Manufacture Modules Technologies Sarl (MMT) is a Swiss company established in Geneva in 2015 which originally specialised in the development and commercialization of "Horological Smartwatch modules", firmware, apps and cloud. Located at Geneva's Skylab high-tech hub, it expanded into the development and manufacturing of "E-Straps" operated with a mobile application. Philippe Fraboulet is the CEO. == History == In June 2015, Fullpower Technologies and Union Horlogère Suisse (Swiss Watchmakers Corporation) formed MMT as a joint venture, which then launched the MotionX Horological Smartwatch Open Platform for the Swiss watch industry. The initial licensees were Frederique Constant, Alpina and Mondaine, brands owned by Union Horlogère Suisse. Fullpower created and managed the circuit design, firmware, smartphone applications (including sleep activity), as well as the cloud Infrastructure. MMT managed the Swiss watch movement development and production as well as licensing and support. In July 2016, Union Horlogere Holding and MMT were spun-out of the Frédérique Constant Group. Fullpower Technologies' 19.99% share was acquired by Union Horlogere Holding BV, giving it 100% of MMT's shares. == Business == The company offers firmware, a cloud, manufacturing, service and over-the-air facilities for upgrades. The company also offers its own apps, which bear the label “Swiss Made software”.
Zoho Office Suite
Zoho Office Suite is an online office suite developed by Zoho Corporation. == History == Zoho Office Suite was launched in 2005 with a web-based word processor. Additional products, such as those for spreadsheets and presentations, were incorporated later into the suite. The applications are distributed as software as a service (SaaS). == Products == Zoho uses an open API for its Writer, Sheet, Show, Creator, Meeting, and Planner products. It also has plugins into Microsoft Word and Excel, an OpenOffice.org plugin, and a plugin for Firefox. Zoho Office Suite is free for individuals but offers a plan for teams, which includes Zoho WorkDrive, Zoho Workplace and other Zoho apps. In October 2009, Zoho integrated some of their applications with the Google Apps online suite.
Artificial intelligence in marketing
Artificial intelligence marketing (AI marketing) is a form of marketing that uses artificial intelligence concepts and models such as machine learning, natural language processing, and computer vision to achieve marketing goals. The main difference between AI marketing and traditional forms of marketing reside in the reasoning, which is performed through a computer algorithm rather than a human. Each form of marketing has a different technique to the core of the marketing theory. Traditional marketing directly focuses on the needs of consumers; meanwhile some believe the shift AI may cause will lead marketing agencies to manage consumer needs instead. AI is used in various digital marketing spaces, such as content marketing, email marketing, online advertisement (in combination with machine learning), social media marketing, affiliate marketing, and beyond. == Historical development == AI in marketing has a long history, which goes all the way back to the 1980s. At this time, AI research was focusing on expert systems and robotics. Despite the initial research and the studies that were carried out, AI adoption remained limited. Research on it came to a stop for a while, until research was revived two decades later with the advancement in technology, the rise of big data, and a significant increase in computational power. Eventually, AI became very popular in the marketing world, and caught the eyes of many researchers as well as professionals. A large‐scale bibliometric study covering 1,580 peer‑reviewed papers published between 1982 and 2020 confirms that scholarly output on AI in marketing has surged since 2017, with Expert Systems with Applications emerging as the most prolific outlet. Prior to the application of artificial Intelligence in marketing, there was something called "collaborative filtering". This was used as early as 1998 by Amazon, and one of the first ways companies predicted consumer behavior, which enabled millions of recommendations to different customers. Personalized recommender systems are now widely used, for example to suggest music on Spotify, or TV shows on Netflix. A big milestone in AI marketing happened in 2014, when programmatic ad buying gained much greater popularity. Marketing consists of numerous manual tasks such as researching target markets, insertion orders, and managing high budgets as well as prices. In order to cut costs, and remove the need for these tedious tasks, many companies started to automate the marketing process with AI. In 2015, Google introduced RankBrain, a machine learning component of its search algorithm designed to interpret the intent behind user queries. RankBrain was followed by further AI-based search updates, including BERT in 2019, which improved the understanding of conversational queries, and the Multitask Unified Model (MUM) in 2021, which is multimodal and processes information across 75 languages. These advances shifted search engine optimization practice away from keyword matching toward content that satisfies user intent. Artificial intelligence is increasingly used in marketing to personalize user experiences and automate decision-making. For example, Netflix uses AI algorithms to recommend content based on viewing history, while Sephora employs chatbots to assist customers with product selection and availability. Programmatic advertising platforms like Google Ads leverage machine learning to optimize bidding strategies and target audiences more effectively. These applications demonstrate how AI enhances efficiency, engagement, and conversion rates across digital channels. === Artificial neural networks === An artificial neural network is a form of computer program modeled on the brain and nervous system of humans. Neural networks are composed of a series of interconnected processing neurons that function in unison to achieve certain outcomes. Using “human-like trial and error learning methods neural networks detect patterns existing within a data set ignoring data that is not significant while emphasizing the data which is most influential”. From a marketing perspective, neural networks are a form of software tool used to assist in decision making. Neural networks are effective in gathering and extracting information from large data sources and have the ability to identify cause and effect within tha data. These neural nets through the process of learning, identify relationships and connections between databases. Once knowledge has been accumulated, neural networks can be relied on to provide generalizations and can apply past knowledge and learning to a variety of situations. Neural networks help fulfill the role of marketing companies through effectively aiding in market segmentation and measurement of performance while reducing costs and improving accuracy. Due to their learning ability, flexibility, adaption, and knowledge discovery, neural networks offer many advantages over traditional models. Neural networks can be used to assist in pattern classification, forecasting and marketing analysis. == Tools and uses == Classification of customers can be facilitated through the neural network approach allowing companies to make informed marketing decisions. An example of this was employed by Spiegel Inc., a firm dealing in direct-mail operations that used neural networks to improve efficiencies. Using software developed by NeuralWare Inc., Spiegel identified the demographics of customers who had made a single purchase and those customers who had made repeat purchases. Neural networks where then able to identify the key patterns and consequently identify the customers that were most likely to repeat purchase. Understanding this information allowed Spiegel to streamline marketing efforts, and reduced costs. Sales forecasting “is the process of estimating future events with the goal of providing benchmarks for monitoring actual performance and reducing uncertainty". Artificial intelligence techniques have emerged to facilitate the process of forecasting through increasing accuracy in the areas of demand for products, distribution, employee turnover, performance measurement, and inventory control. An example of forecasting using neural networks is the Airline Marketing Assistant/Tactician; an application developed by BehabHeuristics which allows for the forecasting of passenger demand and consequent seat allocation through neural networks. This system has been used by National air Canada and USAir. Neural networks provide a useful alternative to traditional statistical models due to their reliability, time-saving characteristics and ability to recognize patterns from incomplete or noisy data. Examples of marketing analysis systems includes the Target Marketing System developed by Churchull Systems for Veratex Corporation. This support system scans a market database to identify dormant customers allowing management to make decisions regarding which key customers to target. When performing marketing analysis, neural networks can assist in the gathering and processing of information ranging from consumer demographics and credit history to the purchase patterns of consumers. Predictive analytics is a form of analytics involving the use of historical data and artificial intelligence algorithms to predict future trends and outcomes. It serves as a tool for anticipating and understanding user behavior based on patterns found in data. Predictive analytics uses artificial intelligence machine learning algorithms to recognize and predict patterns within data. Machine learning algorithms analyze the data, recognize patterns, and make predictions through continuous learning and adaptation. Predictive analytics is widely used across businesses and industries as a way to identify opportunities, avoid risks, and anticipate customer needs based on information derived from the analysis of user data. By analyzing historical customer data, artificial intelligence algorithms can deliver relevant and targeted marketing content. Recent systematic reviews show that generative large‑language models such as GPT‑3 and GPT‑4 are now routinely embedded in predictive‑analytics pipelines to mine unstructured market data and anticipate customer intent with greater precision. Personalization engines use artificial intelligence and machine learning to provide content or advertisements that are relevant to the user. User data is gathered, which then gets processed with machine learning, and patterns and trends among the users are identified. Users with shared characteristics or behaviors are then segmented into groups, and the personalization engine adjusts content and advertisements to match each segment's preferences. By processing a large amount of data, personalization engines are able to match users to advertisements and recommendations that align with their interests or preferences. Field evidence from consumer‑goods and electronics firms indicates that AI‑driven personalization can raise
Wearable computer
A wearable computer, also known as a body-borne computer or wearable, is a computing device worn on the body. The definition of 'wearable computer' may be narrow or broad, extending to smartphones or even ordinary wristwatches. Wearables may be for general use, in which case they are just a particularly small example of mobile computing. Alternatively, they may be for specialized purposes such as fitness trackers. They may incorporate special sensors such as accelerometers, heart rate monitors, or on the more advanced side, electrocardiogram (ECG) and blood oxygen saturation (SpO2) monitors. Under the definition of wearable computers, we also include novel user interfaces such as Google Glass, an optical head-mounted display controlled by gestures. It may be that specialized wearables will evolve into general all-in-one devices, as happened with the convergence of PDAs and mobile phones into smartphones. Wearables are typically worn on the wrist (e.g. fitness trackers), hung from the neck (like a necklace), strapped to the arm or leg (electronic tagging), or on the head (as glasses or a helmet), though some have been located elsewhere (e.g. on a finger or in a shoe). Devices carried in a pocket or bag – such as smartphones and before them, pocket calculators and PDAs, may or may not be regarded as 'worn'. Wearable computers have various technical issues common to other mobile computing, such as batteries, heat dissipation, software architectures, wireless and personal area networks, and data management. Many wearable computers are active all the time, e.g. processing or recording data continuously. == Applications == Wearable computers are not only limited to computers such as fitness trackers that are worn on wrists; they also include wearables such as heart pacemakers and other prosthetics. They are used most often in research that focuses on behavioral modeling, health monitoring systems, IT and media development, where the person wearing the computer actually moves or is otherwise engaged with his or her surroundings. Wearable computers have been used for the following: general-purpose computing (e.g. smartphones and smartwatches) sensory integration, e.g. to help people see better or understand the world better (whether in task-specific applications like camera-based welding helmets or for everyday use like Google Glass) behavioral modeling health care monitoring systems service management electronic textiles and fashion design, e.g. Microsoft's 2011 prototype "The Printing Dress". Wearable computing is the subject of active research, especially the form-factor and location on the body, with areas of study including user interface design, augmented reality, and pattern recognition. The use of wearables for specific applications, for compensating disabilities or supporting elderly people steadily increases. == Operating systems == The dominant operating systems for wearable computing are: FreeRTOS is a real-time operating system kernel for embedded devices; most of the Smartbands that are currently available in the market are based on FreeRTOS, which include Huawei, Honor, Lenovo, realme, TCL and Xiaomi smartbands. LiteOS is a lightweight open source real-time operating system that is part of Huawei's "1+8+N" Internet of Things solution. Tizen OS from Samsung (there was an announcement in May 2021 that Wear OS and Tizen OS will merge and will be called simply Wear.) watchOS watchOS is a proprietary mobile operating system developed by Apple Inc. to run on the Apple Watch. Wear OS Wear OS (previously known as Android Wear) is a smartwatch operating system developed by Google Inc. == History == Due to the varied definitions of wearable and computer, the first wearable computer could be as early as the first abacus on a necklace, a 16th-century abacus ring, a wristwatch and 'finger-watch' owned by Queen Elizabeth I of England, or the covert timing devices hidden in shoes to cheat at roulette by Thorp and Shannon in the 1960s and 1970s. However, a general-purpose computer is not merely a time-keeping or calculating device, but rather a user-programmable item for arbitrary complex algorithms, interfacing, and data management. By this definition, the wearable computer was invented by Steve Mann, in the late 1970s: Steve Mann, a professor at the University of Toronto, was hailed as the father of the wearable computer and the ISSCC's first virtual panelist, by moderator Woodward Yang of Harvard University (Cambridge Mass.). The development of wearable items has taken several steps of miniaturization from discrete electronics over hybrid designs to fully integrated designs, where just one processor chip, a battery, and some interface conditioning items make the whole unit. === 1500s === Queen Elizabeth I of England received a watch from Robert Dudley in 1571, as a New Year's present; it may have been worn on the forearm rather than the wrist. She also possessed a 'finger-watch' set in a ring, with an alarm that prodded her finger. === 1600s === The Qing dynasty saw the introduction of a fully functional abacus on a ring, which could be used while it was being worn. === 1960s === In 1961, mathematicians Edward O. Thorp and Claude Shannon built some computerized timing devices to help them win a game of roulette. One such timer was concealed in a shoe and another in a pack of cigarettes. Various versions of this apparatus were built in the 1960s and 1970s. Thorp refers to himself as the inventor of the first "wearable computer". In other variations, the system was a concealed cigarette-pack-sized analog computer designed to predict the motion of roulette wheels. A data-taker would use microswitches hidden in his shoes to indicate the speed of the roulette wheel, and the computer would indicate an octant of the roulette wheel to bet on by sending musical tones via radio to a miniature speaker hidden in a collaborator's ear canal. The system was successfully tested in Las Vegas in June 1961, but hardware issues with the speaker wires prevented it from being used beyond test runs. This was not a wearable computer because it could not be re-purposed during use; rather it was an example of task-specific hardware. This work was kept secret until it was first mentioned in Thorp's book Beat the Dealer (revised ed.) in 1966 and later published in detail in 1969. === 1970s === Pocket calculators became mass-market devices in 1970, starting in Japan. Programmable calculators followed in the late 1970s, being somewhat more general-purpose computers. The HP-01 algebraic calculator watch by Hewlett-Packard was released in 1977. A camera-to-tactile vest for the blind, launched by C.C. Collins in 1977, converted images into a 1024-point, ten-inch square tactile grid on a vest. === 1980s === The 1980s saw the rise of more general-purpose wearable computers. In 1981, Steve Mann designed and built a backpack-mounted 6502-based wearable multimedia computer with text, graphics, and multimedia capability, as well as video capability (cameras and other photographic systems). Mann went on to be an early and active researcher in the wearables field, especially known for his 1994 creation of the Wearable Wireless Webcam, the first example of lifelogging. Seiko Epson released the RC-20 Wrist Computer in 1984. It was an early smartwatch, powered by a computer on a chip. In 1989, Reflection Technology marketed the Private Eye head-mounted display, which scans a vertical array of LEDs across the visual field using a vibrating mirror. This display gave rise to several hobbyist and research wearables, including Gerald "Chip" Maguire's IBM/Columbia University Student Electronic Notebook, Doug Platt's Hip-PC, and Carnegie Mellon University's VuMan 1 in 1991. The Student Electronic Notebook consisted of the Private Eye, Toshiba diskless AIX notebook computers (prototypes), a stylus based input system and a virtual keyboard. It used direct-sequence spread spectrum radio links to provide all the usual TCP/IP based services, including NFS mounted file systems and X11, which all ran in the Andrew Project environment. The Hip-PC included an Agenda palmtop used as a chording keyboard attached to the belt and a 1.44 megabyte floppy drive. Later versions incorporated additional equipment from Park Engineering. The system debuted at "The Lap and Palmtop Expo" on 16 April 1991. VuMan 1 was developed as part of a Summer-term course at Carnegie Mellon's Engineering Design Research Center, and was intended for viewing house blueprints. Input was through a three-button unit worn on the belt, and output was through Reflection Tech's Private Eye. The CPU was an 8 MHz 80188 processor with 0.5 MB ROM. === 1990s === In the 1990s PDAs became widely used, and in 1999 were combined with mobile phones in Japan to produce the first mass-market smartphone. In 1993, the Private Eye was used in Thad Starner's wearable, based on Doug Platt's system and built from a kit from Park Enterprises, a Pri
Personal, Inc.
Personal (also referred to as Personal.com or Personal, Inc.) was a consumer personal data service and identity management system for individuals to aggregate, manage and reuse their own data. It merged with digi.me in August 2017, a business in Europe that has the same business model. The combined company is called digi.me. One of its product lines, a collaborative data management and information security solution for the workplace called TeamData, was spun off as a new company as a result of the merger. == History == Personal was founded in 2009 in Washington, DC by the management team that built The Map Network, a location data and mapping platform that was acquired by Nokia/NAVTEQ in 2006. Personal was the first online consumer-facing company to be named an Ambassador for Privacy by Design for its technical, business and legal commitments to providing users with control over the data they store in Personal's service. Called a “life management platform” by The Economist and a “personal encrypted cloud service” by TIME for its user-centric approach to data, the company has been associated with both the Infomediary model originated in 1999 by John Hagel III and Mark Singer, as well as the vendor relationship management (VRM) model developed by Doc Searls. Personal raised $30m in funding to develop its platform and products from such leading investors as Steve Case's Revolution Ventures, Grotech Ventures, Allen & Company, Ted Leonsis, Neil Ashe, Jonathan Miller, Bill Miller of Legg Mason, Esther Dyson of EDventures, and Eric C. Anderson. The company received recognition for its user agreement, called the Owner Data Agreement, which acted like a reverse license agreement when data was shared between registered parties and emphasized that data ownership resides with the user. Doc Searls wrote in The Intention Economy: When Customers Take Charge that the Owner Data Agreement “had no precedent and modeled a new legal position, both for vendors and for intermediaries.” Personal was early to embrace “small data,” which it defines as “big data for the benefit of individuals.” The term “small data” may have been originally coined by Jeremie Miller of Sing.ly, who mentioned it in a talk at the Web 2.0 Summit in November 2011 and is cited in The Intention Economy. In 2011, Personal was a part of the first group of companies to join the Personal Data Ecosystem Consortium's Startup Circle. A Small Data Meetup group has also formed in New York City, bringing together technology, legal and business experts to exchange ideas about user-centric and user-driven models for internet products and services. Personal has been included in case studies by Ctrl-Shift and Forrester regarding Personal Data Stores and Personal Identity Management. In 2011, Personal received the Innovator Spotlight Award at Privacy Identity Innovation Conference (pii2011) and participated in the Technology Showcase at pii2012. In 2012, TechHive named Personal as one of the top five apps or web services of SXSW. Personal won the 2013 Campus Technology Innovators Award with Lone Star College in July 2013. Personal was included in a list of Executive Travel Magazine's favorite travel apps for 2013 in its May/June issue. In 2013, Personal was also included as part of NYU GovLab's Open Data 500 and was named by J. Walter Thompson as one of 100 things to watch for in 2014. In 2015, the National Law Journal named Company Chief Policy Officer and General Counsel, Joshua P. Galper, as one of their 50 "Cybersecurity & Privacy Trailblazers." == Products and services == === Overview === The Personal Platform was a privacy- and security-by-design platform for individuals to manage and reuse their own data and information. The Fill It app was a 1-click form-filling solution for web and mobile logins, checkouts and forms, and the Data Vault app served as the main cloud-based repository for a user's data. Personal helped individuals take control and benefit from their information while knowing that the information in their Data Vault remained legally theirs and could not be used without their permission. === Data Vault with Cloud Sync === Personal spent two years building the Personal Platform before launching its Data Vault product in beta in November 2011. Following Privacy by Design principles, Personal only enabled users to see or share the sensitive data and all the files they stored in their Data Vault. Such information was encrypted, and could only be decrypted with a user's password. Only users could choose and know their passwords to their vault because Personal did not store user passwords – and therefore could not reset them without deleting a user's sensitive data and all files stored in their vault. All Personal apps and services were linked to a user's private Data Vault. The Data Vault featured automatic synchronization of data and files added on any device logged into Personal. It also featured a “Secure Share” function that created a live, private network, allowing registered users to share access to data and files through an exchange of encrypted keys without the risk of transmitting the data or files through non-secure, direct means. It also allowed users to immediately update data across their own network and revoke access to it when they choose. Fast Company called the Data Vault “a tool that will simplify our lives.” Personal launched its Android app on November 30, 2011. The iOS Data Vault app was released on May 7, 2012. Personal officially launched its application programming interface (APIs) on October 2, 2012 at the Mashery Business of APIs Conference. A review by CNET highlighted the challenges of getting people to trust such a new service with their sensitive data and spending the time required entering enough data to make it useful. === Fill It App and Form Index === When the Data Vault was launched in November 2011, Mashable posed the question: “Never Fill Out a Form Again?” The World Economic Forum in its February 2013 report highlighted the possibility of saving 10 billion hours globally “and improv[ing] the delivery of public and private sector services” through automated form-filling tools, specifically citing Personal's Fill It app. In January 2013, Personal launched Fill It in beta as a web bookmarklet for automatic form-filling. On June 11, 2014, Personal released Fill It as a web extension and announced that it was publishing an index of over 140,000 1-click online forms at www.fillit.com. The company also announced that a mobile version of the product will launch later in the year. According to a story in Tech Cocktail about the launch, Personal's “web extension and mobile app are able to support over 1,200 different types of reusable data, even enabling them to unlock more confidential information so they can complete longer forms, including patient registrations, job applications, event registrations, school admissions, insurance and bank applications, and government forms.” In November 2014, a mobile version of Fill It was launched that could autofill mobile forms using APIs. Personal's form portal ultimately indexed more than 500,000 forms with three components, which, together, allowed data to be captured and reused across any of the forms: (1) a form graph, which mapped individual form fields to the Personal ontology; (2) a semantic layer, which determined how data was required on a form (e.g. one field vs. three fields for a U.S. telephone number); and (3) a correlations graph, which helped individuals match their specific data to a form without looking at the data value (e.g. knowing which phone number is a mobile phone number, which address is a billing address, or that a person uses their middle name as a first name on most forms). === Monetizing personal data === With the initial public offering of Facebook in May 2012, there was media interest in the question of the monetary value of personal data and whether tools and services might emerge to help consumers monetize their own data. Personal was frequently cited as a company that could potentially offer such a service. Articles and pieces focusing on this subject have appeared in The New York Times, AdWeek, the MIT Technology Review, and on CNN and National Public Radio. Company Co-founder and CEO Shane Green was quoted as saying that “the average American consumer would soon be able to realize over $1,000 per year” by granting limited, anonymous access to their data to marketers, but that figure was never supported by Green or the company. === Launch of TeamData === In May 2016, Personal shifted its product focus to TeamData, which focuses on the problem of securing and collaboratively managing data in the workplace. It is now a separate business.
Graphical Kernel System
The Graphical Kernel System (GKS) is a 2D computer graphics system using vector graphics, introduced in 1977. It was suitable for making line and bar charts and similar tasks. A key concept was cross-system portability, based on an underlying coordinate system that could be represented on almost any hardware. GKS is best known as the basis for the graphics in the GEM GUI system used on the Atari ST and as part of Ventura Publisher. A draft international standard was circulated for review in September 1983. Final ratification of the standard was achieved in 1985, making it the first ISO graphics standard. A 3D system modelled on GKS was introduced as PHIGS, which saw some use in the 1980s and early 1990s. == Overview == GKS provides a set of drawing features for two-dimensional vector graphics suitable for charting and similar duties. The calls are designed to be portable across different programming languages, graphics devices and hardware, so that applications written to use GKS will be readily portable to many platforms and devices. GKS was fairly common on computer workstations in the 1980s and early 1990s. GKS formed the basis of Digital Research's GSX which evolved into VDI, one of the core components of GEM. GEM was the native GUI on the Atari ST and was occasionally seen on PCs, particularly in conjunction with Ventura Publisher. GKS was little used commercially outside these markets, but remains in use in some scientific visualization packages. It is also the underlying API defining the Computer Graphics Metafile. One popular application based on an implementation of GKS is the GR Framework, a C library for high-performance scientific visualization that has become a common plotting backend among Julia users. A main developer and promoter of the GKS was José Luis Encarnação, formerly director of the Fraunhofer Institute for Computer Graphics (IGD) in Darmstadt, Germany. GKS has been standardized in the following documents: ANSI standard ANSI X3.124 of 1985. ISO 7942:1985 standard, revised as ISO 7942:1985/Amd 1:1991 and ISO/IEC 7942-1:1994, as well as ISO/IEC 7942-2:1997, ISO/IEC 7942-3:1999 and ISO/IEC 7942-4:1998 The language bindings are ISO standard ISO 8651. GKS-3D (Graphical Kernel System for Three Dimensions) functional definition is ISO standard ISO 8805, and the corresponding C bindings are ISO/IEC 8806. The functionality of GKS is wrapped up as a data model standard in the STEP standard, section ISO 10303-46.
Collective operation
Collective operations are building blocks for interaction patterns, that are often used in SPMD algorithms in the parallel programming context. Hence, there is an interest in efficient realizations of these operations. A realization of the collective operations is provided by the Message Passing Interface (MPI). == Definitions == In all asymptotic runtime functions, we denote the latency α {\displaystyle \alpha } (or startup time per message, independent of message size), the communication cost per word β {\displaystyle \beta } , the number of processing units p {\displaystyle p} and the input size per node n {\displaystyle n} . In cases where we have initial messages on more than one node we assume that all local messages are of the same size. To address individual processing units we use p i ∈ { p 0 , p 1 , … , p p − 1 } {\displaystyle p_{i}\in \{p_{0},p_{1},\dots ,p_{p-1}\}} . If we do not have an equal distribution, i.e. node p i {\displaystyle p_{i}} has a message of size n i {\displaystyle n_{i}} , we get an upper bound for the runtime by setting n = max ( n 0 , n 1 , … , n p − 1 ) {\displaystyle n=\max(n_{0},n_{1},\dots ,n_{p-1})} . A distributed memory model is assumed. The concepts are similar for the shared memory model. However, shared memory systems can provide hardware support for some operations like broadcast (§ Broadcast) for example, which allows convenient concurrent read. Thus, new algorithmic possibilities can become available. == Broadcast == The broadcast pattern is used to distribute data from one processing unit to all processing units, which is often needed in SPMD parallel programs to dispense input or global values. Broadcast can be interpreted as an inverse version of the reduce pattern (§ Reduce). Initially only root r {\displaystyle r} with i d {\displaystyle id} 0 {\displaystyle 0} stores message m {\displaystyle m} . During broadcast m {\displaystyle m} is sent to the remaining processing units, so that eventually m {\displaystyle m} is available to all processing units. Since an implementation by means of a sequential for-loop with p − 1 {\displaystyle p-1} iterations becomes a bottleneck, divide-and-conquer approaches are common. One possibility is to utilize a binomial tree structure with the requirement that p {\displaystyle p} has to be a power of two. When a processing unit is responsible for sending m {\displaystyle m} to processing units i . . j {\displaystyle i..j} , it sends m {\displaystyle m} to processing unit ⌈ ( i + j ) / 2 ⌉ {\displaystyle \left\lceil (i+j)/2\right\rceil } and delegates responsibility for the processing units ⌈ ( i + j ) / 2 ⌉ . . j {\displaystyle \left\lceil (i+j)/2\right\rceil ..j} to it, while its own responsibility is cut down to i . . ⌈ ( i + j ) / 2 ⌉ − 1 {\displaystyle i..\left\lceil (i+j)/2\right\rceil -1} . Binomial trees have a problem with long messages m {\displaystyle m} . The receiving unit of m {\displaystyle m} can only propagate the message to other units, after it received the whole message. In the meantime, the communication network is not utilized. Therefore pipelining on binary trees is used, where m {\displaystyle m} is split into an array of k {\displaystyle k} packets of size ⌈ n / k ⌉ {\displaystyle \left\lceil n/k\right\rceil } . The packets are then broadcast one after another, so that data is distributed fast in the communication network. Pipelined broadcast on balanced binary tree is possible in O ( α log p + β n ) {\displaystyle {\mathcal {O}}(\alpha \log p+\beta n)} , whereas for the non-pipelined case it takes O ( ( α + β n ) log p ) {\displaystyle {\mathcal {O}}((\alpha +\beta n)\log p)} cost. == Reduce == The reduce pattern is used to collect data or partial results from different processing units and to combine them into a global result by a chosen operator. Given p {\displaystyle p} processing units, message m i {\displaystyle m_{i}} is on processing unit p i {\displaystyle p_{i}} initially. All m i {\displaystyle m_{i}} are aggregated by ⊗ {\displaystyle \otimes } and the result is eventually stored on p 0 {\displaystyle p_{0}} . The reduction operator ⊗ {\displaystyle \otimes } must be associative at least. Some algorithms require a commutative operator with a neutral element. Operators like s u m {\displaystyle sum} , m i n {\displaystyle min} , m a x {\displaystyle max} are common. Implementation considerations are similar to broadcast (§ Broadcast). For pipelining on binary trees the message must be representable as a vector of smaller object for component-wise reduction. Pipelined reduce on a balanced binary tree is possible in O ( α log p + β n ) {\displaystyle {\mathcal {O}}(\alpha \log p+\beta n)} . == All-Reduce == The all-reduce pattern (also called allreduce) is used if the result of a reduce operation (§ Reduce) must be distributed to all processing units. Given p {\displaystyle p} processing units, message m i {\displaystyle m_{i}} is on processing unit p i {\displaystyle p_{i}} initially. All m i {\displaystyle m_{i}} are aggregated by an operator ⊗ {\displaystyle \otimes } and the result is eventually stored on all p i {\displaystyle p_{i}} . Analog to the reduce operation, the operator ⊗ {\displaystyle \otimes } must be at least associative. All-reduce can be interpreted as a reduce operation with a subsequent broadcast (§ Broadcast). For long messages a corresponding implementation is suitable, whereas for short messages, the latency can be reduced by using a hypercube (Hypercube (communication pattern) § All-Gather/ All-Reduce) topology, if p {\displaystyle p} is a power of two. All-reduce can also be implemented with a butterfly algorithm and achieve optimal latency and bandwidth. All-reduce is possible in O ( α log p + β n ) {\displaystyle {\mathcal {O}}(\alpha \log p+\beta n)} , since reduce and broadcast are possible in O ( α log p + β n ) {\displaystyle {\mathcal {O}}(\alpha \log p+\beta n)} with pipelining on balanced binary trees. All-reduce implemented with a butterfly algorithm achieves the same asymptotic runtime. == Prefix-Sum/Scan == The prefix-sum or scan operation is used to collect data or partial results from different processing units and to compute intermediate results by an operator, which are stored on those processing units. It can be seen as a generalization of the reduce operation (§ Reduce). Given p {\displaystyle p} processing units, message m i {\displaystyle m_{i}} is on processing unit p i {\displaystyle p_{i}} . The operator ⊗ {\displaystyle \otimes } must be at least associative, whereas some algorithms require also a commutative operator and a neutral element. Common operators are s u m {\displaystyle sum} , m i n {\displaystyle min} and m a x {\displaystyle max} . Eventually processing unit p i {\displaystyle p_{i}} stores the prefix sum ⊗ i ′ <= i {\displaystyle \otimes _{i'<=i}} m i ′ {\displaystyle m_{i'}} . In the case of the so-called exclusive prefix sum, processing unit p i {\displaystyle p_{i}} stores the prefix sum ⊗ i ′ < i {\displaystyle \otimes _{i'