In computer graphics, the rendering equation is an integral equation that expresses the amount of light leaving a point on a surface as the sum of emitted light and reflected light. It was independently introduced into computer graphics by David Immel et al. and James Kajiya in 1986. The equation is important in the theory of physically based rendering, describing the relationships between the bidirectional reflectance distribution function (BRDF) and the radiometric quantities used in rendering. The rendering equation is defined at every point on every surface in the scene being rendered, including points hidden from the camera. The incoming light quantities on the right side of the equation usually come from the left (outgoing) side at other points in the scene (ray casting can be used to find these other points). The radiosity rendering method solves a discrete approximation of this system of equations. In distributed ray tracing, the integral on the right side of the equation may be evaluated using Monte Carlo integration by randomly sampling possible incoming light directions. Path tracing improves and simplifies this method. The rendering equation can be extended to handle effects such as fluorescence (in which some absorbed energy is re-emitted at different wavelengths) and can support transparent and translucent materials by using a bidirectional scattering distribution function (BSDF) in place of a BRDF. The theory of path tracing sometimes uses a path integral (integral over possible paths from a light source to a point) instead of the integral over possible incoming directions. == Equation form == The rendering equation may be written in the form L o ( x , ω o , λ , t ) = L e ( x , ω o , λ , t ) + L r ( x , ω o , λ , t ) {\displaystyle L_{\text{o}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)=L_{\text{e}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)+L_{\text{r}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)} L r ( x , ω o , λ , t ) = ∫ Ω f r ( x , ω i , ω o , λ , t ) L i ( x , ω i , λ , t ) ( ω i ⋅ n ) d ω i {\displaystyle L_{\text{r}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)=\int _{\Omega }f_{\text{r}}(\mathbf {x} ,\omega _{\text{i}},\omega _{\text{o}},\lambda ,t)L_{\text{i}}(\mathbf {x} ,\omega _{\text{i}},\lambda ,t)(\omega _{\text{i}}\cdot \mathbf {n} )\operatorname {d} \omega _{\text{i}}} where L o ( x , ω o , λ , t ) {\displaystyle L_{\text{o}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)} is the total spectral radiance of wavelength λ {\displaystyle \lambda } directed outward along direction ω o {\displaystyle \omega _{\text{o}}} at time t {\displaystyle t} , from a particular position x {\displaystyle \mathbf {x} } x {\displaystyle \mathbf {x} } is the location in space ω o {\displaystyle \omega _{\text{o}}} is the direction of the outgoing light λ {\displaystyle \lambda } is a particular wavelength of light t {\displaystyle t} is time L e ( x , ω o , λ , t ) {\displaystyle L_{\text{e}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)} is emitted spectral radiance L r ( x , ω o , λ , t ) {\displaystyle L_{\text{r}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)} is reflected spectral radiance ∫ Ω … d ω i {\displaystyle \int _{\Omega }\dots \operatorname {d} \omega _{\text{i}}} is an integral over Ω {\displaystyle \Omega } Ω {\displaystyle \Omega } is the unit hemisphere centered around n {\displaystyle \mathbf {n} } containing all possible values for ω i {\displaystyle \omega _{\text{i}}} where ω i ⋅ n > 0 {\displaystyle \omega _{\text{i}}\cdot \mathbf {n} >0} f r ( x , ω i , ω o , λ , t ) {\displaystyle f_{\text{r}}(\mathbf {x} ,\omega _{\text{i}},\omega _{\text{o}},\lambda ,t)} is the bidirectional reflectance distribution function, the proportion of light reflected from ω i {\displaystyle \omega _{\text{i}}} to ω o {\displaystyle \omega _{\text{o}}} at position x {\displaystyle \mathbf {x} } , time t {\displaystyle t} , and at wavelength λ {\displaystyle \lambda } ω i {\displaystyle \omega _{\text{i}}} is the negative direction of the incoming light L i ( x , ω i , λ , t ) {\displaystyle L_{\text{i}}(\mathbf {x} ,\omega _{\text{i}},\lambda ,t)} is spectral radiance of wavelength λ {\displaystyle \lambda } coming inward toward x {\displaystyle \mathbf {x} } from direction ω i {\displaystyle \omega _{\text{i}}} at time t {\displaystyle t} n {\displaystyle \mathbf {n} } is the surface normal at x {\displaystyle \mathbf {x} } ω i ⋅ n {\displaystyle \omega _{\text{i}}\cdot \mathbf {n} } is the weakening factor of outward irradiance due to incident angle, as the light flux is smeared across a surface whose area is larger than the projected area perpendicular to the ray. This is often written as cos θ i {\displaystyle \cos \theta _{i}} . Two noteworthy features are: its linearity—it is composed only of multiplications and additions, and its spatial homogeneity—it is the same in all positions and orientations. These mean a wide range of factorings and rearrangements of the equation are possible. It is a Fredholm integral equation of the second kind, similar to those that arise in quantum field theory. Note this equation's spectral and time dependence — L o {\displaystyle L_{\text{o}}} may be sampled at or integrated over sections of the visible spectrum to obtain, for example, a trichromatic color sample. A pixel value for a single frame in an animation may be obtained by fixing t ; {\displaystyle t;} motion blur can be produced by averaging L o {\displaystyle L_{\text{o}}} over some given time interval (by integrating over the time interval and dividing by the length of the interval). Note that a solution to the rendering equation is the function L o {\displaystyle L_{\text{o}}} . The function L i {\displaystyle L_{\text{i}}} is related to L o {\displaystyle L_{\text{o}}} via a ray-tracing operation: The incoming radiance from some direction at one point is the outgoing radiance at some other point in the opposite direction. == Applications == Solving the rendering equation for any given scene is the primary challenge in realistic rendering. One approach to solving the equation is based on finite element methods, leading to the radiosity algorithm. Another approach using Monte Carlo methods has led to many different algorithms including path tracing, photon mapping, and Metropolis light transport, among others. == Limitations == Although the equation is very general, it does not capture every aspect of light reflection. Some missing aspects include the following: Transmission, which occurs when light is transmitted through the surface, such as when it hits a glass object or a water surface, Subsurface scattering, where the spatial locations for incoming and departing light are different. Surfaces rendered without accounting for subsurface scattering may appear unnaturally opaque — however, it is not necessary to account for this if transmission is included in the equation, since that will effectively include also light scattered under the surface, Polarization, where different light polarizations will sometimes have different reflection distributions, for example when light bounces at a water surface, Phosphorescence, which occurs when light or other electromagnetic radiation is absorbed at one moment and emitted at a later moment, usually with a longer wavelength (unless the absorbed electromagnetic radiation is very intense), Interference, where the wave properties of light are exhibited, Fluorescence, where the absorbed and emitted light have different wavelengths, Non-linear effects, where very intense light can increase the energy level of an electron with more energy than that of a single photon (this can occur if the electron is hit by two photons at the same time), and emission of light with higher frequency than the frequency of the light that hit the surface suddenly becomes possible, and Doppler effect, where light that bounces off an object moving at a very high speed will get its wavelength changed: if the light bounces off an object that is moving towards it, the light will be blueshifted and the photons will be packed more closely so the photon flux will be increased; if it bounces off an object moving away from it, it will be redshifted and the photon flux will be decreased. This effect becomes apparent only at speeds comparable to the speed of light, which is not the case for most rendering applications. For scenes that are either not composed of simple surfaces in a vacuum or for which the travel time for light is an important factor, researchers have generalized the rendering equation to produce a volume rendering equation suitable for volume rendering and a transient rendering equation for use with data from a time-of-flight camera.
COVID-19 apps
COVID-19 apps include mobile-software applications for digital contact-tracing—i.e. the process of identifying persons ("contacts") who may have been in contact with an infected individual—deployed during the COVID-19 pandemic. Numerous tracing applications have been developed or proposed, with official government support in some territories and jurisdictions. Several frameworks for building contact-tracing apps have been developed. Privacy concerns have been raised, especially about systems that are based on tracking the geographical location of app users. Less overtly intrusive alternatives include the co-option of Bluetooth signals to log a user's proximity to other cellphones. (Bluetooth technology has form in tracking cell-phones' locations.)) On 10 April 2020, Google and Apple jointly announced that they would integrate functionality to support such Bluetooth-based apps directly into their Android and iOS operating systems. India's COVID-19 tracking app Aarogya Setu became the world's fastest growing application—beating Pokémon Go—with 50 million users in the first 13 days of its release. == Rationale == Contact tracing is an important tool in infectious disease control, but as the number of cases rises time constraints make it more challenging to effectively control transmission. Digital contact tracing, especially if widely deployed, may be more effective than traditional methods of contact tracing. In a March 2020 model by the University of Oxford Big Data Institute's Christophe Fraser's team, a coronavirus outbreak in a city of one million people is halted if 80% of all smartphone users take part in a tracking system; in the model, the elderly are still expected to self-isolate en masse, but individuals who are neither symptomatic nor elderly are exempt from isolation unless they receive an alert that they are at risk of carrying the disease. Some proponents advocate for legislation exempting certain COVID-19 apps from general privacy restrictions. == Issues == === Uptake === Ross Anderson, professor of security engineering at Cambridge University, listed a number of potential practical problems with app-based systems, including false positives and the potential lack of effectiveness if takeup of the app is limited to only a small fraction of the population. In Singapore, only one person in three had downloaded the TraceTogether app by the end of June 2020, despite legal requirements for most workers; the app was also underused, as it required users to keep it open at all times on iOS. A team at the University of Oxford simulated the effect of a contact tracing app on a city of 1 million. They estimated that if the app was used in conjunction with the shielding of over-70s, then 56% of the population would have to be using the app for it to suppress the virus. This would be equivalent to 80% of smartphone users in the United Kingdom. They found that the app could still slow the spread of the virus if fewer people downloaded it, with one infection being prevented for every one or two users. In August 2020, the American Civil Liberties Union (ACLU) argued that there were disparities in smartphone use between demographics and minority groups, and that "even the most comprehensive, all-seeing contact tracing system is of little use without social and medical systems in place to help those who may have the virus — including access to medical care, testing, and support for those who are quarantined." === App store restrictions === Addressing concerns about the spread of misleading or harmful apps, Apple, Google and Amazon set limits on which types of organizations could add coronavirus-related apps to its App Store, limiting them to only "official" or otherwise reputable organizations. === Ethical principles of mass surveillance using COVID-19 contact tracing apps === The advent of COVID-19 contact tracing apps has led to concerns around privacy, the rights of app users, and governmental authority. The European Convention on Human Rights, the International Covenant on Civil and Political Rights (ICCPR) and the United Nations and the Siracusa Principles have outlined 4 principles to consider when looking at the ethical principles of mass surveillance with COVID-19 contact tracing apps. These are necessity, proportionality, scientific validity, and time boundedness. Necessity is defined as the idea that governments should only interfere with a person's rights when deemed essential for public health interests. The potential risks associated with infringements of personal privacy must be outweighed by the possibility of reducing significant harm to others. Potential benefits of contact-tracing apps that may be considered include allowing for blanket population-level quarantine measures to be lifted sooner and the minimization of people under quarantine. Hence, some contend that contact-tracing apps are justified as they may be less intrusive than blanket quarantine measures. Furthermore, the delay of an effective contact-tracing app with significant health and economic benefits may be considered unethical. Proportionality refers to the concept that a contact tracing app's potential negative impact on a person's rights should be justifiable by the severity of the health risks that are being addressed. Apps must use the most privacy-preserving options available to achieve their goals, and the selected option should not only be a logical option for achieving the goal but also an effective one. Scientific validity evaluates whether an app is effective, timely and accurate. Traditional manual contact-tracing procedures are not efficient enough for the COVID-19 pandemic, and do not consider asymptomatic transmission. Contact-tracing apps, on the other hand, can be effective COVID-19 contact-tracing tools that reduce R value to less than 1, leading to sustained epidemic suppression. However, for apps to be effective, there needs to be a minimum 56-60% uptake in the population. Apps should be continually modified to reflect current knowledge on the diseases being monitored. Some argue that contact-tracing apps should be considered societal experimental trials where results and adverse effects are evaluated according to the stringent guidelines of social experiments. Analyses should be conducted by independent research bodies and published for wide dissemination. Despite the current urgency of our pandemic situation, we should still adhere to the standard rigors of scientific evaluation. Time boundedness describe the need for establishing legal and technical sunset clauses so that they are only allowed to operate as long as necessary to address the pandemic situation. Apps should be withdrawn as soon as possible after the end of the pandemic. If the end of the pandemic cannot be predicted, the use of apps should be regularly reviewed and decisions about continued use should be made at each review. Collected data should only be retained by public health authorities for research purposes with clear stipulations on how long the data will be held for and who will be responsible for security, oversight, and ownership. === Privacy, discrimination and marginalisation concerns === The American Civil Liberties Union (ACLU) has published a set of principles for technology-assisted contact tracing and Amnesty International and over 100 other organizations issued a statement calling for limits on this kind of surveillance. The organisations declared eight conditions on governmental projects: surveillance would have to be "lawful, necessary and proportionate"; extensions of monitoring and surveillance would have to have sunset clauses; the use of data would have to be limited to COVID-19 purposes; data security and anonymity would have to be protected and shown to be protected based on evidence; digital surveillance would have to address the risk of exacerbating discrimination and marginalisation; any sharing of data with third parties would have to be defined in law; there would have to be safeguards against abuse and the rights of citizens to respond to abuses; "meaningful participation" by all "relevant stakeholders" would be required, including that of public health experts and marginalised groups. The German Chaos Computer Club (CCC) and Reporters Without Borders also issued checklists. The Exposure Notification service intends to address the problem of persistent surveillance by removing the tracing mechanism from their device operating systems once it is no longer needed. On 20 April 2020, it was reported that over 300 academics had signed a statement favouring decentralised proximity tracing applications over centralised models, given the difficulty in precluding centralised options being used "to enable unwarranted discrimination and surveillance." In a centralised model, a central database records the ID codes of meetings between users. In a decentralised model, this information is recorded on individual phones, with the role of the central
Cypherpunks (book)
Cypherpunks: Freedom and the Future of the Internet is a 2012 book by Julian Assange, in discussion with Internet activists and cypherpunks Jacob Appelbaum, Andy Müller-Maguhn and Jérémie Zimmermann. Its primary topic is society's relationship with information security. In the book, the authors warn that the Internet has become a tool of the police state, and that the world is inadvertently heading toward a form of totalitarianism. They promote the use of cryptography to protect against state surveillance. In the introduction, Assange says that the book is "not a manifesto [...] [but] a warning". He told Guardian journalist Decca Aitkenhead: A well-defined mathematical algorithm can encrypt something quickly, but to decrypt it would take billions of years – or trillions of dollars' worth of electricity to drive the computer. So cryptography is the essential building block of independence for organisations on the Internet, just like armies are the essential building blocks of states, because otherwise one state just takes over another. There is no other way for our intellectual life to gain proper independence from the security guards of the world, the people who control physical reality. Assange later wrote in The Guardian: "Strong cryptography is a vital tool in fighting state oppression." saying that was the message of his book, Cypherpunks. Cypherpunks is published by OR Books. It is primarily a transcript of World Tomorrow episode eight, a two-part interview between Assange, Jacob Appelbaum, Andy Müller-Maguhn, and Jérémie Zimmermann. In the foreword, Assange said, "the Internet, our greatest tool for emancipation, has been transformed into the most dangerous facilitator of totalitarianism we have ever seen".
IBM 37xx
IBM 37xx (or 37x5) is a family of IBM Systems Network Architecture (SNA) programmable front-end processors used mainly in mainframe environments. All members of the family ran one of three IBM-supplied programs. Emulation Program (EP) mimicked the operation of the older IBM 270x non-programmable controllers. Network Control Program (NCP) supported Systems Network Architecture devices. Partitioned Emulation Program (PEP) combined the functions of the two. == Models == === 370x series === 3705 — the oldest of the family, introduced in 1972 to replace the non-programmable IBM 270x family. The 3705 could control up to 352 communications lines. 3704 was a smaller version, introduced in 1973. It supported up to 32 lines. === 371x === The 3710 communications controller was introduced in 1984. === 372x series === The 3725 and the 3720 systems were announced in 1983. The 3725 replaced the hardware line scanners used on previous 370x machines with multiple microcoded processors. The 3725 was a large-scale node and front end processor. The 3720 was a smaller version of the 3725, which was sometimes used as a remote concentrator. The 3726 was an expansion unit for the 3725. With the expansion unit, the 3725 could support up to 256 lines at data rates up to 256 kbit/s, and connect to up to eight mainframe channels. Marketing of the 372x machines was discontinued in 1989. IBM discontinued support for the 3705, 3720, 3725 in 1999. === 374x series === The 3745, announced in 1988, provides up to eight T1 circuits. At the time of the announcement, IBM was estimated to have nearly 85% of the over US$825 million market for communications controllers over rivals such as NCR Comten and Amdahl Corporation. The 3745 is no longer marketed, but still supported and used. The 3746 "Nways Controller" model 900, unveiled in 1992, was an expansion unit for the 3745 supporting additional Token Ring and ESCON connections. A stand-alone model 950 appeared in 1995. == Successors == IBM no longer manufactures 37xx processors. The last models, the 3745/46, were withdrawn from marketing in 2002. Replacement software products are Communications Controller for Linux on System z and Enterprise Extender. == Clones == Several companies produced clones of 37xx controllers, including NCR COMTEN and Amdahl Corporation.
Viral marketing
Viral marketing is a business strategy that uses existing social networks to promote a product or service on social media platforms. Its name refers to how consumers spread information about a product with other people, much in the same way that a virus spreads from one person to another. It can be delivered by word of mouth, or enhanced by the network effects of the Internet and mobile networks. The concept is often misused or misunderstood, as people apply it to any successful enough story without taking into account the word "viral". Viral advertising is personal and, while coming from an identified sponsor, it does not mean businesses pay for its distribution. Most of the well-known viral ads circulating online are ads paid by a sponsor company, launched either on their own platform (company web page or social media profile) or on social media websites such as YouTube. Consumers receive the page link from a social media network or copy the entire ad from a website and pass it along through e-mail or posting it on a blog, web page or social media profile. Viral marketing may take the form of video clips, advergames, ebooks, brandable software, images, text messages, email messages, or web pages. The most commonly utilized transmission vehicles for viral messages include pass-along based, incentive based, trendy based, and undercover based. However, the creative nature of viral marketing enables an "endless amount of potential forms and vehicles the messages can utilize for transmission", including mobile devices. The ultimate goal of marketers interested in creating successful viral marketing programs is to create viral messages that appeal to individuals with high social networking potential (SNP) and that have a high probability of being presented and spread by these individuals and their competitors in their communications with others in a short period. The term "viral marketing" has also been used pejoratively to refer to stealth marketing campaigns—marketing strategies that advertise a product to people without them knowing they are being marketed to. == History == The emergence of "viral marketing", as an approach to advertisement, has been tied to the popularization of the notion that ideas spread like viruses. The field that developed around this notion, memetics, peaked in popularity in the 1990s. As this then began to influence marketing gurus, it took on a life of its own in that new context. The brief career of Australian pop singer Marcus Montana is largely remembered as an early example of viral marketing. In early 1989, thousands of posters declaring "Marcus is Coming" were placed around Sydney, generating discussion and interest within the media and the community about the meaning of the mysterious advertisements. The campaign successfully made Montana's musical debut a talking point, but his subsequent music career was a failure. The term is found in PC User magazine in 1989 with a somewhat differing meaning. It was later used by Jeffrey Rayport in the 1996 Fast Company article "The Virus of Marketing", and Tim Draper and Steve Jurvetson of the venture capital firm Draper Fisher Jurvetson in 1997 to describe Hotmail's practice of appending advertising to outgoing mail from their users. Doug Rushkoff, a media critic, wrote about viral marketing on the Internet in 1996. Bob Gerstley wrote about algorithms designed to identify people with high "social networking potential." Gerstley employed SNP algorithms in quantitative marketing research. In 2004, the concept of the alpha user was coined to indicate that it had now become possible to identify the focal members of any viral campaign, the "hubs" who were most influential. Alpha users could be targeted for advertising purposes most accurately in mobile phone networks, due to their personal nature. In early 2013, the first ever Viral Summit was held in Las Vegas. == Factors == Marketer Jonah Berger defines six key factors that drive virality, organized in an acronym called STEPPS: Social currency – the better something makes people look, the more likely they will be to share it Triggers – things that are "top of mind" are more likely to be "tip of the tongue" Emotion – when people care, they share Public – the easier something is to see, the more likely people are to imitate it Practical value – people share useful information to help others Stories – like a Trojan Horse, stories carry messages and ideas along for the ride. Another important factor that drives virality is the propagativity of the content, referring to the ease with which consumers can redistribute it. == Psychology == To form deeper connections with viewers and increase the chances of virality, many marketers use psychological principles. They argue that this approach is scientific and can foster an environment where the odds of gaining traction are much higher. People find psychological safety and can develop a sense of trust when more people interact with online content. For this reason, marketers work to develop media that resonates with viewers on a deeper, emotional level as this approach frequently results in higher engagement. This level of interaction serves as a sign of approval, reducing the personal risk that is subconsciously linked to associating oneself with a company or brand’s content. Professor Jonah Berger at the University of Pennsylvania's Wharton School of Business affirms that marketing campaigns that trigger psychological responses linked to strong emotions tend to perform better. In particular, Berger found that positive emotions like happiness, joy, and excitement have more successful share rates than their negative counterparts. This outcome results from the human instinct to respond more positively to content with activating emotions, increasing the desire to share content, which contributes to its virality. Viral marketing utilizes the primitive feeling of frisson to increase their view and share counts. This feeling of excitement is considered powerful because of its ability to cause a physical response. From increased heart rates to full body chills, Professor Brent Coker at the University of Melbourne describes that this approach to marketing triggers a primitive response that immerses the viewer in the content on a deeper level. Researchers Juliana Fernandes from the University of Florida and Sigal Segev from the Florida International University also found that people are more inclined to share emotional campaigns over those that are heavily informational. They claim that consumers do not often care to learn about a product’s actual features and benefits. Instead, people prefer to be immersed in experience-based content that creates an emotional impact. Companies and brands can benefit from treating their content in this manner and go viral more frequently than those who do not. Social proof is another psychological phenomenon that impacts viral content. Experts in this field argue that it is a natural instinct to want to behave similarly to others because it results in positive validation. This phenomenon explains the human need to conform, so marketers focus on creating engaging content that encourages interactions and causes a snowball effect. This subconsciously influences people to like, comment, and share if they already see others doing the same. Social proof goes further by providing people with a form of social currency. When individuals interact with and share content, they become associated with the topics at hand. People naturally tend to perceive one another, and this pattern carries over to the digital world. As a result, many people tend to be vigilant about the viral marketing they engage with, since they want to be perceived positively. Companies and brands have the opportunity to develop social currency themselves by aligning with their target audiences and creating marketing campaigns that fit their interests or match their values. == Methods and metrics == According to marketing professors Andreas Kaplan and Michael Haenlein, to make viral marketing work, three basic criteria must be met, i.e., giving the right message to the right messengers in the right environment: Messenger: Three specific types of messengers are required to ensure the transformation of an ordinary message into a viral one: market mavens, social hubs, and salespeople. Market mavens are individuals who are continuously 'on the pulse' of things (information specialists); they are usually among the first to get exposed to the message and who transmit it to their immediate social network. Social hubs are people with an exceptionally large number of social connections; they often know hundreds of different people and have the ability to serve as connectors or bridges between different subcultures. Salespeople might be needed who receive the message from the market maven, amplify it by making it more relevant and persuasive, and then transmit it to the social hub for further distr
Pattern theory
Pattern theory, formulated by Ulf Grenander, is a mathematical formalism to describe knowledge of the world as patterns. It differs from other approaches to artificial intelligence in that it does not begin by prescribing algorithms and machinery to recognize and classify patterns; rather, it prescribes a vocabulary to articulate and recast the pattern concepts in precise language. Broad in its mathematical coverage, Pattern Theory spans algebra and statistics, as well as local topological and global entropic properties. In addition to the new algebraic vocabulary, its statistical approach is novel in its aim to: Identify the hidden variables of a data set using real world data rather than artificial stimuli, which was previously commonplace. Formulate prior distributions for hidden variables and models for the observed variables that form the vertices of a Gibbs-like graph. Study the randomness and variability of these graphs. Create the basic classes of stochastic models applied by listing the deformations of the patterns. Synthesize (sample) from the models, not just analyze signals with them. The Brown University Pattern Theory Group was formed in 1972 by Ulf Grenander. Many mathematicians are currently working in this group, noteworthy among them being the Fields Medalist David Mumford. Mumford regards Grenander as his "guru" in Pattern Theory.
InfiniBand
InfiniBand (IB) is a computer networking standard used in high-performance computing that features very high throughput and very low latency. It is used for data interconnect both among and within computers. InfiniBand is also used as either a direct or switched interconnect between servers and storage systems, as well as an interconnect between storage systems. It is designed to be scalable and uses a switched fabric network topology. Between 2014 and June 2016, it was the most commonly used interconnect in the TOP500 list of supercomputers. Mellanox (acquired by Nvidia) manufactures InfiniBand host bus adapters and network switches, which are used by large computer system and database vendors in their product lines. As a computer cluster interconnect, IB competes with Ethernet, Fibre Channel, and Intel Omni-Path. The technology is promoted by the InfiniBand Trade Association. == History == InfiniBand originated in 1999 from the merger of two competing designs: Future I/O and Next Generation I/O (NGIO). NGIO was led by Intel, with a specification released in 1998, and joined by Sun Microsystems and Dell. Future I/O was backed by Compaq, IBM, and Hewlett-Packard. This led to the formation of the InfiniBand Trade Association (IBTA), which included both sets of hardware vendors as well as software vendors such as Microsoft. At the time it was thought some of the more powerful computers were approaching the interconnect bottleneck of the PCI bus, in spite of upgrades like PCI-X. Version 1.0 of the InfiniBand Architecture Specification was released in 2000. Initially the IBTA vision for IB was simultaneously a replacement for PCI in I/O, Ethernet in the machine room, cluster interconnect and Fibre Channel. IBTA also envisaged decomposing server hardware on an IB fabric. Mellanox had been founded in 1999 to develop NGIO technology, but by 2001 shipped an InfiniBand product line called InfiniBridge at 10 Gbit/second speeds. Following the burst of the dot-com bubble there was hesitation in the industry to invest in such a far-reaching technology jump. By 2002, Intel announced that instead of shipping IB integrated circuits ("chips"), it would focus on developing PCI Express, and Microsoft discontinued IB development in favor of extending Ethernet. Sun Microsystems and Hitachi continued to support IB. In 2003, the System X supercomputer built at Virginia Tech used InfiniBand in what was estimated to be the third largest computer in the world at the time. The OpenIB Alliance (later renamed OpenFabrics Alliance) was founded in 2004 to develop an open set of software for the Linux kernel. By February, 2005, the support was accepted into the 2.6.11 Linux kernel. In November 2005 storage devices finally were released using InfiniBand from vendors such as Engenio. Cisco, desiring to keep technology superior to Ethernet off the market, adopted a "buy to kill" strategy. Cisco successfully killed InfiniBand switching companies such as Topspin via acquisition. Of the top 500 supercomputers in 2009, Gigabit Ethernet was the internal interconnect technology in 259 installations, compared with 181 using InfiniBand. In 2010, market leaders Mellanox and Voltaire merged, leaving just one other IB vendor, QLogic, primarily a Fibre Channel vendor. At the 2011 International Supercomputing Conference, links running at about 56 gigabits per second (known as FDR, see below), were announced and demonstrated by connecting booths in the trade show. In 2012, Intel acquired QLogic's InfiniBand technology, leaving only one independent supplier. By 2014, InfiniBand was the most popular internal connection technology for supercomputers, although within two years, 10 Gigabit Ethernet started displacing it. In 2016, it was reported that Oracle Corporation (an investor in Mellanox) might engineer its own InfiniBand hardware. In 2019 Nvidia acquired Mellanox, the last independent supplier of InfiniBand products. == Specification == Specifications are published by the InfiniBand trade association. === Performance === Original names for speeds were single-data rate (SDR), double-data rate (DDR) and quad-data rate (QDR) as given below. Subsequently, other three-letter initialisms were added for even higher data rates. Notes Each link is duplex. Links can be aggregated: most systems use a 4 link/lane connector (QSFP). HDR often makes use of 2x links (aka HDR100, 100 Gb link using 2 lanes of HDR, while still using a QSFP connector). NDR introduced OSFP connectors which host one or two links at 2x (NDR200) or 4x (NDR400). They are not logically configured as a single 8x link, even when connecting switches together with an OSFP cable. InfiniBand provides remote direct memory access (RDMA) capabilities for low CPU overhead. === Topology === InfiniBand uses a switched fabric topology, as opposed to early shared medium Ethernet. All transmissions begin or end at a channel adapter. Each processor contains a host channel adapter (HCA) and each peripheral has a target channel adapter (TCA). These adapters can also exchange information for security or quality of service (QoS). === Messages === InfiniBand transmits data in packets of up to 4 KB that are taken together to form a message. A message can be: a remote direct memory access read or write a channel send or receive a transaction-based operation (that can be reversed) a multicast transmission an atomic operation === Physical interconnection === In addition to a board form factor connection, it can use both active and passive copper (up to 10 meters) and optical fiber cable (up to 10 km). QSFP connectors are used. The InfiniBand Association also specified the CXP connector system for speeds up to 120 Gbit/s over copper, active optical cables, and optical transceivers using parallel multi-mode fiber cables with 24-fiber MPO connectors. === Software interfaces === Mellanox operating system support is available for Solaris, FreeBSD, Red Hat Enterprise Linux, SUSE Linux Enterprise Server (SLES), Windows, HP-UX, VMware ESX, and AIX. InfiniBand has no specific standard application programming interface (API). The standard only lists a set of verbs such as ibv_open_device or ibv_post_send, which are abstract representations of functions or methods that must exist. The syntax of these functions is left to the vendors. Sometimes for reference this is called the verbs API. The de facto standard software is developed by OpenFabrics Alliance and called the Open Fabrics Enterprise Distribution (OFED). It is released under two licenses GPL2 or BSD license for Linux and FreeBSD, and as Mellanox OFED for Windows (product names: WinOF / WinOF-2; attributed as host controller driver for matching specific ConnectX 3 to 5 devices) under a choice of BSD license for Windows. It has been adopted by most of the InfiniBand vendors, for Linux, FreeBSD, and Microsoft Windows. IBM refers to a software library called libibverbs, for its AIX operating system, as well as "AIX InfiniBand verbs". The Linux kernel support was integrated in 2005 into the kernel version 2.6.11. === Ethernet over InfiniBand === Ethernet over InfiniBand, abbreviated to EoIB, is an Ethernet implementation over the InfiniBand protocol and connector technology. EoIB enables multiple Ethernet bandwidths varying on the InfiniBand (IB) version. Ethernet's implementation of the Internet Protocol Suite, usually referred to as TCP/IP, is different in some details compared to the direct InfiniBand protocol in IP over IB (IPoIB).