AI And Analytics

AI And Analytics — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

  • RCUDA

    RCUDA

    rCUDA, which stands for Remote CUDA, is a type of middleware software framework for remote GPU virtualization. Fully compatible with the CUDA application programming interface (API), it allows the allocation of one or more CUDA-enabled GPUs to a single application. Each GPU can be part of a cluster or running inside of a virtual machine. The approach is aimed at improving performance in GPU clusters that are lacking full utilization. GPU virtualization reduces the number of GPUs needed in a cluster, and in turn, leads to a lower cost configuration – less energy, acquisition, and maintenance. The recommended distributed acceleration architecture is a high performance computing cluster with GPUs attached to only a few of the cluster nodes. When a node without a local GPU executes an application needing GPU resources, remote execution of the kernel is supported by data and code transfers between local system memory and remote GPU memory. rCUDA is designed to accommodate this client-server architecture. On one end, clients employ a library of wrappers to the high-level CUDA Runtime API, and on the other end, there is a network listening service that receives requests on a TCP port. Several nodes running different GPU-accelerated applications can concurrently make use of the whole set of accelerators installed in the cluster. The client forwards the request to one of the servers, which accesses the GPU installed in that computer and executes the request in it. Time-multiplexing the GPU, or in other words sharing it, is accomplished by spawning different server processes for each remote GPU execution request. == rCUDA v20.07 == The rCUDA middleware enables the concurrent usage of CUDA-compatible devices remotely. rCUDA employs either the InfiniBand network or the socket API for the communication between clients and servers. rCUDA can be useful in three different environments: Clusters. To reduce the number of GPUs installed in High Performance Clusters. This leads to energy savings, as well as other related savings like acquisition costs, maintenance, space, cooling, etc. Academia. In commodity networks, to offer access to a few high performance GPUs concurrently to many students. Virtual Machines. To enable the access to the CUDA facilities on the physical machine. The current version of rCUDA (v20.07) supports CUDA version 9.0, excluding graphics interoperability. rCUDA v20.07 targets the Linux OS (for 64-bit architectures) on both client and server sides. CUDA applications do not need any change in their source code in order to be executed with rCUDA.

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  • Kurzsignale

    Kurzsignale

    The Short Signal Code, also known as the Short Signal Book (German: Kurzsignalbuch), was a short code system used by the Kriegsmarine (German Navy) during World War II to minimize the transmission duration of messages. == Description == The transmission of radio messages had the potential risks of revealing the submarine's presence and direction; if decoded the content was also revealed. Submarines need to provide information, mostly in standard form (position of convoy to attack and of submarine, weather information), to their bases. Initially Morse code transmissions could be used. To inhibit detection, the duration of messages needed to be minimised; for this, Kurzsignale short-coding was used. To prevent interception, messages needed to be encrypted by the Enigma machine. To shorten transmission even further, the message could be sent by a fast machine instead of a human radio operator. For example, the Kurier system – not implemented in time – decreased the time to send a Morse dot from around 50 milliseconds for a human to 1 millisecond. == Short Signal book == The Kurzsignale code was intended to shorten transmission time to below the time required to get a directional fix. It was not primarily intended to hide signal contents; protection was intended to be achieved by encoding with the Enigma machine. A copy of the Kurzsignale code book was captured from German submarine U-110 on 9 May 1941. In August 1941, Dönitz began addressing U-boats by the names of their commanders, instead of boat numbers. The method of defining U-boat meeting points in the Short Signal Book was regarded as compromised, so a method was defined by B-Dienst cryptanalysts to disguise their positions on the Kriegsmarine German Naval Grid System (German:Gradnetzmeldeverfahren) was introduced and used until the end of the war == Radio direction finding == Aware of the danger presented by radio direction finding (RDF), the Kriegsmarine developed various systems to speed up broadcast. The Kurzsignale code system condensed messages into short codes consisting of short sequences for common terms such as "convoy location" so that additional descriptions would not be needed in the message. The resulting Kurzsignal was then encoded with the Enigma machine and subsequently transmitted as rapidly as possible, typically taking about 20 seconds. Typical length of an information or weather signal was about 25 characters. Conventional RDF needed about a minute to fix the bearing of a radio signal, and the Kurzsignale protected against this. However, the huff-duff system which was in use by the Allies could cope with these short transmissions. The fully automated burst transmission Kurier system, in testing from August 1944, could send a Kurzsignal in not more than 460 milliseconds; this was short enough to prevent location even by huff-duff and, if deployed, would have been a serious setback for Allied anti-submarine and code-breaking activities. By late 1944 the Kurier program was a top priority, but the war ended before the system was operational. == Short Weather cipher == A similar coding system was used for weather reports from U-boats, the Wetterkurzschlüssel (Short Weather Cipher). Code books were captured from U-559 on 30 October 1942.

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  • Campus network

    Campus network

    A campus network, campus area network, corporate area network or CAN is a computer network made up of an interconnection of local area networks (LANs) within a limited geographical area. The networking equipments (switches, routers) and transmission media (optical fiber, copper plant, Cat5 cabling etc.) are almost entirely owned by the campus tenant / owner: an enterprise, university, government etc. A campus area network is larger than a local area network but smaller than a metropolitan area network (MAN) or wide area network (WAN). == University campuses == College or university campus area networks often interconnect a variety of buildings, including administrative buildings, academic buildings, laboratories, university libraries, or student centers, residence halls, gymnasiums, and other outlying structures, like conference centers, technology centers, and training institutes. Early examples include the Stanford University Network at Stanford University, Project Athena at MIT, and the Andrew Project at Carnegie Mellon University. == Corporate campuses == Much like a university campus network, a corporate campus network serves to connect buildings. Examples of such are the networks at Googleplex and Microsoft's campus. Campus networks are normally interconnected with high speed Ethernet links operating over optical fiber such as gigabit Ethernet and 10 Gigabit Ethernet. == Area range == The range of CAN is 1 to 5 km (1 to 3 mi). If two buildings have the same domain and they are connected with a network, then it will be considered as CAN only. Though the CAN is mainly used for corporate campuses so the link will be high speed.

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  • Weird SoundCloud

    Weird SoundCloud

    Weird SoundCloud, or SoundClown, is a mashup parody music scene taking place on the online distribution platform SoundCloud. The scene has been described by its producers and music journalists to be a satirical take on electronic dance music, and useless, throwaway internet content. One critic, Audra Schroeder, categorized it as an in-joke that is "deconstructing and reshaping memes and popular music, recontextualizing the sacred texts of millennial chat rooms." == Origins == In a January 2014 interview, DJ Kevin Wang suggested that the Weird SoundCloud has "been around in the last one to two years", but started to gain much more popularity the previous year through electronic dance music internet blogs. Weird SoundCloud producer Ideaot suggested that some in the phenomenon came from the YouTube poop scene. Another producer in the community, DJ @@ (AT-AT), reasoned that producers joining the scene "want to express their musicality, see it as a more mature form of YouTube Poop," or are "just looking for recognition on social media sites." AT-AT said that it was "a fun thing to do, and after I stopped making proper music I felt I needed a bit of an outlet for my creativity. The fact that people enjoyed it and/or treated it as a travesty (Direct quote from one of my tracks) spurs me on." == Characteristics == Weird SoundCloud is a mash-up and parody music genre labeled by journalist Audra Schroeder as an in-joke that is "deconstructing and reshaping memes and popular music, recontextualizing the sacred texts of millennial chat rooms." Most tracks range from around 30 seconds to one minute in length. The people who make weird SoundCloud are known as SoundClowns, a term coined by producer Dicksoak. Ideaot described the weird SoundCloud community as "largely just people who are friends with each other." Noisey critic Ryan Bassil spotlight the variety of music coming out of the weird SoundCloud landscape: "One minute you could be listening to the Seinfeld theme reimagined as an aneurysm inducing dubstep corker, the next, you're recovering from hearing a version of Tenacious D's "Tribute" that's akin to having a stroke." Bassil analyzes that the tracks "often take the past and repurpose it into something that, although not altogether useful, sounds fresh and reflective of the abstract, confusing panoramic that encapsulates the modern internet." Bassil compared the lexicon of SoundClown's track titles to that of Reddit and Twitter users. According to Dicksoak, most works of the style are critiques of EDM or "are just uploaded because they sound funny." However, Bassil disagreed, writing that there are also many tracks that keep repurposing a certain meme, such as "mom's spaghetti" or the re-use of vocals from recordings by hip hop group Death Grips. He describe the scene's re-use of memes as a satirical take on pointless online content that is only on the internet to "do nothing other than fill the void": They're changing the format of the original work's intended message or audience - a technique often employed by top-tier digital media companies - and in doing so they're sarcastically, ironically, taking the piss out of what Web 2.0's turned into - an open arena where the most ridiculous, unashamed, often pointless piggy-back content can rack up thousands and thousands of clicks. == Notable examples == There are mash-ups that "disrupt the flow of popular music", in the words of writer Schroeder, such as a "flutedrop" remix of the Miley Cyrus song "Wrecking Ball" and Shaliek's mashup of music by Bruno Mars and Korn. In November 2013, Wang released a set of mp3 files on SoundCloud named Best Drops Ever, which included tracks like "A Drop So Epic a Bunch of NYU Bros Already Bought a 3-Day Weekend Pass for It" and "A Drop So Crazy You'll Kill Your Family". All of the tracks start as normal electronic dance music build-ups, before they drop into a "bait and switch" audio or film clip such as Filet-O-Fish commercials, the Whitney Houston song "I Will Always Love You" and the film Bambi (1942) that ruins the anticipation. The collection is a parody of the over-importance and over-focus of the drop and lack of care of the overall quality of a song common in the modern electronic dance music scene. Wang has released more than 45 tracks in the weird SoundCloud, some of them receiving around a million plays. Subgenres of Weird SoundCloud include Macklecore, mash-ups and remixes that include the works of American hip-hop recording artist Macklemore, and Biggiewave, which include samples of songs from the album Ready to Die (1994) by The Notorious B.I.G. Common audio and meme sources used include Skrillex, the Martin Garrix track "Animals", Thomas the Tank Engine, Shrek, Macklemore, "Gangnam Style", the Bruno Mars track "Uptown Funk", the Disturbed track "Down with the Sickness", Space Jam, the Childish Gambino track "Bonfire", the Death Grips track "Takyon" and air horn sound effects. == Reception == Bassil praised the SoundClown scene as "loveable and strangely honest", reasoning that it "just reminds me that we're all humans on the internet, all searching for #content that means something, something to connect with, but usually only dredging up bastardised versions of things we've already read, seen, or watched before." Bassil also described the weird SoundCloud as a more successful version of a similar scene known as weird YouTube; the reason for the success of SoundClowns is due to SoundCloud's discovery algorithm: "Small collectives and trends are able to form, and there's an abundance of tracks from artists who are almost forging careers out of it, as opposed to uploading one viral hit." Publications have made lists of weird SoundCloud works, such as BuzzFeed's "23 Of The Weirdest Songs On Soundcloud", Obsev's "Weird SoundCloud Mashups That Must've Been Made While Drunk", and Thump's "9 of the Best and Most Upsetting Soundclowns we Could Find", where writer Isabelle Hellyer called it the "most influential genre of music in human history." A Your EDM writer called it "oddly addicting."

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  • Personality computing

    Personality computing

    Personality computing is a research field related to artificial intelligence and personality psychology that studies personality by means of computational techniques from different sources, including text, multimedia, and social networks. == Overview == Personality computing addresses three main problems involving personality: automatic personality recognition, perception, and synthesis. Automatic personality recognition is the inference of the personality type of target individuals from their digital footprint. Automatic personality perception is the inference of the personality attributed by an observer to a target individual based on some observable behavior. Automatic personality synthesis is the generation of the style or behaviour of artificial personalities in Avatars and virtual agents. Self-assessed personality tests or observer ratings are always exploited as the ground truth for testing and validating the performance of artificial intelligence algorithms for the automatic prediction of personality types. There is a wide variety of personality tests, such as the Myers Briggs Type Indicator (MBTI) or the MMPI, but the most used are tests based on the Five Factor Model such as the Revised NEO Personality Inventory. Personality computing can be considered as an extension or complement of Affective computing, where the former focuses on personality traits and the latter on affective states. A further extension of the two fields is Character Computing which combines various character states and traits including but not limited to personality and affect. == History == Personality computing began around 2005 with the pioneering research in personality recognition by Shlomo Argamon and later by François Mairesse. These works showed that personality traits could be inferred with reasonable accuracy from text, such as blogs, self-presentations, and email addresses. In 2008, the concept of "portable personality" for the distributed management of personality profiles has been developed. A few years later, research began in personality recognition and perception from multimodal and social signals, such as recorded meetings and voice calls. In the 2010s, the research focused mainly on personality recognition and perception from social media, helped by the first workshops organized by Fabio Celli. In particular personality was extracted from Facebook, Twitter and Instagram. In the same years, automatic personality synthesis helped improve the coherence of simulated behavior in virtual agents. Scientific works by Michal Kosinski demonstrated the validity of Personality Computing from different digital footprints, in particular from user preferences such as Facebook page likes, showed that machines can recognize personality better than humans and raised a warning against Cambridge Analytica and misuse of this kind of technology. == Applications == Personality computing techniques, in particular personality recognition and perception, have applications in Social media marketing, where they can help reducing the cost of advertising campaigns through psychological targeting.

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  • Data Management Association

    Data Management Association

    The Data Management Association (DAMA), formerly known as the Data Administration Management Association, is a global not-for-profit organization which aims to advance concepts and practices about information management and data management. It describes itself as vendor-independent, all-volunteer organization, and has a membership consisting of technical and business professionals. Its international branch is called DAMA International (or DAMA-I), and DAMA also has various continental and national branches around the world. == History == The Data Management Association International was founded in 1980 in Los Angeles. Other early chapters were: San Francisco, Portland, Seattle, Minneapolis, New York, and Washington D.C. == Data Management Body of Knowledge == DAMA has published the Data Management Body of Knowledge (DMBOK), which contains suggestions on best practices and suggestions of a common vernacular for enterprise data management. The first edition (DAMA-DMBOK) was published on 2009 November 1, the second edition (DAMA-DMBOK2) was published on 2017 July 1., and the Revised second edition (DAMA-DMBOK2 rev.2) was published on 2019 March 19. DMBOK has been described by the authors as being an "equivalent" to the Project Management Body of Knowledge (PMBOK) and Business Analysis Body of Knowledge (BABOK). It encompasses topics such as data architecture, security, quality, modelling, governance, big data, data science, and more. DMBOK also includes the DAMA Data Wheel, an infographic which represents core data management practices. The center of the infographic is data governance, and the surrounding segments each represent a different aspect of data management: Data architecture Data modeling and design Data storage and operations Data security Data integration and interoperability Document management Content management Master data management Reference data and master data Data warehousing Metadata management Data quality Business intelligence Data science == Professional Accreditation == DAMA also provides a professional data management certification for individuals known as a Certified Data Management Professional (CDMP), which is based on the DMBOK as a study reference. There are four levels of certification based on career experience and exam results. The highest level, Fellow, requires 25 years of experience and nomination by DAMA members. It is an example of one of many competing certifications for data management professionals.

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  • Media engagement framework

    Media engagement framework

    The media engagement framework is a planning framework used by marketing professionals to understand the behavior of social media marketing-based audiences. The construct was introduced in the book, ROI of Social Media. Powell’s background in marketing ROI and Groves' experience and understanding of the applications of social media in business led to a collaboration. Dimos joined as a brand strategist for Litmus Group, a global management consulting firm. The media engagement framework consists of the definitions of personas (Individuals, Consumers and Influencers), referenced by the competitive set or constraint that applies to that persona and the measurement framework that might be applied to those personas. It is referenced at the center of the marketing process diagram, surrounded by the marketing functions of strategy, tactics, metrics and ROI. The marketing process diagram describes how the media engagement framework can apply to any strategic marketing activity but was developed to establish a completely integrated framework describing how both traditional and social media marketing activities can be planned, executed, measured and improved. == Application == The media engagement framework provides a strategic planning construct in which measurements and metrics play a crucial role. Applying the media engagement framework aids in the development and management of an effective online marketing presence leveraging social media to engage a market or audience. By first personifying the audience, the marketer is able to identify the limiting aspect of the engagements possible with that audience segment and then, understand the type of engagement metrics to apply. Each persona makes decisions differently about how he/she acts in the social media universe. A framework metric can be applied for each of these personas: Endorsement funnel for influencers Community engagement funnel for individuals Purchase funnel for consumers Individuals, influencers and consumers make decisions based on alternatives available to them and constraints put on them. To engage with an individual brands must realize they are competing against the time an individual spends on line. If they find something else more engaging, they will engage with that activity. Brands compete against other brands for the purchases of consumers acting in the category. Lastly, influencers have only so many endorsements they can make and therefore brands compete with other endorsers for the endorsement of an influencer. Creating engaging content by keeping target audience in mind like create content that audience find it funny, interesting, and relatable will encourage audience to share it on social networks. Which will be beneficial for you brand, getting more people to know about your business and brand. Contact Digilord to create engaging content for your brand. Use of listening tools (Google Alerts, Twitter Search, SocialMention.com, Veooz.com, Alterian SM2, Radian6, Sysomos, Buzzient etc.) can be employed within the model to help identify the members of the audience segment and to support the formation of other social engagement planning and management tools.

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  • Perfectly Imperfect (platform)

    Perfectly Imperfect (platform)

    Perfectly Imperfect is an online newsletter and social media platform. It was initially founded in 2020 as a biweekly email newsletter that focused on recommendations. In January 2024, Perfectly Imperfect launched PI.FYI, a social media platform. The platform is based around sharing recommendations. Its main feed is presented in reverse chronological order and is not algorithmically curated. == History == Perfectly Imperfect was started during the COVID-19 pandemic by Tyler Bainbridge, alongside college friends Alex Cushing and Serey Morm, whom he met at UMass Lowell; Morm later departed. Motivated by a dissatisfaction with algorithm-driven recommendation culture, they launched on Substack in September 2020. Its early newsletter format, PI, published brief recommendation lists and personal notes from contributors. Contributors have included a mix of underground artists and more established creative figures, such as Charli XCX, Chloe Cherry, Chloe Wise, and Meetka Otto. In October 2024, PI announced it was leaving Substack to launch its own site. == Overview == The current platform, PI.FYI, features both editorial content (guest columns, long-form essays, staff picks) and user-generated recommendations. The platform also supports "Ask" posts, where users can solicit recommendations from the community, and allows commenting, liking, and profile customization. In August 2025, it launched an events feature. In 2022, Perfectly Imperfect hosted their first offline event at Baby's All Right in Brooklyn, with a performance by The Dare. They have since expanded their event promotion/sponsorship to markets such as Los Angeles, San Francisco, and even Auckland.

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  • MLOps

    MLOps

    MLOps or ML Ops is a paradigm that aims to deploy and maintain machine learning models in production reliably and efficiently. It bridges the gap between machine learning development and production operations, ensuring that models are robust, scalable, and aligned with business goals. The word is a compound of "machine learning" and the continuous delivery practice (CI/CD) of DevOps in the software field. Machine learning models are tested and developed in isolated experimental systems. When an algorithm is ready to be launched, MLOps is practiced between data scientists, DevOps, and machine learning engineers to transition the algorithm to production systems. Similar to DevOps or DataOps approaches, MLOps seeks to increase automation and improve the quality of production models, while also focusing on business and regulatory requirements. While MLOps started as a set of best practices, it is slowly evolving into an independent approach to ML lifecycle management. MLOps applies to the entire lifecycle - from integrating with model generation (software development lifecycle, continuous integration/continuous delivery), orchestration, and deployment, to health, diagnostics, governance, and business metrics. == Definition == MLOps is a paradigm, including aspects like best practices, sets of concepts, as well as a development culture when it comes to the end-to-end conceptualization, implementation, monitoring, deployment, and scalability of machine learning products. Most of all, it is an engineering practice that leverages three contributing disciplines: machine learning, software engineering (especially DevOps), and data engineering. MLOps is aimed at productionizing machine learning systems by bridging the gap between development (Dev) and operations (Ops). Essentially, MLOps aims to facilitate the creation of machine learning products by leveraging these principles: CI/CD automation, workflow orchestration, reproducibility; versioning of data, model, and code; collaboration; continuous ML training and evaluation; ML metadata tracking and logging; continuous monitoring; and feedback loops. == History == Interest in operationalizing machine learning systems began to grow in the mid-2010s as ML projects started moving from experimentation to production use. The challenges associated with sustaining such systems were highlighted in a 2015 paper. The predicted growth in machine learning included an estimated doubling of ML pilots and implementations from 2017 to 2018, and again from 2018 to 2020. Reports show a majority (up to 88%) of corporate machine learning initiatives are struggling to move beyond test stages. However, those organizations that actually put machine learning into production saw a 3–15% profit margin increases. The MLOps market size was USD 2,191.8 Million in 2024, and is projected to be USD 16,613.4 Million in 2030. == Architecture == Machine Learning systems can be categorized in eight different categories: data collection, data processing, feature engineering, data labeling, model design, model training and optimization, endpoint deployment, and endpoint monitoring. Each step in the machine learning lifecycle is built in its own system, but requires interconnection. These are the minimum systems that enterprises need to scale machine learning within their organization. == Goals == There are a number of goals enterprises want to achieve through MLOps systems successfully implementing ML across the enterprise, including: Deployment and automation Reproducibility of models and predictions Diagnostics Governance and regulatory compliance Scalability Collaboration Business uses Monitoring and management A standard practice, such as MLOps, takes into account each of the aforementioned areas, which can help enterprises optimize workflows and avoid issues during implementation. Vendors such as Adaptive ML deliver commercial reinforcement learning operations (RLOps) and MLOps-infrastructure, targeting organizations deploying large language models in production. A common architecture of an MLOps system would include data science platforms where models are constructed and the analytical engines where computations are performed, with the MLOps tool orchestrating the movement of machine learning models, data and outcomes between the systems.

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  • Chunked transfer encoding

    Chunked transfer encoding

    Chunked transfer encoding is a streaming data transfer mechanism available in Hypertext Transfer Protocol (HTTP) version 1.1, defined in RFC 9112 §7.1. In chunked transfer encoding, the data stream is divided into a series of non-overlapping "chunks". The chunks are sent out and received independently of one another. At any given time, no knowledge of the data stream outside the currently-being-processed chunk is necessary for either the sender or the receiver. Each chunk is preceded by its size in bytes and transmission ends when a zero-length chunk is received. The chunked keyword in the Transfer-Encoding header is used to indicate chunked transfer. Chunked transfer encoding is not supported in HTTP/2, which provides its own mechanisms for data streaming. == Rationale == The introduction of chunked encoding provided various benefits: Chunked transfer encoding allows a server to maintain an HTTP persistent connection for dynamically generated content. In this case, the HTTP Content-Length header cannot be used to delimit the content and the next HTTP request/response, as the content size is not yet known. Chunked encoding has the benefit that it is not necessary to generate the full content before writing the header, as it allows streaming of content as chunks and explicitly signaling the end of the content, making the connection available for the next HTTP request/response. Chunked encoding allows the sender to send additional header fields after the message body. This is important in cases where values of a field cannot be known until the content has been produced, such as when the content of the message must be digitally signed. Without chunked encoding, the sender would have to buffer the content until it was complete in order to calculate a field value and send it before the content. == Applicability == For version 1.1 of the HTTP protocol, the chunked transfer mechanism is considered to be always and anyway acceptable, even if not listed in the Transfer-Encoding (TE) request header field, and when used with other transfer mechanisms, should always be applied last to the transferred data and never more than one time. This transfer encoding method also allows additional entity header fields to be sent after the last chunk if the client specified the "trailers" parameter as an argument of the TE request field. The origin server of the response can also decide to send additional entity trailers even if the client did not specify the "trailers" parameter, but only if the metadata is optional (i.e. the client can use the received entity without them). Whenever the trailers are used, the server should list their names in the Trailer header field; three header field types are specifically prohibited from appearing as a trailer field: Content-Length, Trailer, and Transfer-Encoding. == Format == If a Transfer-Encoding field with a value of "chunked" is specified in an HTTP message (either a request sent by a client or the response from the server), the body of the message consists of one or more chunks and one terminating chunk with an optional trailer before the final ␍␊ sequence (i.e. carriage return followed by line feed). Each chunk starts with the number of octets of the data it embeds expressed as a hexadecimal number in ASCII followed by optional parameters (chunk extension) and a terminating ␍␊ sequence, followed by the chunk data. The chunk is terminated by ␍␊. If chunk extensions are provided, the chunk size is terminated by a semicolon and followed by the parameters, each also delimited by semicolons. Each parameter is encoded as an extension name followed by an optional equal sign and value. These parameters could be used for a running message digest or digital signature, or to indicate an estimated transfer progress, for instance. The terminating chunk is a special chunk of zero length. It may contain a trailer, which consists of a (possibly empty) sequence of entity header fields. Normally, such header fields would be sent in the message's header; however, it may be more efficient to determine them after processing the entire message entity. In that case, it is useful to send those headers in the trailer. Header fields that regulate the use of trailers are Transfer-Encoding with the "trailers" parameter (used in requests) and Trailer (used in responses). == Use with compression == HTTP servers often use compression to optimize transmission, for example with Content-Encoding: gzip or Content-Encoding: deflate. If both compression and chunked encoding are enabled, then the content stream is first compressed, then chunked; so the chunk encoding itself is not compressed, and the data in each chunk is compressed holistically (i.e. based on the whole content). The remote endpoint then decodes the stream by concatenating the chunks and uncompressing the result. == Example == === Encoded data === The following example contains three chunks of size 4, 7, and 11 (hexadecimal "B") octets of data. 4␍␊Wiki␍␊7␍␊pedia i␍␊B␍␊n ␍␊chunks.␍␊0␍␊␍␊ Below is an annotated version of the encoded data. 4␍␊ (chunk size is four octets) Wiki (four octets of data) ␍␊ (end of chunk) 7␍␊ (chunk size is seven octets) pedia i (seven octets of data) ␍␊ (end of chunk) B␍␊ (chunk size is eleven octets) n ␍␊chunks. (eleven octets of data) ␍␊ (end of chunk) 0␍␊ (chunk size is zero octets, no more chunks) ␍␊ (end of final chunk with zero data octets) Note: Each chunk's size excludes the two ␍␊ bytes that terminate the data of each chunk. === Decoded data === Decoding the above example produces the following octets: Wikipedia in ␍␊chunks. The bytes above are typically displayed as Wikipedia in chunks.

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  • Interplanetary Internet

    Interplanetary Internet

    The interplanetary Internet is a conceived computer network in space, consisting of a set of network nodes that can communicate with each other. These nodes are the planet's orbiters and landers, and the Earth ground stations. For example, the orbiters collect the scientific data from the Curiosity rover on Mars through near-Mars communication links, transmit the data to Earth through direct links from the Mars orbiters to the Earth ground stations via the NASA Deep Space Network, and finally the data routed through Earth's internal internet. Interplanetary communication is greatly delayed by interplanetary distances, as data transmission can only go as fast as the speed of light, so a new set of protocols and technologies that are tolerant to large delays and errors are required. The interplanetary Internet has been envisioned as a store and forward network of internets that is often disconnected, has a wireless backbone fraught with error-prone links and delays ranging from tens of minutes to even hours, even when there is a connection. As of 2024 agencies and companies working towards bringing the network to fruition include NASA, ESA, SpaceX and Blue Origin. == Challenges and reasons == In the core implementation of Interplanetary Internet, satellites orbiting a planet communicate to other planet's satellites. Simultaneously, these planets revolve around the Sun with long distances, and thus many challenges face the communications. The reasons and the resultant challenges are: The motion and long distances between planets: The interplanetary communication is greatly delayed due to the interplanetary distances and the motion of the planets. The delay is variable and long, ranging from a couple of minutes (Earth-to-Mars), to a couple of hours (Pluto-to-Earth), depending on their relative positions. The interplanetary communication also suspends due to the solar conjunction, when the sun's radiation hinders the direct communication between the planets. As such, the communication characterizes lossy links and intermittent link connectivity. Low embeddable payload: Satellites can only carry a small payload, which poses challenges to the power, mass, size, and cost for communication hardware design. An asymmetric bandwidth would be the result of this limitation. This asymmetry reaches ratios up to 1000:1 as downlink:uplink bandwidth portion. Absence of fixed infrastructure: The graph of participating nodes in a specific planet-to-planet communication keeps changing over time, due to the constant motion. The routes of the planet-to-planet communication are planned and scheduled rather than being opportunistic. The Interplanetary Internet design must address these challenges to operate successfully and achieve good communication with other planets. It also must use the few available resources efficiently in the system. == Development == Space communication technology has steadily evolved from expensive, one-of-a-kind point-to-point architectures, to the re-use of technology on successive missions, to the development of standard protocols agreed upon by space agencies of many countries. This last phase has gone on since 1982 through the efforts of the Consultative Committee for Space Data Systems (CCSDS), a body composed of the major space agencies of the world. It has 11 member agencies, 32 observer agencies, and over 119 industrial associates. The evolution of space data system standards has gone on in parallel with the evolution of the Internet, with conceptual cross-pollination where fruitful, but largely as a separate evolution. Since the late 1990s, familiar Internet protocols and CCSDS space link protocols have integrated and converged in several ways; for example, the successful FTP file transfer to Earth-orbiting STRV 1B on January 2, 1996, which ran FTP over the CCSDS IPv4-like Space Communications Protocol Specifications (SCPS) protocols. Internet Protocol use without CCSDS has taken place on spacecraft, e.g., demonstrations on the UoSAT-12 satellite, and operationally on the Disaster Monitoring Constellation. Having reached the era where networking and IP on board spacecraft have been shown to be feasible and reliable, a forward-looking study of the bigger picture was the next phase. The Interplanetary Internet study at NASA's Jet Propulsion Laboratory (JPL) was started by a team of scientists at JPL led by internet pioneer Vinton Cerf and the late Adrian Hooke. Cerf was appointed as a distinguished visiting scientist at JPL in 1998, while Hooke was one of the founders and directors of CCSDS. While IP-like SCPS protocols are feasible for short hops, such as ground station to orbiter, rover to lander, lander to orbiter, probe to flyby, and so on, delay-tolerant networking is needed to get information from one region of the Solar System to another. It becomes apparent that the concept of a region is a natural architectural factoring of the Interplanetary Internet. A region is an area where the characteristics of communication are the same. Region characteristics include communications, security, the maintenance of resources, perhaps ownership, and other factors. The Interplanetary Internet is a "network of regional internets". What is needed then, is a standard way to achieve end-to-end communication through multiple regions in a disconnected, variable-delay environment using a generalized suite of protocols. Examples of regions might include the terrestrial Internet as a region, a region on the surface of the Moon or Mars, or a ground-to-orbit region. The recognition of this requirement led to the concept of a "bundle" as a high-level way to address the generalized Store-and-Forward problem. Bundles are an area of new protocol development in the upper layers of the OSI model, above the Transport Layer with the goal of addressing the issue of bundling store-and-forward information so that it can reliably traverse radically dissimilar environments constituting a "network of regional internets". Delay-tolerant networking (DTN) was designed to enable standardized communications over long distances and through time delays. At its core is the Bundle Protocol (BP), which is similar to the Internet Protocol, or IP, that serves as the heart of the Internet here on Earth. The big difference between the regular Internet Protocol (IP) and the Bundle Protocol is that IP assumes a seamless end-to-end data path, while BP is built to account for errors and disconnections — glitches that commonly plague deep-space communications. Bundle Service Layering, implemented as the Bundling protocol suite for delay-tolerant networking, will provide general-purpose delay-tolerant protocol services in support of a range of applications: custody transfer, segmentation and reassembly, end-to-end reliability, end-to-end security, and end-to-end routing among them. The Bundle Protocol was first tested in space on the UK-DMC satellite in 2008. An example of one of these end-to-end applications flown on a space mission is the CCSDS File Delivery Protocol (CFDP), used on the Deep Impact comet mission. CFDP is an international standard for automatic, reliable file transfer in both directions. CFDP should not be confused with Coherent File Distribution Protocol, which has the same acronym and is an IETF-documented experimental protocol for rapidly deploying files to multiple targets in a highly networked environment. In addition to reliably copying a file from one entity (such as a spacecraft or ground station) to another entity, CFDP has the capability to reliably transmit arbitrarily small messages defined by the user, in the metadata accompanying the file, and to reliably transmit commands relating to file system management that are to be executed automatically on the remote end-point entity (such as a spacecraft) upon successful reception of a file. == Protocol == The Consultative Committee for Space Data Systems (CCSDS) packet telemetry standard defines the protocol used for the transmission of spacecraft instrument data over the deep-space channel. Under this standard, an image or other data sent from a spacecraft instrument is transmitted using one or more packets. === CCSDS packet definition === A packet is a block of data with length that can vary between successive packets, ranging from 7 to 65,542 bytes, including the packet header. Packetized data is transmitted via frames, which are fixed-length data blocks. The size of a frame, including frame header and control information, can range up to 2048 bytes. Packet sizes are fixed during the development phase. Because packet lengths are variable but frame lengths are fixed, packet boundaries usually do not coincide with frame boundaries. === Telecom processing notes === Data in a frame is typically protected from channel errors by error-correcting codes. Even when the channel errors exceed the correction capability of the error-correcting code, the presence of errors is nearly always detected by the e

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  • Social media measurement

    Social media measurement

    Social media measurement, also called social media controlling, is the management practice of evaluating successful social media communications of brands, companies, or other organizations. Key performance indicators may be measured by extracting information from social media channels, such as blogs, wikis, micro-blogs such as Twitter, social networking sites, or video/photo sharing websites, forums from time to time. It is also used by companies to gauge current trends in the industry. The process first gathers data from different websites and then performs analysis based on different metrics like time spent on the page, click through rate, content share, comments, text analytics to identify positive or negative emotions about the brand. Some other social media metrics include share of voice, owned mentions, and earned mentions. The social media measurement process starts with defining a goal that needs to be achieved and defining the expected outcome of the process. The expected outcome varies per the goal and is usually measured by a variety of metrics. This is followed by defining possible social strategies to be used to achieve the goal. Then the next step is designing strategies to be used and setting up configuration tools that ease the process of collecting the data. In the next step, strategies and tools are deployed in real-time. This step involves conducting Quality Assurance tests of the methods deployed to collect the data. And in the final step, data collected from the system is analyzed and if the need arises, it is refined on the run time to enhance the methodologies used. The last step ensures that the result obtained is more aligned with the goal defined in the first step. == Data Acquisition == Acquiring data from social media is in demand of an exploring the user participation and population with the purpose of retrieving and collecting so many kinds of data(ex: comments, downloads etc.). There are several prevalent techniques to acquire data such as Network traffic analysis, Ad-hoc application and Crawling Network Traffic Analysis - Network traffic analysis is the process of capturing network traffic and observing it closely to determine what is happening in the network. It is primarily done to improve the performance, security and other general management of the network. However concerned about the potential tort of privacy on the Internet, network traffic analysis is always restricted by the government. Furthermore, high-speed links are not adaptable to traffic analysis because of the possible overload problem according to the packet sniffing mechanism Ad-hoc Application - Ad-hoc application is a kind of application that provides services and games to social network users by developing the APIs offered by social network companies (Facebook Developer Platform). The infrastructure of Ad-hoc application allows the user to interact with the interface layer instead of the application servers. The API provides a path for application to access information after the user login. Moreover, the size of the data set collected vary with the popularity of the social media platform i.e. social media platforms having high number of users will have more data than platforms having less user base. Scraping is a process in which the APIs collect online data from social media. The data collected from Scraping is in raw format. However, having access to these types of data is a bit difficult because of its commercial value. Crawling - Crawling is a process in which a web crawler creates indexes of all the words in a web-page, stores them, then follows all the hyperlinks and indexes on that page and again stores them. It is the most popular technique for data acquisition and is also well known for its easy operation based on prevalent Object-Orientated Programming Language (Java or Python etc.). And most important, social network companies (YouTube, Flicker, Facebook, Instagram, etc.) are friendly to crawling techniques by providing public APIs == Applications == === For branding === Monitoring social media allows researchers to find insights into a brand's overall visibility on social media, to measure the impact of campaigns, to identify opportunities for engagement, to assess competitor activity and share of voice, and to detect impending crises. It can also provide valuable information about emerging trends and what consumers and clients think about specific topics, brands or products. This is the work of a cross-section of groups that include market researchers, PR staff, marketing teams, social-engagement, and community staff, agencies and sales teams. Several different providers have developed tools to facilitate the monitoring of a variety of social media channels - from blogging to internet video to internet forums. This allows companies to track what consumers say about their brands and actions. Companies can then react to these conversations and interact with consumers through social media platforms. === In government === Apart from commercial applications, social media monitoring has become a pervasive technique applied by public organizations and governments. Monitoring is a tradition within the public sector, and social-media monitoring provides a real-time approach to detecting and responding to social developments. Governments have come to realize the need for strategies to cope with surprises from the rapid expansion of public issues. Sobkowicz introduced a framework with three blocks of social-media opinion tracking, simulating and forecasting. It includes: real-time detection of emotions, topics and opinions information-flow modelling and agent-based simulation modeling of opinion networks Bekkers introduced the application of social media monitoring in the Netherlands. Public organizations in the Netherlands (such as the Tax Agency and the Education Ministry) have started to use social media monitoring to obtain better insights into the sentiments of target groups. On the one hand, the public sector will be enabled to provide timely and efficient answers to the public by using social media monitoring techniques, but on the other hand, they also have to deal with concerns about ethical issues such as transparency and privacy. == Quantifying social media == Social media management software (SMMS) is an application program or software that facilitates an organization's ability to successfully engage in social media across different communication channels. SMMS is used to monitor inbound and outbound conversations, support customer interaction, audit or document social marketing initiatives and evaluate the usefulness of a social media presence. It can be difficult to measure all social media conversations. Due to privacy settings and other issues, not all social media conversations can be found and reported by monitoring tools. However, whilst social media monitoring cannot give absolute figures, it can be extremely useful for identifying trends and for benchmarking, in addition to the uses mentioned above. These findings can, in turn, influence and shape future business decisions. In order to access social media data (posts, Tweets, and meta-data) and to analyze and monitor social media, many companies use software technologies built for business. These range from in-platform analytics dashboards to dedicated third-party platforms, which offer more advanced capabilities including cross-platform audience intelligence, sentiment analysis, and trend detection at scale. == Location-based == Most social media networks allow users to add a location to their posts (reference all of our feeds). The location can be classified as either 'at-the-location' or 'about-the-location'. "'At-the-location' services can be defined as services where location-based content is created at the geographic location. 'About-the-location' services can be defined as services which are referring to a particular location but the content is not necessarily created in this particular physical place." The added information available from geotagged (link to Geotagging article) posts means that they can be displayed on a map. This means that a location can be used as the start of a social media search rather than a keyword or hashtag. This has major implications for disaster relief, event monitoring, safety and security professionals since a large portion of their job is related to tracking and monitoring specific locations. == Technologies used == Various monitoring platforms use different technologies for social media monitoring and measurement. These technology providers may connect to the API provided by social platforms that are created for 3rd party developers to develop their own applications and services that access data. Facebook's Graph API is one such API that social media monitoring solution products would connect to pull data from. Some social media monitoring and analytics companies use calls to data providers each time an end-user d

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  • Tabletopia

    Tabletopia

    Tabletopia is an online portal for users to play and create virtual tabletop games. The platform is developed by Tabletopia Inc and initially was released as a web browser based service after a successful crowdfunding campaign in August 2015. In December 2016 Tabletopia was released on Steam, and later in 2018 became available in AppStore and Google Play. == Gameplay == Tabletopia is a sandbox system for running any game. That means no AI or rules enforcement. Participating players will have to know how to play the game. Nevertheless, the platform has some automated actions available, like card-shuffling and dealing, dice-rolling, magnetic placement of components in special zones, hand management, and some others. Tabletopia also features ready game setups for various player numbers to facilitate gameplay. It also has customisable camera controls which let players save camera positions and switch between them using hot keys. People can use the Game Designer mode to design and create their own board games using the component library. They can then monetise the games with a 70/30 split to the game designer. == Development == Tabletopia was created in early 2014, by Tim Bokarev and his partners Artem Zinoviev and Dmitry Sergeev. These co-founders already had experience in the video and board games industry. Their other projects include Promo Interactive, an internet advertising agency, Playtox, a mobile MMORPG, Igrology, a game studio, and Tesera.ru, the main Russian-speaking board gaming portal. By Spring 2014, Artem, Dmitry and Tim created Tabletopia Inc. USA and started development. Tabletopia is a multinational crew that includes professionals from USA, Ukraine, Australia, Ireland, and Germany. The Kickstarter campaign in August 2015 earned $133,721 by 2,545 backers. Tabletopia received Green Light on Steam in September 2015 and was released on Steam in March 2016. The platform remained in Early Access until December 2016, when it was officially released on Steam and on the web. In February 2018 it was released as a stand-alone app for iOS tablets, and in September 2018 for Android tablets.

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  • Social commerce

    Social commerce

    Social commerce is a subset of electronic commerce that involves social media and online media that supports social interaction, and user contributions to assist online buying and selling of products and services. More succinctly, social commerce is the use of social network(s), and user-generated content in the context of e-commerce transactions. The term social commerce was introduced by Yahoo! in November 2005 which describes a set of online collaborative shopping tools such as shared pick lists, user ratings and other user-generated content of online product information and advice. The concept of social commerce was developed by David Beisel to denote user-generated advertorial content on e-commerce sites, and by Steve Rubel to include collaborative e-commerce tools that enable shoppers "to get advice from trusted individuals, find goods and services and then purchase them". The social networks that spread this advice have been found to increase the customer's trust in one retailer over another. Social commerce may assist companies in achieving the following purposes: Firstly, social commerce helps companies engage customers with their brands according to the customers' social behaviors. Secondly, it provides an incentive for customers to return to their website. Thirdly, it provides customers with a platform to talk about their brand on their website. Fourthly, it provides all the information customers need to research, compare, and ultimately choose you over your competitor, thus purchasing from you and not others. In these days, the range of social commerce has been expanded to include social media tools and content used in the context of e-commerce, especially in the fashion industry. Examples of social commerce include customer ratings and reviews, user recommendations and referrals, social shopping tools (sharing the act of shopping online), forums and communities, social media optimization, social applications and social advertising. Technologies such as augmented reality have also been integrated with social commerce, allowing shoppers to visualize apparel items on themselves and solicit feedback through social media tools. Some academics have sought to distinguish "social commerce" from "social shopping", with the former being referred to as collaborative networks of online vendors; the latter, the collaborative activity of online shoppers. == Timeline == 2005: The term "social commerce" was first introduced on Yahoo! in 2005. 2021: The Global Web Index associated one's use of social media to his/her eagerness to buy. Social media with its entertaining and inspirational content can increase a product's profitability. This explains why Instagram expanded its Checkout feature to similar content like IG Stories, IGTV, and Reels. == Elements == The attraction and effectiveness of Social Commerce can be understood in terms of Robert Cialdini's Principles of InfluenceInfluence: Science and Practice": Reciprocity – When a company gives a person something for free, that person will feel the need to return the favor, whether by buying again or giving good recommendations for the company. Community – When people find an individual or a group that shares the same values, likes, beliefs, etc., they find community. People are more committed to a community that they feel accepted within. When this commitment happens, they tend to follow the same trends as a group and when one member introduces a new idea or product, it is accepted more readily based on the previous trust that has been established. It would be beneficial for companies to develop partnerships with social media sites to engage social communities with their products. Social proof – To receive positive feedback, a company needs to be willing to accept social feedback and to show proof that other people are buying, and like, the same things that I like. This can be seen in a lot of online companies such as eBay and Amazon, that allow public feedback of products and when a purchase is made, they immediately generate a list showing purchases that other people have made in relation to my recent purchase. It is beneficial to encourage open recommendation and feedback. This creates trust for you as a seller. 55% of buyers turn to social media when they're looking for information. Authority – Many people need proof that a product is of good quality. This proof can be based on the recommendations of others who have bought the same product. If there are many user reviews about a product, then a consumer will be more willing to trust their own decision to buy this item. Liking – People trust based on the recommendations of others. If there are a lot of "likes" of a particular product, then the consumer will feel more confident and justified in making this purchase. Scarcity – As part of supply and demand, a greater value is assigned to products that are regarded as either being in high demand or are seen as being in a shortage. Therefore, if a person is convinced that they are purchasing something that is unique, special, or not easy to acquire, they will have more of a willingness to make a purchase. If there is trust established from the seller, they will want to buy these items immediately. This can be seen in the cases of Zara and Apple Inc. who create demand for their products by convincing the public that there is a possibility of missing out on being able to purchase them. == Types == === Onsite === Onsite social commerce refers to retailers including social sharing and other social functionality on their website. Some notable examples include Zazzle which enables users to share their purchases, Macy's which allows users to create a poll to find the right product, and Fab.com which shows a live feed of what other shoppers are buying. Onsite user reviews are also considered a part of social commerce. This approach has been successful in improving customer engagement, conversion and word-of-mouth branding according to several industry sources. === Offsite === Offsite social commerce includes activities that happen outside of the retailers' website. This may include posting products on social networks such as Facebook, X, and TikTok. It may also include advertising on shopping forums such as SlickDeals, Red Flag Deals, and LatestDeals.co.uk. == Measurements == Social commerce can be measured by any of the principle ways to measure social media. Return on Investment: measures the effect or action of social media on sales. Reputation: indices measure the influence of social media investment in terms of changes to online reputation – made up of the volume and valence of social media mentions. Reach: metrics use traditional media advertising metrics to measure the exposure rates and levels of an audience with social media. == Business applications == This category is based on individuals' shopping, selling, recommending behaviors. Social network-driven sales (Soldsie) – Facebook commerce and Twitter commerce belong to this part. Sales take place on established social network sites. Peer-to-peer sales platforms (eBay, Etsy, Amazon) – In these websites, users can directly communicate and sell products to other users. Group buying (Groupon, LivingSocial) – Users can buy products or services at a lower price when enough users agree to make this purchase. Peer recommendations and reviews (Amazon, Yelp, Bazaarvoice) – Users can see recommendations and reviews from other users. User-curated shopping (The Fancy, Lyst) – Users create and share lists of products and services for others to shop from. Participatory commerce (Betabrand, Threadless, Kickstarter) – Users can get involved in the production process. Social shopping (Squadded) – Allowing e-commerce to provide their users live chat sessions and shared shopping lists so they can communicate with their friends or other shoppers for advice. == Business examples == Here are some notable business examples of Social Commerce: Betabrand: an online brand using participatory design to release new, community-created ideas every week. Cafepress: an online retailer of stock and user-customized on demand products. Etsy: an e-commerce website focused on handmade or vintage items and supplies, as well as unique factory-manufactured items under Etsy's new guidelines. Eventbrite: an online ticketing service that allows event organizers to plan, set up ticket sales and promote events (event management) and publish them across Facebook, Twitter and other social-networking tools directly from the site's interface. Groupon: a deal-of-the-day website that features discounted gift certificates usable at local or national companies. Houzz: a web site and online community about architecture, interior design and decorating, landscape design and home improvement. LivingSocial: an online marketplace that allows clients to buy and share things to do in their city. Lockerz: an international social commerce website based in Seattle, Washington. OpenSky: is a r

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  • Symmetric Boolean function

    Symmetric Boolean function

    In mathematics, a symmetric Boolean function is a Boolean function whose value does not depend on the order of its input bits, i.e., it depends only on the number of ones (or zeros) in the input. For this reason they are also known as Boolean counting functions. There are 2n+1 symmetric n-ary Boolean functions. Instead of the truth table, traditionally used to represent Boolean functions, one may use a more compact representation for an n-variable symmetric Boolean function: the (n + 1)-vector, whose i-th entry (i = 0, ..., n) is the value of the function on an input vector with i ones. Mathematically, the symmetric Boolean functions correspond one-to-one with the functions that map n+1 elements to two elements, f : { 0 , 1 , . . . , n } → { 0 , 1 } {\displaystyle f:\{0,1,...,n\}\rightarrow \{0,1\}} . Symmetric Boolean functions are used to classify Boolean satisfiability problems. == Special cases == A number of special cases are recognized: Majority function: their value is 1 on input vectors with more than n/2 ones Threshold functions: their value is 1 on input vectors with k or more ones for a fixed k All-equal and not-all-equal function: their values is 1 when the inputs do (not) all have the same value Exact-count functions: their value is 1 on input vectors with k ones for a fixed k One-hot or 1-in-n function: their value is 1 on input vectors with exactly one one One-cold function: their value is 1 on input vectors with exactly one zero Congruence functions: their value is 1 on input vectors with the number of ones congruent to k mod m for fixed k, m Parity function: their value is 1 if the input vector has odd number of ones The n-ary versions of AND, OR, XOR, NAND, NOR and XNOR are also symmetric Boolean functions. == Properties == In the following, f k {\displaystyle f_{k}} denotes the value of the function f : { 0 , 1 } n → { 0 , 1 } {\displaystyle f:\{0,1\}^{n}\rightarrow \{0,1\}} when applied to an input vector of weight k {\displaystyle k} . === Weight === The weight of the function can be calculated from its value vector: | f | = ∑ k = 0 n ( n k ) f k {\displaystyle |f|=\sum _{k=0}^{n}{\binom {n}{k}}f_{k}} === Algebraic normal form === The algebraic normal form either contains all monomials of certain order m {\displaystyle m} , or none of them; i.e. the Möbius transform f ^ {\displaystyle {\hat {f}}} of the function is also a symmetric function. It can thus also be described by a simple (n+1) bit vector, the ANF vector f ^ m {\displaystyle {\hat {f}}_{m}} . The ANF and value vectors are related by a Möbius relation: f ^ m = ⨁ k 2 ⊆ m 2 f k {\displaystyle {\hat {f}}_{m}=\bigoplus _{k_{2}\subseteq m_{2}}f_{k}} where k 2 ⊆ m 2 {\displaystyle k_{2}\subseteq m_{2}} denotes all the weights k whose base-2 representation is covered by the base-2 representation of m (a consequence of Lucas’ theorem). Effectively, an n-variable symmetric Boolean function corresponds to a log(n)-variable ordinary Boolean function acting on the base-2 representation of the input weight. For example, for three-variable functions: f ^ 0 = f 0 f ^ 1 = f 0 ⊕ f 1 f ^ 2 = f 0 ⊕ f 2 f ^ 3 = f 0 ⊕ f 1 ⊕ f 2 ⊕ f 3 {\displaystyle {\begin{array}{lcl}{\hat {f}}_{0}&=&f_{0}\\{\hat {f}}_{1}&=&f_{0}\oplus f_{1}\\{\hat {f}}_{2}&=&f_{0}\oplus f_{2}\\{\hat {f}}_{3}&=&f_{0}\oplus f_{1}\oplus f_{2}\oplus f_{3}\end{array}}} So the three variable majority function with value vector (0, 0, 1, 1) has ANF vector (0, 0, 1, 0), i.e.: Maj ( x , y , z ) = x y ⊕ x z ⊕ y z {\displaystyle {\text{Maj}}(x,y,z)=xy\oplus xz\oplus yz} === Unit hypercube polynomial === The coefficients of the real polynomial agreeing with the function on { 0 , 1 } n {\displaystyle \{0,1\}^{n}} are given by: f m ∗ = ∑ k = 0 m ( − 1 ) | k | + | m | ( m k ) f k {\displaystyle f_{m}^{}=\sum _{k=0}^{m}(-1)^{|k|+|m|}{\binom {m}{k}}f_{k}} For example, the three variable majority function polynomial has coefficients (0, 0, 1, -2): Maj ( x , y , z ) = ( x y + x z + y z ) − 2 ( x y z ) {\displaystyle {\text{Maj}}(x,y,z)=(xy+xz+yz)-2(xyz)} == Examples ==

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