) cryptography is used in support of the encryption service. The procedures are intended to be compatible with a wide range of public key management approaches, including both ad hoc and certificate-based schemes. Mechanisms are provided to support many public key management approaches. == Spreading == MOSS was never widely deployed and is now abandoned, largely due to the popularity of PGP.

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