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  The Future of Work and Death

  The Future of Work and Death is a 2016 documentary by Sean Blacknell and Wayne Walsh about the exponential growth of technology. The film showed at several film festivals including Raindance Film Festival, International Film Festival Rotterdam, Academia Film Olomouc and CPH:DOX. In May 2017 it received an official screening at the European Commission. It was distributed by First Run Features and Journeyman Pictures and was released on iTunes, Amazon Prime and On-demand on 9 May 2017. The film was made available on Sundance Now on 27 November 2017. A companion piece to the film, The Cost of Living, a documentary concerning universal basic income in Britain, was released on Amazon Prime on 8 October 2020. == Synopsis == World experts in the fields of futurology, anthropology, neuroscience, and philosophy consider the impact of technological advances on the two 'certainties' of human life; work and death. Charting human developments from Homo habilis, past the Industrial Revolution, to the digital age and beyond, the film looks at the shocking exponential rate at which mankind has managed to create technologies to ease the process of living. As we embark on the next phase of our adaptation, with automation and artificial intelligence signifying the complete move from man to machine, the film asks what the implications are for human fulfilment in an approaching era of job obsolescence and extreme longevity. == Cast == Dudley Sutton – Narrator Aubrey de Grey – Biomedical gerontologist and CSO of the SENS Research Foundation Will Self – Writer, journalist, political commentator and Professor of Contemporary Thought at Brunel University Rudolph E. Tanzi – Professor of Neurology at Harvard University and Director of the Genetics and Aging Research Unit at Massachusetts General Hospital (MGH) Martin Ford – Futurist and author Steve Fuller – Auguste Comte Chair in Social Epistemology at the Department of sociology at University of Warwick Murray Shanahan – Professor of Cognitive Robotics at Imperial College London Gray Scott – Futurist, executive producer of this production Vivek Wadhwa – Entrepreneur, academic and Director of Research at the Center for Entrepreneurship and Research Commercialization at the Pratt School of Engineering, Duke University Zoltan Istvan – Transhumanist and journalist Joanna Cook – Anthropologist, University College London Nicholas Kamara – Physician, Kable Hospital David Pearce – Transhumanist philosopher and co-founder of Humanity+ Peter Cochrane – Futurist and entrepreneur John Harris – Bioethicist, philosopher and Director of the Institute for Science, Ethics and Innovation at the University of Manchester Riva Melissa-Tez – Entrepreneur and transhumanist Ian Pearson – Futurologist Stuart Armstrong – Artificial intelligence researcher at Future of Humanity Institute

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  Secure state

  A secure state is an information systems security term to describe where entities in a computer system are divided into subjects and objects, and it can be formally proven that each state transition preserves security by moving from one secure state to another secure state. Thereby it can be inductively proven that the system is secure. As defined in the Bell–LaPadula model, the secure state is built on the concept of a state machine with a set of allowable states in a system. The transition from one state to another state is defined by transition functions. A system state is defined to be "secure" if the only permitted access modes of subjects to objects are in accordance with a security policy.

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  Jeremy Renner Official

  Jeremy Renner Official (or Jeremy Renner on the Google Play Store) was a mobile app created by American actor Jeremy Renner. He created the app in March 2017 to hear the input and comments of his fans. The app was shut down in September 2019 in part due to the frequent bullying and trolling that the platform had experienced. The app featured optional microtransactions, with some ranging up to roughly US$400 despite the app itself being free. Upon shutting down the app, Renner issued a mass-refund for the collectible "stars" in the app for purchases made within the last ninety days, from the day the announcement was posted. He then posted an apology to the app itself, and the app was deleted from both the Google Play Store and the App Store shortly after. == Usage == Upon downloading the app, the user was faced with a video of Renner speaking about his fans and superfans, regular giveaways, and real-life updates. While the app was active, Renner posted regular questions and comments for fans. Renner occasionally livestreamed about his work and day-to-day life. The community developed to include memes, selfies, and a "Happy Rennsday" event on Wednesdays. == History == === 2017–2019 === The app launched in March 2017 with a promotional contest. Renner's fans were encouraged to download the app and create comments about being Renner's biggest fan; Renner would then choose a winner and transport the winner and a guest to have lunch with him at the Calgary Expo. In the first few months Renner teased behind-the-scenes of projects he was working on, which he now sporadically does on Instagram. The app was similarly designed to Instagram as well, with a near identically styled layout. Around midway through 2019, a hoax account of Renner was made to mock the celebrity, joking about masturbating to porn and defending another hoax account of Casey Anthony. FastCompany wrote extensively about Renner's app in April 2019, calling it "a surprising new kind of social media". The Ringer stated "Jeremy Renner's Jeremy Renner app is the Jeremy Renner of apps." === After deletion (2019–2020) === After the shutdown of the app, a comedy-based pseudo-app with modular endings was released, called "The Jeremy Renner App Experience", in which the player plays as Jeremy Renner on the day of the Jeremy Renner Official app's shutdown. The app details several different choices on how Renner handles the situation. A six-part podcast was also created to mock the app's deletion, called The Renner Files, featuring Carolyn Goldfarb and Sarah Ramos. == Controversies == === Marketing === One of the main controversies of Renner's app was its marketing. The app's developers, Escapex, specialized in and grew famous for making similar monetized apps for celebrities. The marketing campaign was based on direct contact with Renner, whose chances were increased with regular payments for "stars", although very few encounters seemed to happen with Renner himself. The multiple problems with the app led the CEO of Escapex, Sephi Shapira, to call the app a "freak situation", and added "Am I concerned about this? Not more than I'm concerned about 50 other things I'm dealing with as a startup company." Along with the marketing failures, the app was seen as misrepresenting itself as seemingly erotic with some advertisements featuring Renner suggestively staring at the camera, despite the actual app being initially considered safe for children. === Harassment === After its release in 2017, the app was met with waves of harassment and bullying by many users on the app, most frequently by using impersonation — referenced in Renner's apology/deletion notice. Some death threats were made across the app by fraud accounts pretending to be several controversial celebrities, including O. J. Simpson and Casey Anthony. As early as October 2017, there were claims of censorship, bullying, and "contest-rigging". In September 2019, comedian Stefan Heck publicized his discovery of the fact that replies through the app appeared as if they were sent by Renner himself in push notifications. After several users abused this feature, Renner asked Escapex to shut down the app.

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  Big data

  Big data primarily refers to data sets that are too large or complex to be dealt with by traditional data-processing software. Data with many entries (rows) offers greater statistical power, while data with higher complexity (more attributes or columns) may lead to a higher false discovery rate. Big data analysis challenges include capturing data, data storage, data analysis, search, sharing, transfer, visualization, querying, updating, information privacy, and data sources. Big data was originally associated with three key concepts: volume, variety, and velocity. The analysis of big data that have only volume, velocity, and variety can pose challenges in sampling. A fourth concept, veracity, which refers to the level of reliability of data, was thus added. Without sufficient investment in expertise to ensure big data veracity, the volume and variety of data can produce costs and risks that exceed an organization's capacity to create and capture value from big data. Current usage of the term big data tends to refer to the use of predictive analytics, user behavior analytics, or certain other advanced data analytics methods that extract value from big data, and seldom to a particular size of data set. "There is little doubt that the quantities of data now available are indeed large, but that's not the most relevant characteristic of this new data ecosystem." Analysis of data sets can find new correlations to "spot business trends, prevent diseases, combat crime and so on". Scientists, business executives, medical practitioners, advertising and governments alike regularly meet difficulties with large datasets in areas including Internet searches, fintech, healthcare analytics, geographic information systems, urban informatics, and business informatics. Scientists encounter limitations in e-Science work, including meteorology, genomics, connectomics, complex physics simulations, biology, and environmental research. The size and number of available data sets have grown rapidly as data is collected by devices such as mobile devices, cheap and numerous information-sensing Internet of things devices, aerial (remote sensing) equipment, software logs, cameras, microphones, radio-frequency identification (RFID) readers and wireless sensor networks. The world's technological per-capita capacity to store information has roughly doubled every 40 months since the 1980s; as of 2012, every day 2.5 exabytes (2.17×260 bytes) of data are generated. Based on an IDC report prediction, the global data volume was predicted to grow exponentially from 4.4 zettabytes to 44 zettabytes between 2013 and 2020. By 2025, IDC predicts there will be 163 zettabytes of data. According to IDC, global spending on big data and business analytics (BDA) solutions is estimated to reach $215.7 billion in 2021. Statista reported that the global big data market is forecasted to grow to $103 billion by 2027. In 2011 McKinsey & Company reported, if US healthcare were to use big data creatively and effectively to drive efficiency and quality, the sector could create more than $300 billion in value every year. In the developed economies of Europe, government administrators could save more than €100 billion ($149 billion) in operational efficiency improvements alone by using big data. And users of services enabled by personal-location data could capture $600 billion in consumer surplus. One question for large enterprises is determining who should own big-data initiatives that affect the entire organization. Relational database management systems and desktop statistical software packages used to visualize data often have difficulty processing and analyzing big data. The processing and analysis of big data may require "massively parallel software running on tens, hundreds, or even thousands of servers". What qualifies as "big data" varies depending on the capabilities of those analyzing it and their tools. Furthermore, expanding capabilities make big data a moving target. "For some organizations, facing hundreds of gigabytes of data for the first time may trigger a need to reconsider data management options. For others, it may take tens or hundreds of terabytes before data size becomes a significant consideration." == Definition == The term big data has been in use since the 1990s, with some giving credit to John Mashey for popularizing the term. Big data usually includes data sets with sizes beyond the ability of commonly used software tools to capture, curate, manage, and process data within a tolerable elapsed time. Big data philosophy encompasses unstructured, semi-structured and structured data; however, the main focus is on unstructured data. Big data "size" is a constantly moving target; as of 2012 ranging from a few dozen terabytes to many zettabytes of data. Big data requires a set of techniques and technologies with new forms of integration to reveal insights from datasets that are diverse, complex, and of a massive scale. Variability is often included as an additional quality of big data. A 2018 definition states "Big data is where parallel computing tools are needed to handle data", and notes, "This represents a distinct and clearly defined change in the computer science used, via parallel programming theories, and losses of some of the guarantees and capabilities made by Codd's relational model." In a comparative study of big datasets, Kitchin and McArdle found that none of the commonly considered characteristics of big data appear consistently across all of the analyzed cases. For this reason, other studies identified the redefinition of power dynamics in knowledge discovery as the defining trait. Instead of focusing on the intrinsic characteristics of big data, this alternative perspective pushes forward a relational understanding of the object claiming that what matters is the way in which data is collected, stored, made available and analyzed. === Big data vs. business intelligence === The growing maturity of the concept more starkly delineates the difference between "big data" and "business intelligence": Business intelligence uses applied mathematics tools and descriptive statistics with data with high information density to measure things, detect trends, etc. Big data uses mathematical analysis, optimization, inductive statistics, and concepts from nonlinear system identification to infer laws (regressions, nonlinear relationships, and causal effects) from large sets of data with low information density to reveal relationships and dependencies, or to perform predictions of outcomes and behaviors. == Characteristics == Big data can be described by the following characteristics: Volume The quantity of generated and stored data. The size of the data determines the value and potential insight, and whether it can be considered big data or not. The size of big data is usually larger than terabytes and petabytes. Variety The type and nature of the data. Earlier technologies like RDBMSs were capable to handle structured data efficiently and effectively. However, the change in type and nature from structured to semi-structured or unstructured challenged the existing tools and technologies. Big data technologies evolved with the prime intention to capture, store, and process the semi-structured and unstructured (variety) data generated with high speed (velocity), and huge in size (volume). Later, these tools and technologies were explored and used for handling structured data also but preferable for storage. Eventually, the processing of structured data was still kept as optional, either using big data or traditional RDBMSs. This helps in analyzing data towards effective usage of the hidden insights exposed from the data collected via social media, log files, sensors, etc. Big data draws from text, images, audio, video; plus it completes missing pieces through data fusion. Velocity The speed at which the data is generated and processed to meet the demands and challenges that lie in the path of growth and development. Big data is often available in real-time. Compared to small data, big data is produced more continually. Two kinds of velocity related to big data are the frequency of generation and the frequency of handling, recording, and publishing. Veracity The truthfulness or reliability of the data, which refers to the data quality and the data value. Big data must not only be large in size, but also must be reliable in order to achieve value in the analysis of it. The data quality of captured data can vary greatly, affecting an accurate analysis. Value The worth in information that can be achieved by the processing and analysis of large datasets. Value also can be measured by an assessment of the other qualities of big data. Value may also represent the profitability of information that is retrieved from the analysis of big data. Variability The characteristic of the changing formats, structure, or sources of big data. Big data can include structured, unstructured,

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  Optical sorting

  Optical sorting (sometimes called digital sorting) is the automated process of sorting solid products using cameras and/or lasers. Depending on the types of sensors used and the software-driven intelligence of the image processing system, optical sorters can recognize an object's color, size, shape, structural properties and chemical composition. The sorter compares objects to user-defined accept/reject criteria to identify and remove defective products and foreign material (FM) from the production line, or to separate product of different grades or types of materials. Optical sorters are in widespread use in the food industry worldwide, with the highest adoption in processing harvested foods such as potatoes, fruits, vegetables and nuts where it achieves non-destructive, 100 percent inspection in-line at full production volumes. The technology is also used in pharmaceutical manufacturing and nutraceutical manufacturing, tobacco processing, waste recycling and other industries. Compared to manual sorting, which is subjective and inconsistent, optical sorting helps improve product quality, maximize throughput and increase yields while reducing labor costs. == History == Optical sorting is an idea that first came out of the desire to automate industrial sorting of agricultural goods like fruits and vegetables. Before automated optical sorting technology was conceived in the 1930s, companies like Unitec were producing wooden machinery to assist in the mechanical sorting of fruit processing. In 1931, a company known as “the Electric Sorting Company” was incorporated and began the creation of the world’s first color sorters, which were being installed and used in Michigan’s bean industry by 1932. In 1937, optical sorting technology had advanced to allow for systems based on a two-color principle of selection. The next few decades saw the installation of new and improved sorting mechanisms, like gravity feed systems and the implementation of optical sorting in more agricultural industries. In the late 1960s, optical sorting began to be implemented to new industries beyond agriculture, like the sorting of ferrous and non-ferrous metals. By the 1990s, optical sorting was being used heavily in the sorting of solid wastes. With the large technological revolution happening in the late 1990s and early 2000s, optical sorters were being made more efficient via the implementation of new optical sensors, like CCD, UV, and IR cameras. Today, optical sorting is used in a wide variety of industries and, as such, is implemented with a varying selection of mechanisms to assist in that specific sorter’s task. == The sorting system == In general, optical sorters feature four major components: the feed system, the optical system, image processing software, and the separation system. The objective of the feed system is to spread products into a uniform monolayer so products are presented to the optical system evenly, without clumps, at a constant velocity. The optical system includes lights and sensors housed above and/or below the flow of the objects being inspected. The image processing system compares objects to user-defined accept/reject thresholds to classify objects and actuate the separation system. The separation system — usually compressed air for small products and mechanical devices for larger products, like whole potatoes — pinpoints objects while in-air and deflects the objects to remove into a reject chute while the good product continues along its normal trajectory. The ideal sorter to use depends on the application. Therefore, the product's characteristics and the user's objectives determine the ideal sensors, software-driven capabilities and mechanical platform. == Sensors == Optical sorters require a combination of lights and sensors to illuminate and capture images of the objects so the images can be processed. The processed images will determine if the material should be accepted or rejected. There are camera sorters, laser sorters and sorters that feature a combination of the two on one platform. Lights, cameras, lasers and laser sensors can be designed to function within visible light wavelengths as well as the infrared (IR) and ultraviolet (UV) spectrums. The optimal wavelengths for each application maximize the contrast between the objects to be separated. Cameras and laser sensors can differ in spatial resolution, with higher resolutions enabling the sorter to detect and remove smaller defects. === Cameras === Monochromatic cameras detect shades of gray from black to white and can be effective when sorting products with high-contrast defects. Sophisticated color cameras with high color resolution are capable of detecting millions of colors to better distinguish more subtle color defects. Trichromatic color cameras (also called three-channel cameras) divide light into three bands, which can include red, green and/or blue within the visible spectrum as well as IR and UV. The interaction of different materials with parts of the electromagnetic spectrum make these contrasts more evident than how they appear to the naked human eye. Coupled with intelligent software, sorters that feature cameras are capable of recognizing each object's color, size and shape; as well as the color, size, shape and location of a defect on a product. Some intelligent sorters even allow the user to define a defective product based on the total defective surface area of any given object. === Lasers === While cameras capture product information based primarily on material reflectance, lasers and their sensors are able to distinguish a material's structural properties along with their color. This structural property inspection allows lasers to detect a wide range of organic and inorganic foreign material such as insects, glass, metal, sticks, rocks and plastic; even if they are the same color as the good product. Lasers can be designed to operate within specific wavelengths of light; whether on the visible spectrum or beyond. For example, lasers can detect chlorophyll by stimulating fluorescence using specific wavelengths; which is a process that is very effective for removing foreign material from green vegetables. === Camera/laser combinations === Sorters equipped with cameras and lasers on one platform are generally capable of identifying the widest variety of attributes. Cameras are often better at recognizing color, size and shape while laser sensors identify differences in structural properties to maximize foreign material detection and removal. === Hyperspectral Imaging === Driven by the need to solve previously impossible sorting challenges, a new generation of sorters that feature multispectral and hyperspectral imaging Optical Sorters. Like trichromatic cameras, multispectral and hyperspectral cameras collect data from the electromagnetic spectrum. Unlike trichromatic cameras, which divide light into three bands, hyperspectral systems can divide light into hundreds of narrow bands over a continuous range that covers a vast portion of the electromagnetic spectrum. This opens the door for more detailed analysis that leads to a more consistent product. Using IR alone might detect some defects, but combining it with a broader range of the spectrum makes it more effective. Compared to the three data points per pixel collected by trichromatic cameras, hyperspectral cameras can collect hundreds of data points per pixel, which are combined to create a unique spectral signature (also called a fingerprint) for each object. When complemented by capable software intelligence, a hyperspectral sorter processes those fingerprints to enable sorting on the chemical composition of the product. This is an emerging area of chemometrics. == Software-driven intelligence == Once the sensors capture the object's response to the energy source, image processing is used to manipulate the raw data. The image processing extracts and categorizes information about specific features. The user then defines accept/reject thresholds that are used to determine what is good and bad in the raw data flow. The art and science of image processing lies in developing algorithms that maximize the effectiveness of the sorter while presenting a simple user-interface to the operator. Object-based recognition is a classic example of software-driven intelligence. It allows the user to define a defective product based on where a defect lies on the product and/or the total defective surface area of an object. It offers more control in defining a wider range of defective products. When used to control the sorter's ejection system, it can improve the accuracy of ejecting defective products. This improves product quality and increases yields. New software-driven capabilities are constantly being developed to address the specific needs of various applications. As computing hardware becomes more powerful, new software-driven advancements become possible. Some of these advancements enhance the effectivene

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  Clipmap

  In computer graphics, clipmapping is a method of clipping a mipmap to a subset of data pertinent to the geometry being displayed. This is useful for loading as little data as possible when memory is limited, such as on a graphics processing unit. The technique is used for LODing in NVIDIA’s implementation of voxel cone tracing. The high-resolution levels of the mipmapped scene representation are clipped to a region near the camera, while lower resolution levels are clipped further away. == MegaTexture == MegaTexture is a clipmap implementation developed by id Software. It was introduced in their id Tech 4 engine and also appeared in id Tech 5 and id Tech 6 before being removed in id Tech 7. MegaTexture is a texture allocation technique that uses a single, extremely large texture rather than repeating multiple smaller textures. It is also featured in Splash Damage's game Enemy Territory: Quake Wars, and was developed by id Software former technical director John Carmack. MegaTexture employs a single large texture space for static terrain. The texture is stored on removable media or a computer's hard drive and streamed as needed, allowing large amounts of detail and variation over a large area with comparatively little RAM usage. Depending on the pixel resolution per square meter, covering a large area could require several gigabytes of memory. However, RAM is also filled by the rest of the game and the underlying operating system, limiting the amount available for texturing. As the player moves around the game, different sections of the MegaTexture are loaded into memory. They are then scaled to the correct size and applied to the 3D models of the terrain. Id has presented a more advanced technique that builds upon the MegaTexture idea and virtualizes both the geometry and the textures to obtain unique geometry down to the equivalent of the texel: the sparse voxel octree (SVO). It works by raycasting the geometry represented by voxels (instead of triangles) stored in an octree. The goal is to stream parts of the octree into video memory, going further down along the tree for nearby objects to give them more details, and to use higher level, larger voxels for farther objects, which give an automatic level of detail (LOD) system for both geometry and textures at the same time. The geometric detail that can be obtained using this method is nearly infinite, which removes the need for faking 3-dimensional details with techniques such as normal mapping. Despite that most voxel rendering tests use very large amounts of memory (up to several GB), Jon Olick of id Software claimed the technology is able to compress such SVO to 1.15 bits per voxel of position data. == Virtual texturing == Unlike clipmaps, which clip each mip level around a viewpoint-dependent clipcenter and therefore work best for terrain, virtual texturing preprocesses texture data into equally sized tiles that can be streamed for arbitrary textured geometry. Rage, powered by the id Tech 5 engine, uses a more advanced technique called virtual texturing. Textures can measure up to 128000×128000 pixels and are also used for in-game models and sprites, etc. and not just the terrain. Wolfenstein: The New Order and the 2016 version of Doom also use these. Carmageddon: Reincarnation also uses virtual texturing, though unlike id's virtual texturing system, which is designed for unique texture-mapping everywhere, their system is designed to use storage space sparingly while still offering good blend of texture variation and resolution.

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  Generatrix

  In geometry, a generatrix () or describent is a point, curve or surface that, when moved along a given path, generates a new shape. The path directing the motion of the generatrix motion is called a directrix or dirigent. == Examples == A cone can be generated by moving a line (the generatrix) fixed at the future apex of the cone along a closed curve (the directrix); if that directrix is a circle perpendicular to the line connecting its center to the apex, the motion is rotation around a fixed axis and the resulting shape is a circular cone. The generatrix of a cylinder, a limiting case of a cone, is a line that is kept parallel to some axis.

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  Sanchar Saathi

  Sanchar Saathi (lit. 'Communication Partner' or 'Communication Companion') is an Indian state-owned app and web portal, operated by the Department of Telecommunications, designed to assist Indian mobile users in tracking and blocking stolen or lost mobile devices. In late 2025, a government order requiring Sanchar Saathi to be pre-installed on all mobile devices sold nationwide, with explicit provisions on preventing users from deleting the app or disabling any of its broad functionalities, triggered widespread backlash. The order was subsequently withdrawn. == Background == The Telecommunications Act 2023 introduced an exceptionally broad definition of the term "telecommunications" and conferred wide-ranging powers on the government. Although the Department of Telecommunications (DoT) assured reporters that this definition would not be used to justify government overreach, a November 2024 amendment to the Telecom Cyber Security Rules expanded it further and introduced the concept of the Telecommunication Identifier User Entity (TIEU), enabling users to be personally identified through their phone numbers. Sanchar Saathi was launched amid a widespread rise in cybercrime and hacking, as part of the Indian government's effort to prevent stolen phones from being used for fraud and to promote a state-backed application. In an official statement, the DoT said, "India has big second-hand mobile device market. Cases have also been observed where stolen or blacklisted devices are being re-sold. It makes the purchaser abettor in crime and causes financial loss to them." == Launch == Sanchar Saathi was originally launched as a web portal in May 2023. It was later launched as a mobile app in January 2025. Describing itself as a "citizen-centric" safety tool, Sanchar Saathi allows users to check a device's IMEI, report and block lost or stolen phones, and flag suspected fraud communications. Under Sanchar Saathi's privacy policy, it can make and manage phone calls, view and send messages, read call logs, access photos and files, access the location and camera of the device in which the app is used, as well as read and write into the device's storage. According to official government data, by December 2025, the Sanchar Saathi app had helped recover more than 700,000 lost and stolen mobile devices across India. Users report around 2,000 fraud incidents through the app each day. == Pre-installation controversy == On 28 November 2025, the Bharatiya Janata Party government, led by prime minister Narendra Modi, privately ordered phone manufacturers, including Apple, Samsung, Xiaomi, Vivo, Oppo, among others, to pre-install the Sanchar Saathi app on new devices sold in the country, alongside mandating that old devices get issued a software update for the installation of the app. The order had a 90-day deadline and further included explicit provisions to ensure that the app is to be "readily visible and accessible to the end users at the time of first use or device setup" and that users should neither be able to delete the app nor disable or restrict any of its broad functionalities. The order caused widespread political backlash. K. C. Venugopal, a general secretary of the main opposition party, the Indian National Congress (or simply the Congress), called the order "beyond unconstitutional" and said, "A pre-loaded government app that cannot be uninstalled is a dystopian tool to monitor every Indian. It is a means to watch over every movement, interaction and decision of each citizen", adding, "Big Brother cannot watch us." Another Congress general secretary, Priyanka Gandhi, termed Sanchar Saathi a "snooping app", and attacked the government for "turning this country into a dictatorship". Uddhav Thackeray, former chief minister of Maharashtra, compared Sanchar Saathi to the Pegasus spyware. Sanjay Hegde, a senior advocate at the Supreme Court of India, said "Here in the garb of security, the intrusion is vast, unfettered, unguided and is totally disproportionate. The app ought to be struck down on that account". The Internet Freedom Foundation (IFF), an Indian digital rights advocacy organisation, said, "Forcing every smartphone to carry a permanent government app for a simple verification task is excessive and violates the Puttaswamy proportionality standard", referring to Puttaswamy v. Union of India, a 2017 landmark decision of the Supreme Court, which asserted that the right to privacy should be protected as a fundamental right. The IFF further said, "For this to work in practice, the app will almost certainly need system level or root level access, similar to carrier or OEM system apps, so that it cannot be disabled. That design choice erodes the protections that normally prevent one app from peering into the data of others, and turns Sanchar Saathi into a permanent, non-consensual point of access sitting inside the operating system of every Indian smartphone user." Moreover, the organisation said that while the app was being "framed as a benign IMEI checker", a server-side update could allow the app to engage in "client side scanning for 'banned' applications, flag VPN usage, correlate SIM activity, or trawl SMS logs in the name of fraud detection. Nothing in the order constrains these possibilities." In reaction to the controversy, Jyotiraditya Scindia, the union minister of communications, said, "There is no snooping or call monitoring", adding, "Obviously you can delete it. There is no problem. This is a matter of customer protection. It is not mandatory. If you don't want to register, and don't want to use the app, don't use it; don't register, and it will lay dormant." Scindia compared the app to other pre-installed mobile apps such as Google Maps, which he said could be deleted if users wished so. However, contrary to Scindia's statement, on many phone brands, such pre-installed apps cannot be deleted, although users can disable them. Furthermore, upon enquiry, Scindia did not clarify whether his remarks applied to the app after the order took effect, making no comment on the provision in the order that would prevent users from deleting the app. When Congress member Renuka Chowdhury submitted an adjournment motion notice in the Rajya Sabha seeking the suspension of all other matters to discuss the Sanchar Saathi issue, Kiren Rijiju, the union minister of parliamentary affairs, accused the opposition of "manufacturing issues" to stall session proceedings. By 2 December, it had been reported that Apple did not plan to comply with the order, citing privacy and security concerns for the iOS ecosystem and the fact that the order would violate its internal policy against the pre-installation of third-party software in iPhones. Although it was clarified that Apple did not intend to take the matter to court or publicly oppose the government, it was said that Apple "can't do this. Period." The order would have also required Google to create a custom version of Android solely for India which would include the Sanchar Saathi app, a requirement described to "not be acceptable to the company". Following the backlash, the order was revoked on 3 December 2025. In a press release, the government said, "Given Sanchar Saathi's increasing acceptance, Government has decided not to make the pre-installation mandatory for mobile manufacturers".

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  Trazzler

  Trazzler is a travel destination app that specializes in unique and local destinations. The initial concept was developed by Adam Rugel and Biz Stone in 2006 at Twitter's original offices under the name "71 miles". More than 10,000 writers and photographers have contributed and more than $350,000 in freelance contracts have been issued as a result of Trazzeler's weekly writing and photography contests. Investors in the company include SV Angel, AOL Founder Steve Case, and the Twitter founders, Evan Williams, Jack Dorsey, and Biz Stone. The company's partners are the City of Chicago, Hawaii Tourism Authority, Fairmont Hotels & Resorts, Salon.com, and Air New Zealand. Trazzler is designed for use on the iOS, Android, and Facebook.

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  IEEE Transactions on Visualization and Computer Graphics

  IEEE Transactions on Visualization and Computer Graphics is a peer-reviewed scientific journal published by the IEEE Computer Society. It covers subjects related to computer graphics and visualization techniques, systems, software, hardware, and user interface issues. TVCG has been considered the top journal in the field of visualization. Since 2011, TVCG has allowed authors to present recently accepted papers at partner conferences. These include: IEEE Visualization (VIS), including VAST, InfoVis, and SciVis. IEEE Virtual Reality Conference (IEEE VR) IEEE International Symposium on Mixed and Augmented Reality (ISMAR) ACM Symposium on Interactive 3D Graphics and Games (I3D) IEEE Pacific Visualization Conference (IEEE PacificVis) ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA) Eurographics Symposium on Geometry Processing (SGP) Pacific Graphics Conference (PG) Eurovis - The EG and VGTC Conference on Visualization Graphics Interfaces (GI)

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  Roadie (app)

  Roadie Inc. is an American package delivery company for business and private same-day, urgent and scheduled delivery in the United States. The company was founded in 2014 and launched its web and mobile apps in January 2015. As of September 2021, it reported having over 200,000 drivers covering more than 20,000 zip codes. Roadie states it matches gig drivers with deliveries that are directed along the routes they plan to travel. Major customers include The Home Depot, Walmart, Tractor Supply Company, Best Buy and Delta Air Lines. In September 2021, UPS entered into an agreement to acquire Roadie for an undisclosed amount with the transaction expected to be closed in the fourth quarter. == History == Roadie was founded by Marc Gorlin, a co-founder of Kabbage and founder of VerticalOne and Pretty Good Privacy, as a same-day and urgent delivery company in 2014. In January 2015, Roadie launched the first consumer to consumer (C2C) version of its app with a Series A funding round of $10 million. In February, Roadie announced a partnership with Waffle House to designate its restaurants "Roadie Roadhouses", offering a neutral meeting place for drivers and senders. Drivers receive free food and drink through the partnership. In May, late-night host Jimmy Kimmel discussed the Roadie-Waffle House relationship in an opening monologue on Jimmy Kimmel Live!. Roadie's driver network expanded significantly as a result. Roadie closed a Series B round of funding in June, raising $15 million, and its first business to business (B2B) app version launched that November. In 2015, Delta Air Lines signed an agreement with Roadie to deliver mishandled luggage, becoming Roadie’s first enterprise customer. Roadie launched a pilot program with Delta at Daytona Beach International Airport. Since then, the relationship has expanded to include over 70 airports around the United States and a first mile/last mile line haul relationship with Delta Cargo. In 2017, the company signed a deal with The Home Depot, also based in Atlanta, and in February 2019, closed a Series C round of funding. In October 2019, Roadie and Delta Cargo announced a partnership to create a same-day cross-country delivery offering, DASH Door-to-Door, the first of its kind from a U.S. passenger airline. Tractor Supply Company became the first general merchandise retailer to offer same-day delivery from every store in April 2020 through Roadie. In September 2021, UPS entered an agreement to acquire Roadie for an undisclosed amount. The transaction was expected to close in the fourth quarter of 2021. Roadies, which at the time reported having 200,000 operators serving over 20,000 ZIP Codes, was expected to continue operations under its name as a separate company with no transfer of packages between the UPS and Roadies networks. The relationship between the companies goes back several years with UPS being an early investor. Earlier in 2021, UPS had begun a pilot program testing same-day deliveries via Roadies. == Operations == === On-the-way model === Roadie’s app works by connecting drivers with senders, businesses or consumers who have items that need to be delivered. Deliveries within the app are referred to as "Gigs", which Gorlin said was inspired by live music road crews, also known as roadies. A sender creates a Gig on Roadie's web app or via its API. Drivers then review deliveries in their area on their mobile app and may choose to offer to take on individual or groups of deliveries along the same route. Gigs are then assigned to drivers by Roadie's algorithm. According to the company, this model encourages drivers to choose Gigs that align with their planned schedules and routes. Roadie calls this its "on-the-way" delivery model. The go-to-market approach taken by Roadie also differs from its competitors. Rather than launching in major cities and sequentially adding new markets city-by-city, Roadie launched nationwide from its inception. The company relies on retail and airline partners to drive volume of deliveries in individual markets, which in turn builds up a network of drivers in those areas, making it easier for small businesses and consumers to send deliveries as well. This strategy allows Roadie to reach smaller cities and towns in rural or exurban communities, traditionally difficult markets for delivery providers to serve. === Service lines === Roadie’s platform is most popular for same-day, on-demand or scheduled first mile/last mile delivery, especially delivery from stores and warehouses. Some retailers also use it for returns and reverse logistics, moving inventory, and hot shot shipping. Roadie operates 1-hour grocery delivery for Walmart, and delivers perishable food items for others including small, independent retailers. The on-the-way model complements the grocery industry’s just in time model, making last-mile deliveries that do not break the cold chain. === Cross-country same-day delivery === In October 2019, Roadie and Delta Cargo launched DASH Door-to-Door, a 24/7 door-to-door pick-up and delivery service. Roadie handles the first and last mile and Delta manages the line haul via passenger flights. The service launched originally from Atlanta to 55 cities and is an industry-first for a US commercial airline. === Promotion, awards and corporate citizenship === In September 2015, Roadie announced a partnership with Atlanta-based musician Ludacris, to promote the app. Following the devastation caused by flooding in Baton Rouge in 2016, Roadie offered free pickup and delivery for all deliveries traveling to and from the Baton Rouge area. In December 2020, Walmart named Roadie its top delivery partner for "Highest Driver Customer Satisfaction" and "Highest Net Promoter Score", after expanding into general merchandise deliveries as well as grocery that same year.

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  Data commingling

  Data commingling, in computer science, occurs when different items or kinds of data are stored in such a way that they become commonly accessible when they are supposed to remain separated. In cloud computing, this can occur where different customer data sits on the same server. Data that is commingled can present a security vulnerability. Data commingling can also occur due to high speed data transmission mixing. In this situation, data of one security level can inadvertently or purposely be mixed with data of a lower or higher security level on the same transmission portal. Portal vehicles can be wire, fiber optics, microwave or various radio frequency transmission portals. This commingling can cause breaches of security and become a source of legal issues to any entity, corporation or individual. Data commingling can also occur when personal computers and personal software programs are used for business, security, government, etc. uses. In the early formulation stages of entities, non-profit or profit corporations, LLC's, LLP's, etc., the creation and use of stand-alone computers and stand-alone networks, "absolutely unconnected" to involved individuals, is the easiest, and safest way to prevent Data Commingling.

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  Cross-entropy method

  The cross-entropy (CE) method is a Monte Carlo method for importance sampling and optimization. It is applicable to both combinatorial and continuous problems, with either a static or noisy objective. The method approximates the optimal importance sampling estimator by repeating two phases: Draw a sample from a probability distribution. Minimize the cross-entropy between this distribution and a target distribution to produce a better sample in the next iteration. Reuven Rubinstein developed the method in the context of rare-event simulation, where tiny probabilities must be estimated, for example in network reliability analysis, queueing models, or performance analysis of telecommunication systems. The method has also been applied to the traveling salesman, quadratic assignment, DNA sequence alignment, max-cut and buffer allocation problems. == Estimation via importance sampling == Consider the general problem of estimating the quantity ℓ = E u [ H ( X ) ] = ∫ H ( x ) f ( x ; u ) d x {\displaystyle \ell =\mathbb {E} _{\mathbf {u} }[H(\mathbf {X} )]=\int H(\mathbf {x} )\,f(\mathbf {x} ;\mathbf {u} )\,{\textrm {d}}\mathbf {x} } , where H {\displaystyle H} is some performance function and f ( x ; u ) {\displaystyle f(\mathbf {x} ;\mathbf {u} )} is a member of some parametric family of distributions. Using importance sampling this quantity can be estimated as ℓ ^ = 1 N ∑ i = 1 N H ( X i ) f ( X i ; u ) g ( X i ) {\displaystyle {\hat {\ell }}={\frac {1}{N}}\sum _{i=1}^{N}H(\mathbf {X} _{i}){\frac {f(\mathbf {X} _{i};\mathbf {u} )}{g(\mathbf {X} _{i})}}} , where X 1 , … , X N {\displaystyle \mathbf {X} _{1},\dots ,\mathbf {X} _{N}} is a random sample from g {\displaystyle g\,} . For positive H {\displaystyle H} , the theoretically optimal importance sampling density (PDF) is given by g ∗ ( x ) = H ( x ) f ( x ; u ) / ℓ {\displaystyle g^{}(\mathbf {x} )=H(\mathbf {x} )f(\mathbf {x} ;\mathbf {u} )/\ell } . This, however, depends on the unknown ℓ {\displaystyle \ell } . The CE method aims to approximate the optimal PDF by adaptively selecting members of the parametric family that are closest (in the Kullback–Leibler sense) to the optimal PDF g ∗ {\displaystyle g^{}} . == Generic CE algorithm == Choose initial parameter vector v ( 0 ) {\displaystyle \mathbf {v} ^{(0)}} ; set t = 1. Generate a random sample X 1 , … , X N {\displaystyle \mathbf {X} _{1},\dots ,\mathbf {X} _{N}} from f ( ⋅ ; v ( t − 1 ) ) {\displaystyle f(\cdot ;\mathbf {v} ^{(t-1)})} Solve for v ( t ) {\displaystyle \mathbf {v} ^{(t)}} , where v ( t ) = argmax v ⁡ 1 N ∑ i = 1 N H ( X i ) f ( X i ; u ) f ( X i ; v ( t − 1 ) ) log ⁡ f ( X i ; v ) {\displaystyle \mathbf {v} ^{(t)}=\mathop {\textrm {argmax}} _{\mathbf {v} }{\frac {1}{N}}\sum _{i=1}^{N}H(\mathbf {X} _{i}){\frac {f(\mathbf {X} _{i};\mathbf {u} )}{f(\mathbf {X} _{i};\mathbf {v} ^{(t-1)})}}\log f(\mathbf {X} _{i};\mathbf {v} )} If convergence is reached then stop; otherwise, increase t by 1 and reiterate from step 2. In several cases, the solution to step 3 can be found analytically. Situations in which this occurs are When f {\displaystyle f\,} belongs to the natural exponential family When f {\displaystyle f\,} is discrete with finite support When H ( X ) = I { x ∈ A } {\displaystyle H(\mathbf {X} )=\mathrm {I} _{\{\mathbf {x} \in A\}}} and f ( X i ; u ) = f ( X i ; v ( t − 1 ) ) {\displaystyle f(\mathbf {X} _{i};\mathbf {u} )=f(\mathbf {X} _{i};\mathbf {v} ^{(t-1)})} , then v ( t ) {\displaystyle \mathbf {v} ^{(t)}} corresponds to the maximum likelihood estimator based on those X k ∈ A {\displaystyle \mathbf {X} _{k}\in A} . == Continuous optimization—example == The same CE algorithm can be used for optimization, rather than estimation. Suppose the problem is to maximize some function S {\displaystyle S} , for example, S ( x ) = e − ( x − 2 ) 2 + 0.8 e − ( x + 2 ) 2 {\displaystyle S(x)={\textrm {e}}^{-(x-2)^{2}}+0.8\,{\textrm {e}}^{-(x+2)^{2}}} . To apply CE, one considers first the associated stochastic problem of estimating P θ ( S ( X ) ≥ γ ) {\displaystyle \mathbb {P} _{\boldsymbol {\theta }}(S(X)\geq \gamma )} for a given level γ {\displaystyle \gamma \,} , and parametric family { f ( ⋅ ; θ ) } {\displaystyle \left\{f(\cdot ;{\boldsymbol {\theta }})\right\}} , for example the 1-dimensional Gaussian distribution, parameterized by its mean μ t {\displaystyle \mu _{t}\,} and variance σ t 2 {\displaystyle \sigma _{t}^{2}} (so θ = ( μ , σ 2 ) {\displaystyle {\boldsymbol {\theta }}=(\mu ,\sigma ^{2})} here). Hence, for a given γ {\displaystyle \gamma \,} , the goal is to find θ {\displaystyle {\boldsymbol {\theta }}} so that D K L ( I { S ( x ) ≥ γ } ‖ f θ ) {\displaystyle D_{\mathrm {KL} }({\textrm {I}}_{\{S(x)\geq \gamma \}}\|f_{\boldsymbol {\theta }})} is minimized. This is done by solving the sample version (stochastic counterpart) of the KL divergence minimization problem, as in step 3 above. It turns out that parameters that minimize the stochastic counterpart for this choice of target distribution and parametric family are the sample mean and sample variance corresponding to the elite samples, which are those samples that have objective function value ≥ γ {\displaystyle \geq \gamma } . The worst of the elite samples is then used as the level parameter for the next iteration. This yields the following randomized algorithm that happens to coincide with the so-called Estimation of Multivariate Normal Algorithm (EMNA), an estimation of distribution algorithm. === Pseudocode === // Initialize parameters μ := −6 σ2 := 100 t := 0 maxits := 100 N := 100 Ne := 10 // While maxits not exceeded and not converged while t < maxits and σ2 > ε do // Obtain N samples from current sampling distribution X := SampleGaussian(μ, σ2, N) // Evaluate objective function at sampled points S := exp(−(X − 2) ^ 2) + 0.8 exp(−(X + 2) ^ 2) // Sort X by objective function values in descending order X := sort(X, S) // Update parameters of sampling distribution via elite samples μ := mean(X(1:Ne)) σ2 := var(X(1:Ne)) t := t + 1 // Return mean of final sampling distribution as solution return μ == Related methods == Simulated annealing Genetic algorithms Harmony search Estimation of distribution algorithm Tabu search Natural Evolution Strategy Ant colony optimization algorithms

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  Molecular graphics

  Molecular graphics is the discipline and philosophy of studying molecules and their properties through graphical representation. IUPAC limits the definition to representations on a "graphical display device". Ever since Dalton's atoms and Kekulé's benzene, there has been a rich history of hand-drawn atoms and molecules, and these representations have had an important influence on modern molecular graphics. Colour molecular graphics are often used on chemistry journal covers artistically. == History == Prior to the use of computer graphics in representing molecular structure, Robert Corey and Linus Pauling developed a system for representing atoms or groups of atoms from hard wood on a scale of 1 inch = 1 angstrom connected by a clamping device to maintain the molecular configuration. These early models also established the CPK coloring scheme that is still used today to differentiate the different types of atoms in molecular models (e.g. carbon = black, oxygen = red, nitrogen = blue, etc). This early model was improved upon in 1966 by W.L. Koltun and are now known as Corey-Pauling-Koltun (CPK) models. The earliest efforts to produce models of molecular structure was done by Project MAC using wire-frame models displayed on a cathode ray tube in the mid 1960s. In 1965, Carroll Johnson distributed the Oak Ridge thermal ellipsoid plot (ORTEP) that visualized molecules as a ball-and-stick model with lines representing the bonds between atoms and ellipsoids to represent the probability of thermal motion. Thermal ellipsoid plots quickly became the de facto standard used in the display of X-ray crystallography data, and are still in wide use today. The first practical use of molecular graphics was a simple display of the protein myoglobin using a wireframe representation in 1966 by Cyrus Levinthal and Robert Langridge working at Project MAC. Among the milestones in high-performance molecular graphics was the work of Nelson Max in "realistic" rendering of macromolecules using reflecting spheres. Initially much of the technology concentrated on high-performance 3D graphics. During the 1970s, methods for displaying 3D graphics using cathode ray tubes were developed using continuous tone computer graphics in combination with electro-optic shutter viewing devices. The first devices used an active shutter 3D system, generating different perspective views for the left and right channel to provide the illusion of three-dimensional viewing. Stereoscopic viewing glasses were designed using lead lanthanum zirconate titanate (PLZT) ceramics as electronically controlled shutter elements. Active 3D glasses require batteries and work in concert with the display to actively change the presentation by the lenses to the wearer's eyes. Many modern 3D glasses use a passive, polarized 3D system that enables the wearer to visualize 3D effects based on their own perception. Passive 3D glasses are more common today since they are less expensive. The requirements of macromolecular crystallography also drove molecular graphics because the traditional techniques of physical model-building could not scale. The first two protein structures solved by molecular graphics without the aid of the Richards' Box were built with Stan Swanson's program FIT on the Vector General graphics display in the laboratory of Edgar Meyer at Texas A&M University: First Marge Legg in Al Cotton's lab at A&M solved a second, higher-resolution structure of staph. nuclease (1975) and then Jim Hogle solved the structure of monoclinic lysozyme in 1976. A full year passed before other graphics systems were used to replace the Richards' Box for modelling into density in 3-D. Alwyn Jones' FRODO program (and later "O") were developed to overlay the molecular electron density determined from X-ray crystallography and the hypothetical molecular structure. === Timeline === == Types == === Ball-and-stick models === In the ball-and-stick model, atoms are drawn as small sphered connected by rods representing the chemical bonds between them. === Space-filling models === In the space-filling model, atoms are drawn as solid spheres to suggest the space they occupy, in proportion to their van der Waals radii. Atoms that share a bond overlap with each other. === Surfaces === In some models, the surface of the molecule is approximated and shaded to represent a physical property of the molecule, such as electronic charge density. === Ribbon diagrams === Ribbon diagrams are schematic representations of protein structure and are one of the most common methods of protein depiction used today. The ribbon shows the overall path and organization of the protein backbone in 3D, and serves as a visual framework on which to hang details of the full atomic structure, such as the balls for the oxygen atoms bound to the active site of myoglobin in the adjacent image. Ribbon diagrams are generated by interpolating a smooth curve through the polypeptide backbone. α-helices are shown as coiled ribbons or thick tubes, β-strands as arrows, and non-repetitive coils or loops as lines or thin tubes. The direction of the polypeptide chain is shown locally by the arrows, and may be indicated overall by a colour ramp along the length of the ribbon.

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  Supertoroid

  In geometry and computer graphics, a supertoroid or supertorus is usually understood to be a family of doughnut-like surfaces (technically, a topological torus) whose shape is defined by mathematical formulas similar to those that define the superellipsoids. The plural of "supertorus" is either supertori or supertoruses. The family was described and named by Alan Barr in 1994. Barr's supertoroids have been fairly popular in computer graphics as a convenient model for many objects, such as smooth frames for rectangular things. One quarter of a supertoroid can provide a smooth and seamless 90-degree joint between two superquadric cylinders. However, they are not algebraic surfaces (except in special cases). == Formulas == Alan Barr's supertoroids are defined by parametric equations similar to the trigonometric equations of the torus, except that the sine and cosine terms are raised to arbitrary powers. Namely, the generic point P(u, v) of the surface is given by P ( u , v ) = ( X ( u , v ) Y ( u , v ) Z ( u , v ) ) = ( ( a + C u s ) C v t ( b + C u s ) S v t S u s ) {\displaystyle P(u,v)=\left({\begin{array}{c}X(u,v)\\Y(u,v)\\Z(u,v)\end{array}}\right)=\left({\begin{array}{c}(a+C_{u}^{s})C_{v}^{t}\\(b+C_{u}^{s})S_{v}^{t}\\S_{u}^{s}\end{array}}\right)} where C θ ε = sgn ⁡ ( cos ⁡ θ ) | cos ⁡ θ | ε , S θ ε = sgn ⁡ ( sin ⁡ θ ) | sin ⁡ θ | ε , {\displaystyle {\begin{aligned}C_{\theta }^{\varepsilon }&=\operatorname {sgn} (\cos \theta )\,\left|\,\cos \theta \,\right|^{\varepsilon },\\S_{\theta }^{\varepsilon }&=\operatorname {sgn} (\sin \theta )\ \left|\,\sin \theta \ \right|^{\varepsilon },\end{aligned}}} sgn is the sign function, and the parameters u, v range from 0 to 360 degrees (0 to 2π radians). In these formulas, the parameter s > 0 controls the "squareness" of the vertical sections, t > 0 controls the squareness of the horizontal sections, and a, b ≥ 1 are the major radii in the x and y directions. With s = t = 1 and a = b = R one obtains the ordinary torus with major radius R and minor radius 1, with the center at the origin and rotational symmetry about the z-axis. In general, the supertorus defined as above spans the intervals: − ( a + 1 ) ≤ x ≤ + ( a + 1 ) − ( b + 1 ) ≤ y ≤ + ( b + 1 ) − 1 ≤ z ≤ + 1 {\displaystyle {\begin{array}{rcccl}-(a+1)&\leq &x&\leq &+(a+1)\\[4pt]-(b+1)&\leq &y&\leq &+(b+1)\\[4pt]-1&\leq &z&\leq &+1\end{array}}} The whole shape is symmetric about the planes x = 0, y = 0, and z = 0. The hole runs in the z direction and spans the intervals − ( a − 1 ) ≤ x ≤ + ( a − 1 ) − ( b − 1 ) ≤ y ≤ + ( b − 1 ) − ∞ ≤ z ≤ + ∞ {\displaystyle {\begin{array}{rcccl}-(a-1)&\leq &x&\leq &+(a-1)\\[4pt]-(b-1)&\leq &y&\leq &+(b-1)\\[4pt]-\infty &\leq &z&\leq &+\infty \end{array}}} A curve of constant u on this surface is a horizontal Lamé curve with exponent ⁠ 2 t , {\displaystyle {\tfrac {2}{t}},} ⁠ scaled in x and y and displaced in z. A curve of constant v, projected on the plane x = 0 or y = 0, is a Lamé curve with exponent ⁠ 2 s , {\displaystyle {\tfrac {2}{s}},} ⁠ scaled and horizontally shifted. If v = 0, the curve is planar and spans the intervals: a − 1 ≤ x ≤ a + 1 − 1 ≤ z ≤ + 1 {\displaystyle {\begin{array}{rcccl}a-1&\leq &x&\leq &a+1\\[4pt]-1&\leq &z&\leq &+1\end{array}}} and similarly if v = 90°, 180°, 270°. The curve is also planar if a = b. In general, if a ≠ b and v is not a multiple of 90 degrees, the curve of constant v will not be planar; and, conversely, a vertical plane section of the supertorus will not be a Lamé curve. The basic supertoroid shape defined above is often modified by non-uniform scaling to yield supertoroids of specific width, length, and vertical thickness. == Plotting code == The following GNU Octave code generates plots of a supertorus:

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