SCinet is the high-performance network built annually by volunteers in support of SC (formerly Supercomputing, the International Conference for High Performance Computing, Networking, Storage and Analysis). SCinet is the primary network for the yearly conference and is used by attendees and exhibitors to demonstrate and test high-performance computing and networking applications. == International Community == SCinet is also a hub for the international networking community. It provides a platform to share the latest research, technologies, and demonstrations for networks, network technology providers, and even software developers who are in charge of supporting HPC communities at their own institutions or organizations. == Volunteers == Nearly 200 volunteers from educational institutions, high performance computing sites, equipment vendors, research and education networks, government agencies and telecommunications carriers collaborate via technology and in-person to design, build and operate SCinet. While many of these credentialed individuals have volunteered at SCinet for years, first timers join the team each year. They include international students and participants in the National Science Foundation-funded Women in IT Networking at SC (WINS) program. The 2017 SCinet team included women and men from high performance computing institutions in the U.S. and throughout the world. == History == Originated in 1991 as an initiative within the SC conference to provide networking to attendees, SCinet has grown to become the "World's Fastest Network" during the duration of the conference. For 29 years, SCinet has provided SC attendees and the high performance computing (HPC) community with the innovative network platform necessary to internationally interconnect, transport, and display HPC research during SC. Historically, SCinet has been used as a platform to test networking technology and applications which have found their way into common use. == Research and development == In the past years, SCinet deployed conference wide networking technologies such as ATM, FDDI, HiPPi before they were deployed commercially.
Microsoft Teams
Microsoft Teams is a team collaboration platform developed by Microsoft as part of the Microsoft 365 suite. It offers features such as workspace chat, video conferencing, file storage, and integration with both Microsoft and third-party applications and services. Teams gradually replaced earlier Microsoft messaging and collaboration platforms, including Skype for Business, Skype, Flip, and Microsoft Classroom. The platform saw significant growth during the COVID-19 pandemic, alongside competitors such as Zoom, Slack, and Google Meet, as organizations shifted to remote work and virtual meetings. As of January 2023, Microsoft reported approximately 280 million monthly active users. == History == On August 29, 2007, Microsoft acquired Parlano, the developer of the persistent group chat tool MindAlign. Years later, on March 4, 2016, Microsoft considered acquiring Slack for $8 billion. However, the proposal was reportedly opposed by Bill Gates, who advocated for focusing on enhancing Skype for Business instead. Lu Qi, then executive vice president of Applications and Services, had led the initiative to pursue the Slack acquisition. Following Lu's departure later that year, Microsoft announced Microsoft Teams on November 2, 2016, at an event in New York City, positioning it as a direct competitor to Slack. Teams launched worldwide on March 14, 2017. The service was initially led by corporate vice president Brian MacDonald. In response to the launch, Slack published a full-page advertisement in The New York Times welcoming the competition and outlining its product philosophy. Although Slack was used by 28 companies in the Fortune 100, The Verge wrote that executives would question paying for the service if Teams provides a similar function in their company's existing Office 365 subscription. However, ZDNET noted that the platforms initially served different markets, as Teams did not support external users, making it less appealing to small businesses and freelancers, a limitation Microsoft later addressed. In response to Teams' announcement, Slack deepened in-product integration with Google services. In May 2017, Microsoft announced that Teams would replace Microsoft Classroom in Office 365 Education. A free version of Teams was released on July 12, 2018, offering most core features at no cost, albeit with limits on users and storage. In January 2019, Microsoft introduced updates targeting "Firstline Workers" to improve Teams’ performance across shared or limited-access devices. In September 2019, Microsoft announced the retirement of Skype for Business in favor of Teams, which took effect on July 31, 2021. In early 2020, Microsoft introduced a push-to-talk "Walkie Talkie" feature aimed at firstline workers using smartphones and tablets over Wi-Fi or cellular networks. The COVID-19 pandemic significantly boosted usage of Teams. On March 19, 2020, Microsoft reported 44 million daily active users. In April, the platform logged 4.1 billion meeting minutes in a single day. A public preview of Microsoft Teams for Linux was released in December 2019, but the Linux client was discontinued in 2022. In July 2020, Microsoft shut down its video game livestreaming platform Mixer, and announced that some of its technologies would be repurposed for use in Teams. On February 28, 2025, Microsoft announced that Skype would be fully retired on May 5, 2025, with users given options to export their data or transition to Microsoft Teams. In October 2025, together with other Microsoft 365 suite apps, Teams had its logo updated. == Usage == == Underlying software == Microsoft Teams, as part of the Microsoft 365 suite, utilizes SharePoint and Exchange Online. Each Team, Shared Channel, and Private Channel has its own Microsoft 365 Group and SharePoint Site used for file storage. Messages are stored in Cosmos DB and are journaled to Exchange Online mailboxes. Private messages, including messages in Private Channels, are journaled to the sender and recipients' mailboxes. Public Channel messages are journaled to their corresponding Team's group mailbox, whereas, messages from Shared Channels are journaled to their own mailboxes. Contacts and voicemail are stored in Exchange Online. Microsoft Teams client is a web-based desktop app, originally developed on top of the Electron framework which combines the Chromium rendering engine and the Node.js JavaScript platform. Version 2.0 client was rebuilt using the Evergreen version of Microsoft Edge WebView2 in place of Electron. == Features == === Chats === Teams allows users to communicate in two-way persistent chats with one or multiple participants. Participants can message using text, emojis, stickers and gifs, as well as sharing links and files. In August 2022, the chat feature was updated for "chat with yourself"; allowing for the organization of files, notes, comments, images, and videos within a private chat tab. === Teams === Teams allows communities, groups, or teams to contribute in a shared workspace where messages and digital content on a specific topic are shared. Team members can join through an invitation sent by a team administrator or owner or sharing of a specific URL. Teams for Education allows admins and teachers to set up groups for classes, professional learning communities (PLCs), staff members, and everyone. === Channels === Channels allow team members to communicate without the use of email or group SMS (texting). Users can reply to posts with text, images, GIFs, and image macros. Direct messages send private messages to designated users rather than the entire channel. Connectors can be used within a channel to submit information contacted through a third-party service. Connectors include Mailchimp, Facebook Pages, Twitter, Power BI and Bing News. === Group conversations === Ad-hoc groups can be created to share instant messaging, audio calls (VoIP), and video calls inside the client software. === Telephone replacement === A feature on one of the higher cost licencing tiers allows connectivity to the public switched telephone network (PSTN) telephone system. This allows users to use Teams as if it were a telephone, making and receiving calls over the PSTN, including the ability to host "conference calls" with multiple participants. === Meeting === Meetings can be scheduled with multiple participants able to share audio, video, chat and presented content with all participants. Multiple users can connect via a meeting link. Automated minutes are possible using the recording and transcript features. Teams has a plugin for Microsoft Outlook to schedule a Teams Meeting in Outlook for a specific date and time and invite others to attend. If a meeting is scheduled within a channel, users visiting the channel are able to see if a meeting is in progress. ==== Teams Live Events ==== Teams Live Events replaces Skype Meeting Broadcast for users to broadcast to 10,000 participants on Teams, Yammer, or Microsoft Stream. ==== Breakout Rooms ==== Breakout rooms split a meeting into small groups. This is often utilized for collaboration during trainings or any environment where having all participants speak at once could be disruptive or unfeasible. Breakout rooms can be set by the hosts to a certain length of time, after which all participants will automatically rejoin the main meeting room. ==== Front Row ==== Front Row adjusts the layout of the viewer's screen, placing the speaker or content in the center of the gallery with other meeting participant's video feeds reduced in size and located below the speaker. === Education === Microsoft Teams for Education allows teachers to distribute, provide feedback, and grade student assignments turned in via Teams using the Assignments tab through Office 365 for Education subscribers. Quizzes can also be assigned to students through an integration with Office Forms. === Protocols === Microsoft Teams is based on a number of Microsoft-specific protocols. Video conferences are realized over the protocol MNP24, known from the Skype consumer version. VoIP and video conference clients based on SIP and H.323 need special gateways to connect to Microsoft Teams servers. With the help of Interactive Connectivity Establishment (ICE), clients behind Network address translation routers and restrictive firewalls are also able to connect, if peer-to-peer is not possible. === Integrations === Microsoft Teams has integrations through Microsoft AppSource, its integration marketplace. In 2020, Microsoft partnered with KUDO, a cloud-based solution with language interpretation, to allow integrated language meeting controls. In June 2022, an update was released using AI to improve call audio through the elimination of background feedback loops and cancelling non-vocal audio. == Anti-trust controversy == In July 2023, the European Commission opened an anti-trust investigation into the possibility that Microsoft unfairly used its office suite market power to increase sales of Teams and hurt
Application software
Application software is software that is intended for end-user use – not operating, administering or programming a computer. It includes programs such as word processors, web browsers, media players, and mobile applications used in daily tasks. An application (app, application program, software application) is any program that can be categorized as application software. Application is a subjective classification that is often used to differentiate from system and utility software. Application software represents the user-facing layer of computing systems, designed to translate complex system capabilities into task-oriented, goal-driven workflows. Unlike system software, which focuses on hardware orchestration and resource management, application software is centered on problem abstraction, user interaction, and domain-specific functionality. The abbreviation app became popular with the 2008 introduction of the iOS App Store, to refer to applications for mobile devices such as smartphones and tablets. Later, with the release of the Mac App Store in 2010 and the Windows Store in 2011, it began to be used to refer to end-user software in general, regardless of platform. Applications may be bundled with the computer and its system software or published separately. Applications may be proprietary or open-source. == Terminology == === Meaning program and software === When used as an adjective, application can have a broader meaning than that described in this article. For example, concepts such as application programming interface (API), application server, application virtualization, application lifecycle management and portable application refer to programs and software in general. === Distinction between system and application software === The distinction between system and application software is subjective and has been the subject of controversy. For example, one of the key questions in the United States v. Microsoft Corp. antitrust trial was whether Microsoft's Internet Explorer web browser was part of its Windows operating system or a separate piece of application software. As another example, the GNU/Linux naming controversy is, in part, due to disagreement about the relationship between the Linux kernel and the operating systems built over this kernel. In some types of embedded systems, the application software and the operating system software may be indistinguishable by the user, as in the case of software used to control a VCR, DVD player, or microwave oven. The above definitions may exclude some applications that may exist on some computers in large organizations. For an alternative definition of an app: see Application Portfolio Management. === Killer application === A killer application (killer app, coined in the late 1980s) is an application that is so popular that it causes demand for its host platform to increase. For example, VisiCalc was the first modern spreadsheet software for the Apple II and helped sell the then-new personal computers into offices. For the BlackBerry, it was its email software. === Software suite === As software suite consists of multiple applications bundled together. They usually have related functions, features, and user interfaces, and may be able to interact with each other, e.g. open each other's files. Business applications often come in suites, e.g. Microsoft Office, LibreOffice and iWork, which bundle together a word processor, a spreadsheet, etc.; but suites exist for other purposes, e.g. graphics or music. == Ways to classify == As there so many applications and since their attributes vary so dramatically, there are many different ways to classify them. === By legal aspects === Proprietary software is protected under an exclusive copyright, and a software license grants limited usage rights. Such applications may allow add-ons from third parties. Free and open-source software (FOSS) can be run, distributed, sold, and extended for any purpose. FOSS software released under a free license may be perpetual and also royalty-free. Perhaps, the owner, the holder or third-party enforcer of any right (copyright, trademark, patent, or ius in re aliena) are entitled to add exceptions, limitations, time decays or expiring dates to the license terms of use. Public-domain software is a type of FOSS that is royalty-free and can be run, distributed, modified, reversed, republished, or created in derivative works without any copyright attribution and therefore revocation. It can even be sold, but without transferring the public domain property to other single subjects. Public-domain software can be released under a (un)licensing legal statement, which enforces those terms and conditions for an indefinite duration (for a lifetime, or forever). === By platform === An application can be categorized by the host platform on which it runs. Notable platforms include operating system (native), web browser, cloud computing and mobile. For example a web application runs in a web browser whereas a more traditional, native application runs in the environment of a computer's operating system. There has been a contentious debate regarding web applications replacing native applications for many purposes, especially on mobile devices such as smartphones and tablets. Web apps have indeed greatly increased in popularity for some uses, but the advantages of applications make them unlikely to disappear soon, if ever. Furthermore, the two can be complementary, and even integrated. === Horizontal vs. vertical === Application software can be seen as either horizontal or vertical. Horizontal applications are more popular and widespread, because they are general purpose, for example word processors or databases. Vertical applications are niche products, designed for a particular type of industry or business, or department within an organization. Integrated suites of software will try to handle every specific aspect possible of, for example, manufacturing or banking worker, accounting, or customer service. === By purpose === There are many types of application software: Enterprise Addresses the needs of an entire organization's processes and data flows, across several departments, often in a large distributed environment. Examples include enterprise resource planning systems, customer relationship management (CRM) systems, data replication engines, and supply chain management software. Departmental Software is a sub-type of enterprise software with a focus on smaller organizations or groups within a large organization. (Examples include travel expense management and IT Helpdesk.) Enterprise infrastructure Provides common capabilities needed to support enterprise software systems. (Examples include databases, email servers, and systems for managing networks and security.) Application platform as a service (aPaaS) A cloud computing service that offers development and deployment environments for application services. Knowledge worker Lets users create and manage information, often for and individual media editors may aid in multiple information worker tasks. Content access Used primarily to access content without editing, but may include software that allows for content editing. Such software addresses the needs of individuals and groups to consume digital entertainment and published digital content. (Examples include media players, web browsers, and help browsers.) Educational Related to content access software, but has the content or features adapted for use by educators or students. For example, it may deliver evaluations (tests), track progress through material, or include collaborative capabilities. Simulation Simulates physical or abstract systems for either research, training, or entertainment purposes. Media development Generates print and electronic media for others to consume, most often in a commercial or educational setting. This includes graphic-art software, desktop publishing software, multimedia development software, HTML editors, digital-animation editors, digital audio and video composition, and many others. Engineering Used in developing hardware and software products. This includes computer-aided design (CAD), computer-aided engineering (CAE), computer language editing and compiling tools, integrated development environments, and application programmer interfaces. Entertainment Refers to video games, screen savers, programs to display motion pictures or play recorded music, and other forms of entertainment which can be experienced through the use of a computing device. == Taxonomy == This section is a taxonomy of kinds of applications. This organization is but one of many different ways to organize them. A kind is included in only one category even if it logically fits in multiple. === General-purpose === Calculator Spreadsheet Web browser Web mapping E-commerce Social media === Communication === Chat Email Presentation software Phone Messages Networking software Web conferencing === Documentation === Desktop
LRE Map
The LRE Map (Language Resources and Evaluation) is a freely accessible large database on resources dedicated to Natural language processing. The original feature of LRE Map is that the records are collected during the submission of different major Natural language processing conferences. The records are then cleaned and gathered into a global database called "LRE Map". The LRE Map is intended to be an instrument for collecting information about language resources and to become, at the same time, a community for users, a place to share and discover resources, discuss opinions, provide feedback, discover new trends, etc. It is an instrument for discovering, searching and documenting language resources, here intended in a broad sense, as both data and tools. The large amount of information contained in the Map can be analyzed in many different ways. For instance, the LRE Map can provide information about the most frequent type of resource, the most represented language, the applications for which resources are used or are being developed, the proportion of new resources vs. already existing ones, or the way in which resources are distributed to the community. == Context == Several institutions worldwide maintain catalogues of language resources (ELRA, LDC, NICT Universal Catalogue, ACL Data and Code Repository, OLAC, LT World, etc.) However, it has been estimated that only 10% of existing resources are known, either through distribution catalogues or via direct publicity by providers (web sites and the like). The rest remains hidden, the only occasions where it briefly emerges being when a resource is presented in the context of a research paper or report at some conference. Even in this case, nevertheless, it might be that a resource remains in the background simply because the focus of the research is not on the resource per se. == History == The LRE Map originated under the name "LREC Map" during the preparation of LREC 2010 conference. More specifically, the idea was discussed within the FlaReNet project, and in collaboration with ELRA and the Institute of Computational Linguistics of CNR in Pisa, the Map was put in place at LREC 2010. The LREC organizers asked the authors to provide some basic information about all the resources (in a broad sense, i.e. including tools, standards and evaluation packages), either used or created, described in their papers. All these descriptors were then gathered in a global matrix called the LREC Map. The same methodology and requirements from the authors has been then applied and extended to other conferences, namely COLING-2010, EMNLP-2010, RANLP-2011, LREC 2012, LREC 2014 and LREC 2016. After this generalization to other conferences, the LREC Map has been renamed as the LRE Map. == Size and content == The size of the database increases over time. The data collected amount to 4776 entries. Each resource is described according to the following attributes: Resource type, e.g. lexicon, annotation tool, tagger/parser. Resource production status, e.g. newly created finished, existing-updated. Resource availability, e.g. freely available, from data center. Resource modality, e.g. speech, written, sign language. Resource use, e.g. named entity recognition, language identification, machine translation. Resource language, e.g. English, 23 European Union languages, official languages of India. == Uses == The LRE map is a very important tool to chart the NLP field. Compared to other studied based on subjective scorings, the LRE map is made of real facts. The map has a great potential for many uses, in addition to being an information gathering tool: It is a great instrument for monitoring the evolution of the field (useful for funders), if applied in different contexts and times. It can be seen as a huge joint effort, the beginning of an even larger cooperative action not just among few leaders but among all the researchers. It is also an "educational" means towards the broad acknowledgment of the need of meta-research activities with the active involvement of many. It is also instrumental in introducing the new notion of "citation of resources" that could provide an award and a means of scholarly recognition for researchers engaged in resource creation. It is used to help the organization of the conferences of the field like LREC. == Derived matrices == The data were then cleaned and sorted by Joseph Mariani (CNRS-LIMSI IMMI) and Gil Francopoulo (CNRS-LIMSI IMMI + Tagmatica) in order to compute the various matrices of the final FLaReNet reports. One of them, the matrix for written data at LREC 2010 is as follows: English is the most studied language. Secondly, come French and German languages and then Italian and Spanish. == Future == The LRE Map has been extended to Language Resources and Evaluation Journal and other conferences.
Huawei Member Center
Huawei Member Center is a benefits app which runs using Huawei Mobile Services. Originally launched in China, Huawei Member Center is now being developed primarily around devices such as P40 Pro and the Nova 7. == Membership Levels == The Huawei Member Center provides rewards in two primary ways, 1) device-specific & promotions and 2) via frequent use of Huawei products and apps, using points to redeem additional benefits. In China, Huawei members are already classified into three levels, the highest being “elite”. Membership level determines the level of perks received, from priority access to the service hotline, new device events & proprietary early-access opportunities. Huawei ran a number of member events in 2019 called "Huawei Member Day" to promote the Member Center including providing tips for the Mate 30 Pro and offering a 50Gb cloud storage upgrade to users. == HMC in China == Huawei Member Center Has seen significant adoption in China and the east, the rewards for use on the app have ranged from free book coupons, discounted travel and exclusive gifts of new devices, such as the Huawei Enjoy Z.
StatMuse
StatMuse Inc. is an American artificial intelligence company founded in 2014. It operates an eponymous website that hosts a database of sports statistics covering the four major North American sports leagues, the Women's National Basketball Association (WNBA), NCAA Division I men's basketball, NCAA Division I Football Bowl Subdivision, the Big Five association football leagues in Europe, and various professional golf tours. == History == The company was founded by friends Adam Elmore and Eli Dawson in 2014. In email correspondence to the Springfield News-Leader, Elmore detailed that he and Dawson, fans of the National Basketball Association (NBA), were compelled to create StatMuse after they realized there was no online platform where they could search "Lebron James most points" [sic] and quickly get a result "showing his highest scoring games." As a startup, the company's goal was to utilize a type of artificial intelligence called natural language processing (NLP) for sports. In 2015, the company was part of the second group of startups accepted into the Disney Accelerator program. The company secured support from several investors, including The Walt Disney Company, Techstars, Allen & Company, the NFL Players Association, Greycroft and NBA Commissioner David Stern. As part of their partnership with Disney, StatMuse signed a content deal with ESPN (owned by Disney) to provide stats content on social media and television during the 2015–16 NBA season. Initially, the company only had stats available for the NBA, but eventually expanded to provide stats for the other major North American sports leagues. The company's initial demographic was players of fantasy sports, but it eventually expanded to target general sports fans as well. StatMuse offers responses to user queries in the voices of sports-related public figures. Dawson shared with VentureBeat that StatMuse brings people in and records them saying different words and phrases. These celebrity voices were made accessible through Google's Google Assistant service, Microsoft's Cortana virtual assistant, and Amazon's Echo devices. The company launched its phone app in September 2017. The app allows users to access StatMuse's sports statistics database by submitting queries in their natural language. Upon the launch of the phone app, Fitz Tepper of TechCrunch wrote that: "The technology isn't perfect – some of the pauses between words are a bit awkward, making it clear that some phrases are being stitched together on the fly. But this is the exception, and on the whole, most responses sound pretty good." StatMuse plug-ins for Slack and Facebook Messenger were also made, providing text-based sports stats. In 2019, StatMuse received investment from the Google Assistant Investment program. The service launched a premium option dubbed StatMuse+ in May 2023, offering options that had previously been included for free, such as unlimited searches and full results in data tables. The premium version also included early access to new features and a personalized search history, as well as not having ads. The app received a variety of feedback. In January 2024, the service launched a Premier League version of the website dubbed StatMuse FC. It is planned to introduce more leagues on the website.
Superquadrics
In mathematics, the superquadrics or super-quadrics (also superquadratics) are a family of geometric shapes defined by formulas that resemble those of ellipsoids and other quadrics, except that the squaring operations are replaced by arbitrary powers. They can be seen as the three-dimensional relatives of the superellipses. The term may refer to the solid object or to its surface, depending on the context. The equations below specify the surface; the solid is specified by replacing the equality signs by less-than-or-equal signs. The superquadrics include many shapes that resemble cubes, octahedra, cylinders, lozenges and spindles, with rounded or sharp corners. Because of their flexibility and relative simplicity, they are popular geometric modeling tools, especially in computer graphics. It becomes an important geometric primitive widely used in computer vision, robotics, and physical simulation. Some authors, such as Alan Barr, define "superquadrics" as including both the superellipsoids and the supertoroids. In modern computer vision literatures, superquadrics and superellipsoids are used interchangeably, since superellipsoids are the most representative and widely utilized shape among all the superquadrics. Comprehensive coverage of geometrical properties of superquadrics and methods of their recovery from range images and point clouds are covered in several computer vision literatures. == Formulas == === Implicit equation === The surface of the basic superquadric is given by | x | r + | y | s + | z | t = 1 {\displaystyle \left|x\right|^{r}+\left|y\right|^{s}+\left|z\right|^{t}=1} where r, s, and t are positive real numbers that determine the main features of the superquadric. Namely: less than 1: a pointy octahedron modified to have concave faces and sharp edges. exactly 1: a regular octahedron. between 1 and 2: an octahedron modified to have convex faces, blunt edges and blunt corners. exactly 2: a sphere greater than 2: a cube modified to have rounded edges and corners. infinite (in the limit): a cube Each exponent can be varied independently to obtain combined shapes. For example, if r=s=2, and t=4, one obtains a solid of revolution which resembles an ellipsoid with round cross-section but flattened ends. This formula is a special case of the superellipsoid's formula if (and only if) r = s. If any exponent is allowed to be negative, the shape extends to infinity. Such shapes are sometimes called super-hyperboloids. The basic shape above spans from -1 to +1 along each coordinate axis. The general superquadric is the result of scaling this basic shape by different amounts A, B, C along each axis. Its general equation is | x A | r + | y B | s + | z C | t = 1. {\displaystyle \left|{\frac {x}{A}}\right|^{r}+\left|{\frac {y}{B}}\right|^{s}+\left|{\frac {z}{C}}\right|^{t}=1.} === Parametric description === Parametric equations in terms of surface parameters u and v (equivalent to longitude and latitude if m equals 2) are x ( u , v ) = A g ( v , 2 r ) g ( u , 2 r ) y ( u , v ) = B g ( v , 2 s ) f ( u , 2 s ) z ( u , v ) = C f ( v , 2 t ) − π 2 ≤ v ≤ π 2 , − π ≤ u < π , {\displaystyle {\begin{aligned}x(u,v)&{}=Ag\left(v,{\frac {2}{r}}\right)g\left(u,{\frac {2}{r}}\right)\\y(u,v)&{}=Bg\left(v,{\frac {2}{s}}\right)f\left(u,{\frac {2}{s}}\right)\\z(u,v)&{}=Cf\left(v,{\frac {2}{t}}\right)\\&-{\frac {\pi }{2}}\leq v\leq {\frac {\pi }{2}},\quad -\pi \leq u<\pi ,\end{aligned}}} where the auxiliary functions are f ( ω , m ) = sgn ( sin ω ) | sin ω | m g ( ω , m ) = sgn ( cos ω ) | cos ω | m {\displaystyle {\begin{aligned}f(\omega ,m)&{}=\operatorname {sgn}(\sin \omega )\left|\sin \omega \right|^{m}\\g(\omega ,m)&{}=\operatorname {sgn}(\cos \omega )\left|\cos \omega \right|^{m}\end{aligned}}} and the sign function sgn(x) is sgn ( x ) = { − 1 , x < 0 0 , x = 0 + 1 , x > 0. {\displaystyle \operatorname {sgn}(x)={\begin{cases}-1,&x<0\\0,&x=0\\+1,&x>0.\end{cases}}} === Spherical product === Barr introduces the spherical product which given two plane curves produces a 3D surface. If f ( μ ) = ( f 1 ( μ ) f 2 ( μ ) ) , g ( ν ) = ( g 1 ( ν ) g 2 ( ν ) ) {\displaystyle f(\mu )={\begin{pmatrix}f_{1}(\mu )\\f_{2}(\mu )\end{pmatrix}},\quad g(\nu )={\begin{pmatrix}g_{1}(\nu )\\g_{2}(\nu )\end{pmatrix}}} are two plane curves then the spherical product is h ( μ , ν ) = f ( μ ) ⊗ g ( ν ) = ( f 1 ( μ ) g 1 ( ν ) f 1 ( μ ) g 2 ( ν ) f 2 ( μ ) ) {\displaystyle h(\mu ,\nu )=f(\mu )\otimes g(\nu )={\begin{pmatrix}f_{1}(\mu )\ g_{1}(\nu )\\f_{1}(\mu )\ g_{2}(\nu )\\f_{2}(\mu )\end{pmatrix}}} This is similar to the typical parametric equation of a sphere: x = x 0 + r sin θ cos φ y = y 0 + r sin θ sin φ ( 0 ≤ θ ≤ π , 0 ≤ φ < 2 π ) z = z 0 + r cos θ {\displaystyle {\begin{aligned}x&=x_{0}+r\sin \theta \;\cos \varphi \\y&=y_{0}+r\sin \theta \;\sin \varphi \qquad (0\leq \theta \leq \pi ,\;0\leq \varphi <2\pi )\\z&=z_{0}+r\cos \theta \end{aligned}}} which give rise to the name spherical product. Barr uses the spherical product to define quadric surfaces, like ellipsoids, and hyperboloids as well as the torus, superellipsoid, superquadric hyperboloids of one and two sheets, and supertoroids. == Plotting code == The following GNU Octave code generates a mesh approximation of a superquadric: