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:
Multiple satellite imaging
Multiple satellite imaging is the process of using multiple satellites to gather more information than a single satellite so that a better estimate of the desired source is possible. Something that cannot be resolved with one telescope might be visible with two or more telescopes. == Background == Interferometry is the process of combining waves in such a way that they constructively interfere. When two or more independent sources detect a signal at the same given frequency those signals can be combined and the result is better than each one individually. An overview of Astronomical interferometers and a History of astronomical interferometry can be referenced from their respective pages. The NASA Origins Program was created in the 1990s to ultimately search for the origin of the universe. The theory that the Origins Program is based on is: since light travels at a constant speed until it is absorbed by something; there is still light that was part of the first light ever created traveling about the universe and ultimately some of that light is coming in the general direction of Earth. So a satellite system capable of collecting light from the beginning of the universe would be able to tell us more about where we came from. There is also the constant search for life in other worlds. A satellite system using the interferometric technologies mentioned above would be able to have a much higher resolution than any of the current deep space imaging systems. == Future == NASA is currently focused on the Vision for Space Exploration and has reduced current funding for scientific unmanned space exploration in favor of human exploration. These budget cuts have slowed the multiple satellite imaging development and relevant scientific missions as Project Prometheus and Terrestrial Planet Finder have ended as well but research continues.
Interstellar communication
Interstellar communication is the transmission of signals between planetary systems. Sending interstellar messages is potentially much easier than interstellar travel, being possible with technologies and equipment which are currently available. However, the distances from Earth to other potentially inhabited systems introduce prohibitive delays, assuming the limitations of the speed of light. Even an immediate reply to radio communications sent to stars tens of thousands of light-years away would take many human generations to arrive. == Radio == The SETI project has for the past several decades been conducting a search for signals being transmitted by extraterrestrial life located outside the Solar System, primarily in the radio frequencies of the electromagnetic spectrum. Special attention has been given to the Water Hole, the frequency of one of neutral hydrogen's absorption lines, due to the low background noise at this frequency and its symbolic association with the basis for what is likely to be the most common system of biochemistry (but see alternative biochemistry). The regular radio pulses emitted by pulsars were briefly thought to be potential intelligent signals; the first pulsar to be discovered was originally designated "LGM-1", for "Little Green Men." They were quickly determined to be of natural origin, however. Several attempts have been made to transmit signals to other stars as well. (See "Realized projects" at Active SETI.) One of the earliest and most famous was the 1974 radio message sent from the largest radio telescope in the world, the Arecibo Observatory in Puerto Rico. An extremely simple message was aimed at a globular cluster of stars known as M13 in the Milky Way Galaxy and at a distance of 30,000 light years from the Solar System. These efforts have been more symbolic than anything else, however. Further, a possible answer needs double the travel time, i.e. tens of years (near stars) or 60,000 years (M13). == Other methods == It has also been proposed that higher frequency signals, such as lasers operating at visible light frequencies, may prove to be a fruitful method of interstellar communication; at a given frequency it takes surprisingly small energy output for a laser emitter to outshine its local star from the perspective of its target. Other more exotic methods of communication have been proposed, such as modulated neutrino or gravitational wave emissions. These would have the advantage of being essentially immune to interference by intervening matter. Sending physical mail packets between stars may prove to be optimal for many applications. While mail packets would likely be limited to speeds far below that of electromagnetic or other light-speed signals (resulting in very high latency), the amount of information that could be encoded in only a few tons of physical matter could more than make up for it in terms of average bandwidth. The possibility of using interstellar messenger probes for interstellar communication — known as Bracewell probes — was first suggested by Ronald N. Bracewell in 1960, and the technical feasibility of this approach was demonstrated by the British Interplanetary Society's starship study Project Daedalus in 1978. Starting in 1979, Robert Freitas advanced arguments for the proposition that physical space-probes provide a superior mode of interstellar communication to radio signals, then undertook telescopic searches for such probes in 1979 and 1982.
Digital edition
A digital edition is an online magazine or online newspaper delivered in electronic form which is formatted identically to the print version. Digital editions are often called digital facsimiles to underline the likeness to the print version. Digital editions have the benefit of reduced cost to the publisher and reader by avoiding the time and the expense to print and deliver paper edition. This format is considered more environmentally friendly due to the reduction of paper and energy use. These editions also often feature interactive elements such as hyperlinks both within the publication itself and to other internet resources, search option and bookmarking, and can also incorporate multimedia such as video or animation to enhance articles themselves or for advertisement purposes. Some delivery methods also include animation and sound effects that replicate turning of the page to further enhance the experience of their print counterparts. Magazine publishers have traditionally relied on two revenue sources: selling ads and selling magazines. Additionally some publishers are using other electronic publication methods such as RSS to reach out to readers and inform them when new digital editions are available. Current technologies are generally either reader-based, requiring a download of an application and subsequent download of each edition, or browser-based, often using Macromedia Flash, requiring no application download (such as Adobe Acrobat). Some application-based readers allow users to access editions while not connected to internet. Dedicated hardware such as the Amazon Kindle and the iPad is also available for reading digital editions of select books, popular national magazines such as Time, The Atlantic, and Forbes and popular national newspapers such as the New York Times, Wall Street Journal, and Washington Post. Archives of print newspapers, in some cases dating hundreds of years back, are being digitized and made available online. Google is indexing existing digital archives produced by the newspapers themselves or by third parties. Newspaper and magazine archival began with microform film formats solving the problem of efficiently storing and preserving. This format, however, lacked accessibility. Many libraries, especially state libraries in the United States are archiving their collections digitally and converting existing microfilm to digital format. The Library of Congress provides project planning assistance and the National Endowment for the Humanities procures funding through grants from its National Digital Newspaper Program. Digital magazines, ezines, e-editions and emags are sometimes referred to as digital editions, however some of these formats are published only in digital format unlike digital editions which replicate a printed edition as well. == Digital magazines == Digital-replica magazines number in thousands—consumer and business publications, house magazines for associations, institutions and corporations – and conversion from print to digital was still increasing as of 2009. A 2008 report funded by digital-replica technology providers and auditing agencies counted 1,786 digital-replica editions having more than 7 million circulation among business-to-business publications, of which 230 editions were audited The same report counted 1,470 digital-replica editions of consumer magazines having 5.5 million digital circulation, of which 240 editions were audited. These authors estimated that by year end of 2009 there would be 8,000 digital magazines, having a combined distribution of more than 30 million people. Surveys have shown that, while not all subscribers prefer a digital edition, some do because of the environmental benefit and also because digital magazines are searchable and may easily be passed along or linked to. One such survey funded by a digital publisher reported on inputs from more than 30,000 subscribers to business, consumer and other digital magazines. == Digital magazine business models == === Reduced printing and distribution costs === The publishers' choice to save by moving some or all subscribers from print to digital is widely accepted. Oracle magazine, which has 176,000 of its 516,000 subscribers receiving digital according to its June 2009 BPA circulation statement, is said to be the most widely circulated digital edition of a business-to-business publication. Publishers who do this need to choose whether to make some issues all-digital, move some subscribers to digital edition, add some digital-only subscribers, or send all subscribers the digital edition. === Paid subscription revenue === In 2009, a major consumer magazine, PC Magazine, went all-digital, charging an annual subscription fee for its digital-replica edition. Many consumer magazines and newspapers are already available in eReader formats that are sold through booksellers. === Sponsorship and advertising revenue === Digital editions often carry special "front cover" advertising, or advertising on the email message alerting the subscriber of the digital edition. Publishers also produce special digital-only inserts and rich-media ads or advertorials. === Designed-for-digital issues === Another approach is to fully replace printed issues with digital ones, or to use digital editions for extra issues that would otherwise have to be printed.
Temporal resolution
Temporal resolution (TR) refers to the discrete resolution of a measurement with respect to time. It is defined as the amount of time needed to revisit and acquire data for the same location. When applied to remote sensing, this amount of time is influenced by the sensor platform's orbital characteristics and the features of the sensor itself. The temporal resolution is low when the revisiting delay is high and vice versa. Temporal resolution is typically expressed in days. == Physics == Often there is a trade-off between the temporal resolution of a measurement and its spatial resolution, due to Heisenberg's uncertainty principle. In some contexts, such as particle physics, this trade-off can be attributed to the finite speed of light and the fact that it takes a certain period of time for the photons carrying information to reach the observer. In this time, the system might have undergone changes itself. Thus, the longer the light has to travel, the lower the temporal resolution. == Technology == === Computing === In another context, there is often a tradeoff between temporal resolution and computer storage. A transducer may be able to record data every millisecond, but available storage may not allow this, and in the case of 4D PET imaging the resolution may be limited to several minutes. === Electronic displays === In some applications, temporal resolution may instead be equated to the sampling period, or its inverse, the refresh rate, or update frequency in Hertz, of a TV, for example. The temporal resolution is distinct from temporal uncertainty. This would be analogous to conflating image resolution with optical resolution. One is discrete, the other, continuous. The temporal resolution is a resolution somewhat the 'time' dual to the 'space' resolution of an image. In a similar way, the sample rate is equivalent to the pixel pitch on a display screen, whereas the optical resolution of a display screen is equivalent to temporal uncertainty. Note that both this form of image space and time resolutions are orthogonal to measurement resolution, even though space and time are also orthogonal to each other. Both an image or an oscilloscope capture can have a signal-to-noise ratio, since both also have measurement resolution. === Oscilloscopy === An oscilloscope is the temporal equivalent of a microscope, and it is limited by temporal uncertainty the same way a microscope is limited by optical resolution. A digital sampling oscilloscope has also a limitation analogous to image resolution, which is the sample rate. A non-digital non-sampling oscilloscope is still limited by temporal uncertainty. The temporal uncertainty can be related to the maximum frequency of continuous signal the oscilloscope could respond to, called the bandwidth and given in Hertz. But for oscilloscopes, this figure is not the temporal resolution. To reduce confusion, oscilloscope manufacturers use 'Sa/s' instead of 'Hz' to specify the temporal resolution. Two cases for oscilloscopes exist: either the probe settling time is much shorter than the real time sampling rate, or it is much larger. The case where the settling time is the same as the sampling time is usually undesirable in an oscilloscope. It is more typical to prefer a larger ratio either way, or if not, to be somewhat longer than two sample periods. In the case where it is much longer, the most typical case, it dominates the temporal resolution. The shape of the response during the settling time also has as strong effect on the temporal resolution. For this reason probe leads usually offer an arrangement to 'compensate' the leads to alter the trade off between minimal settling time, and minimal overshoot. If it is much shorter, the oscilloscope may be prone to aliasing from radio frequency interference, but this can be removed by repeatedly sampling a repetitive signal and averaging the results together. If the relationship between the 'trigger' time and the sample clock can be controlled with greater accuracy than the sampling time, then it is possible to make a measurement of a repetitive waveform with much higher temporal resolution than the sample period by upsampling each record before averaging. In this case the temporal uncertainty may be limited by clock jitter.
Summify
Summify was a social news aggregator founded by Mircea Paşoi and Cristian Strat, two former Google and Microsoft interns from Romania. The service emailed its users a periodic summary of news articles shared from their social networks based on their relevance and importance. The platform supported Twitter, Facebook, and Google Reader accounts. == History == In 2009, Paşoi and Strat created ReadFu, a plugin that provided a contextual summary and statistics of the target page of a hyperlink. In January 2010, ReadFu was accepted into the Vancouver-based start-up incubator Bootup Labs. On March 20, 2010 the service was renamed to Summify and a private beta began. On August 11, 2010 Paşoi and Strat announced a new direction for the service. It would become a real-time social news reader that aggregates incoming news from social networks and displays articles by importance using social reactions. After some feedback that the users preferred article digests by email more than the real-time news reader version, Summify discontinued the news reader version. In March 2011, Summify completed a Seed round, with investors including Rob Glaser, Accel Partners, and Stewart Butterfield. Summify received coverage from various news and media outlets such as TechCrunch. It was also featured in various news platforms, such as Time, The Globe and Mail, Mashable, VentureBeat, Gizmodo, Lifehacker, and The Next Web. Summify released a free app on the Apple App Store on July 8, 2011. The app allowed users to read their web summaries from iOS mobile devices. Summify was acquired by Twitter on January 19, 2012. The service shut down soon after, on June 22, 2012.
Technology company
A technology company, or tech company, is a company that focuses primarily on the manufacturing, support, research and development of—most commonly computing, telecommunication and consumer electronics–based—technology-intensive products and services, which include businesses relating to digital electronics, software, optics, new energy, and Internet-related services such as cloud storage and e-commerce services. Big Tech refers to the 6 largest companies, both in the United States and globally, symbolized by the metonym 'Silicon Valley', where 4 of them are based. == Details == According to Fortune, as of 2020, the ten largest technology companies by revenue are: Apple Inc., Samsung, Foxconn, Alphabet Inc., Microsoft, Huawei, Dell Technologies, Hitachi, IBM, and Sony. Amazon has higher revenue than Apple, but is classified by Fortune in the retail sector. The most profitable listed in 2020 are Apple Inc., Microsoft, Alphabet Inc., Intel, Meta Platforms, Samsung, and Tencent. Apple Inc., Alphabet Inc. (owner of Google), Meta Platforms (owner of Facebook), Microsoft, and Amazon.com, Inc. are often referred to as the Big Five multinational technology companies based in the United States. These five technology companies dominate major functions, e-commerce channels, and information of the entire Internet ecosystem. As of 2017, the Big Five had a combined valuation of over $3.3 trillion and make up more than 40 percent of the value of the Nasdaq-100 index. Many large tech companies have a reputation for innovation, spending large sums of money annually on research and development. According to PwC's 2017 Global Innovation 1000 ranking, tech companies made up nine of the 20 most innovative companies in the world, with the top R&D spender (as measured by expenditure) being Amazon, followed by Alphabet Inc., and then Intel. As a result of numerous influential tech companies and tech startups opening offices in proximity to one another, a number of technology districts have developed in various areas across the globe. These include: Silicon Valley in the San Francisco Bay Area, Silicon Wadi in Israel, Silicon Docks in Dublin, Silicon Hills in Austin, Tech City in London; Digital Media City in Seoul, Zhongguancun in Beijing, Cyberjaya in Malaysia and Cyberabad in Hyderabad, India. As of 2026, Europe has six of the world's 100 most valuable tech companies, compared with 56 in the United States and 16 in China.