An eigenface ( EYE-gən-) is the name given to a set of eigenvectors when used in the computer vision problem of human face recognition. The approach of using eigenfaces for recognition was developed by Sirovich and Kirby and used by Matthew Turk and Alex Pentland in face classification. The eigenvectors are derived from the covariance matrix of the probability distribution over the high-dimensional vector space of face images. The eigenfaces themselves form a basis set of all images used to construct the covariance matrix. This produces dimension reduction by allowing the smaller set of basis images to represent the original training images. Classification can be achieved by comparing how faces are represented by the basis set. == History == The eigenface approach began with a search for a low-dimensional representation of face images. Sirovich and Kirby showed that principal component analysis could be used on a collection of face images to form a set of basis features. These basis images, known as eigenpictures, could be linearly combined to reconstruct images in the original training set. If the training set consists of M images, principal component analysis could form a basis set of N images, where N < M. The reconstruction error is reduced by increasing the number of eigenpictures; however, the number needed is always chosen less than M. For example, if you need to generate a number of N eigenfaces for a training set of M face images, you can say that each face image can be made up of "proportions" of all the K "features" or eigenfaces: Face image1 = (23% of E1) + (2% of E2) + (51% of E3) + ... + (1% En). In 1991 M. Turk and A. Pentland expanded these results and presented the eigenface method of face recognition. In addition to designing a system for automated face recognition using eigenfaces, they showed a way of calculating the eigenvectors of a covariance matrix such that computers of the time could perform eigen-decomposition on a large number of face images. Face images usually occupy a high-dimensional space and conventional principal component analysis was intractable on such data sets. Turk and Pentland's paper demonstrated ways to extract the eigenvectors based on matrices sized by the number of images rather than the number of pixels. Once established, the eigenface method was expanded to include methods of preprocessing to improve accuracy. Multiple manifold approaches were also used to build sets of eigenfaces for different subjects and different features, such as the eyes. == Generation == A set of eigenfaces can be generated by performing a mathematical process called principal component analysis (PCA) on a large set of images depicting different human faces. Informally, eigenfaces can be considered a set of "standardized face ingredients", derived from statistical analysis of many pictures of faces. Any human face can be considered to be a combination of these standard faces. For example, one's face might be composed of the average face plus 10% from eigenface 1, 55% from eigenface 2, and even −3% from eigenface 3. Remarkably, it does not take many eigenfaces combined together to achieve a fair approximation of most faces. Also, because a person's face is not recorded by a digital photograph, but instead as just a list of values (one value for each eigenface in the database used), much less space is taken for each person's face. The eigenfaces that are created will appear as light and dark areas that are arranged in a specific pattern. This pattern is how different features of a face are singled out to be evaluated and scored. There will be a pattern to evaluate symmetry, whether there is any style of facial hair, where the hairline is, or an evaluation of the size of the nose or mouth. Other eigenfaces have patterns that are less simple to identify, and the image of the eigenface may look very little like a face. The technique used in creating eigenfaces and using them for recognition is also used outside of face recognition: handwriting recognition, lip reading, voice recognition, sign language/hand gestures interpretation and medical imaging analysis. Therefore, some do not use the term eigenface, but prefer to use 'eigenimage'. === Practical implementation === To create a set of eigenfaces, one must: Prepare a training set of face images. The pictures constituting the training set should have been taken under the same lighting conditions, and must be normalized to have the eyes and mouths aligned across all images. They must also be all resampled to a common pixel resolution (r × c). Each image is treated as one vector, simply by concatenating the rows of pixels in the original image, resulting in a single column with r × c elements. For this implementation, it is assumed that all images of the training set are stored in a single matrix T, where each column of the matrix is an image. Subtract the mean. The average image a has to be calculated and then subtracted from each original image in T. Calculate the eigenvectors and eigenvalues of the covariance matrix S. Each eigenvector has the same dimensionality (number of components) as the original images, and thus can itself be seen as an image. The eigenvectors of this covariance matrix are therefore called eigenfaces. They are the directions in which the images differ from the mean image. Usually this will be a computationally expensive step (if at all possible), but the practical applicability of eigenfaces stems from the possibility to compute the eigenvectors of S efficiently, without ever computing S explicitly, as detailed below. Choose the principal components. Sort the eigenvalues in descending order and arrange eigenvectors accordingly. The number of principal components k is determined arbitrarily by setting a threshold ε on the total variance. Total variance v = ( λ 1 + λ 2 + . . . + λ n ) {\displaystyle v=(\lambda _{1}+\lambda _{2}+...+\lambda _{n})} , n = number of components, and λ {\displaystyle \lambda } represents component eigenvalue. k is the smallest number that satisfies ( λ 1 + λ 2 + . . . + λ k ) v > ϵ {\displaystyle {\frac {(\lambda _{1}+\lambda _{2}+...+\lambda _{k})}{v}}>\epsilon } These eigenfaces can now be used to represent both existing and new faces: we can project a new (mean-subtracted) image on the eigenfaces and thereby record how that new face differs from the mean face. The eigenvalues associated with each eigenface represent how much the images in the training set vary from the mean image in that direction. Information is lost by projecting the image on a subset of the eigenvectors, but losses are minimized by keeping those eigenfaces with the largest eigenvalues. For instance, working with a 100 × 100 image will produce 10,000 eigenvectors. In practical applications, most faces can typically be identified using a projection on between 100 and 150 eigenfaces, so that most of the 10,000 eigenvectors can be discarded. === Matlab example code === Here is an example of calculating eigenfaces with Extended Yale Face Database B. To evade computational and storage bottleneck, the face images are sampled down by a factor 4×4=16. Note that although the covariance matrix S generates many eigenfaces, only a fraction of those are needed to represent the majority of the faces. For example, to represent 95% of the total variation of all face images, only the first 43 eigenfaces are needed. To calculate this result, implement the following code: === Computing the eigenvectors === Performing PCA directly on the covariance matrix of the images is often computationally infeasible. If small images are used, say 100 × 100 pixels, each image is a point in a 10,000-dimensional space and the covariance matrix S is a matrix of 10,000 × 10,000 = 108 elements. However the rank of the covariance matrix is limited by the number of training examples: if there are N training examples, there will be at most N − 1 eigenvectors with non-zero eigenvalues. If the number of training examples is smaller than the dimensionality of the images, the principal components can be computed more easily as follows. Let T be the matrix of preprocessed training examples, where each column contains one mean-subtracted image. The covariance matrix can then be computed as S = TTT and the eigenvector decomposition of S is given by S v i = T T T v i = λ i v i {\displaystyle \mathbf {Sv} _{i}=\mathbf {T} \mathbf {T} ^{T}\mathbf {v} _{i}=\lambda _{i}\mathbf {v} _{i}} However TTT is a large matrix, and if instead we take the eigenvalue decomposition of T T T u i = λ i u i {\displaystyle \mathbf {T} ^{T}\mathbf {T} \mathbf {u} _{i}=\lambda _{i}\mathbf {u} _{i}} then we notice that by pre-multiplying both sides of the equation with T, we obtain T T T T u i = λ i T u i {\displaystyle \mathbf {T} \mathbf {T} ^{T}\mathbf {T} \mathbf {u} _{i}=\lambda _{i}\mathbf {T} \mathbf {u} _{i}} Meaning that, if ui is an eigenvector of TTT, then vi = Tui is an eigenvector of S. If we have
Suno (platform)
Suno is a generative artificial intelligence music creation platform. It is designed to generate music that can include vocals and instrumentation. The platform was initially developed by Suno, Inc., of Cambridge, Massachusetts. Suno has been widely available since December 20, 2023, after the launch of a web application and a partnership with Microsoft, which included Suno as a plugin in Microsoft Copilot. The program operates by producing songs based on text or audio prompts provided by its users. Suno does not disclose the dataset used to train its artificial intelligence. == History == Suno, Inc., was founded by four people: Michael Shulman, Georg Kucsko, Martin Camacho, and Keenan Freyberg. They all worked for Kensho, an AI startup, before starting their own company in Cambridge, Massachusetts. In April 2023, Suno released their open-source text-to-speech and audio model called "Bark" on GitHub. On March 21, 2024, Suno released its V3 version for all users. The new version allowed users to create a limited number of four-minute songs using a free account. Users can pay for more features. In April 2024, a sentimental ballad was generated with Suno based on the text of the MIT License. In June 2024, a lawsuit, led by the Recording Industry Association of America, was filed against Suno and Udio alleging widespread infringement of copyrighted sound recordings. The lawsuit sought to bar the companies from training on copyrighted music, as well as damages of up to $150,000 per work from infringements that have already taken place. On July 1, 2024, a mobile app for Suno was released. On November 19, 2024, Suno upgraded its AI song model program to v4. In January 2025, Michael Shulman remarked on a podcast, "I think the majority of people don't enjoy the majority of the time they spend making music." In March 2025, one day after thousands of musicians including Thom Yorke and ABBA's Björn Ulvaeus signed a letter calling for Suno to stop training its model on copyrighted music, Timbaland endorsed Suno in a video on the company's website. In July 2025, Suno user imoliver signed a record deal with Hallwood Media, which became the first instance of a traditional music label signing an AI-based creator. Hallwood later signed with AI-artist Xania Monet for US$3 million. Monet's songs were generated by Suno AI by poet Telisha Jones. In November 2025, Suno agreed to a $500 million dollar lawsuit settlement, in which Suno would be allowed to train its models on Warner Music Group's music catalog, and WMG would control aspects of AI likeness, music, audio, software, copyrights, AI tools and music created by users on Suno. As part of the settlement, Suno also acquired the concert discovery platform Songkick from WMG. == Controversy == Suno, Inc., has been sued by the Recording Industry Association of America for copyright infringement, and thousands of musicians have signed a letter demanding that the company cease using copyrighted music in their training data. Suno does not disclose the dataset used to train its artificial intelligence.
User-subjective approach
The user-subjective approach is the first interaction design approach dedicated specifically to personal information management (PIM). The approach offers design principles with which PIM systems (e.g. operating systems, email applications and web browsers) can make systematic use of subjective (i.e. user-dependent) attributes. The approach evolved in three stages: (a) theoretical foundations first published in a Journal of the American Society for Information Science and Technology during 2003. The paper introduces the approach and its design principles (b) evidence and implementation was published in another JASIST paper in 2008. The paper gives empirical evidence in support of the approach as well as seven novel design schemes that derives from it. It has won the Best JASIST paper award in 2009.(c) specific design evaluation this stage has already begun with evaluation of the first user-subjective design prototype called GrayArea in a Conference on Human Factors in Computing Systems paper published in 2009. == Theoretical foundations == The user-subjective approach takes advantage of the fact that in PIM the person who retrieves the information is the same person who had previously stored it. PIM can be seen as a communication between the person and him\her self at two different times: the time of storage and the time of retrieval. The PIM system design should help facilitate that unique communication by allowing the user use subjective (user-dependent) attributes in addition to the standard objective ones. PIM systems should capture these subjective attributes when the user interacts with the information item (either automatically or by using direct manipulation interface) in order to help the user retrieve the item later on. The user-subjective approach identifies three subjective attributes – the project which the item was classified to, its degree of importance to the user, and the context in which the item was used during the interaction with it. The approach also assigns a design principle for each. The principles (discussed below) are deliberately abstract to allow for a variety of different implementations. === The subjective project classification principle === The subjective project classification principle suggests that PIM systems design should allow all information items related to a project be classified under the same category regardless of whether they are files, emails, Web Favorites or of any other format. This stands in sharp contrast with the present PIM system design where there are distinct folder hierarchies for each of these formats. The current design forces the user to store information related to a single project in separate locations depending on their format causing the project fragmentation problem. === The subjective importance principle === The subjective importance principle suggests that the subjective importance of information should affect its degree of visual salience and accessibility: important information items should be highly visible and accessible as they are more likely to be retrieved (the promotion principle) and those of lower importance should be demoted (i.e. making them less visible) so as not to distract the user (the demotion principle). While the promotion principle is not new and has been widely applied in PIM system design, the demotion principle is novel and has been applied only sporadically in these systems. Currently these systems allow only two options: keeping information (where unneeded information items could clutter folders and obscure the target item) and deleting it (where there is a risk that the item will not be there when needed). Demotion suggests a third option where the item is less visible so it doesn’t distract the user but is kept within its original context in case the user would need it after all. === The subjective context principle === The subjective context principle suggests that PIM systems should allow users retrieve their information items in the same context that they had previously used in order to bridge the time gap between these two events. By "context" the approach refers to other information items that were used at the time of interaction with the item, thoughts that the users may have regarding the item, the phase the user got to in the interaction with the item and other people the user collaborates with regarding the information item. == Evidence and implementations == === Evidence === The user-subjective approach was evaluated in a multioperational designed study which used questionnaires, screen shots and in-depth interviews (N = 84). The research tested the use of subjective attributes in current PIM systems and its dependency on design. Results show that participants used subjective attributes whenever design allowed them to. When it didn't, they either used their own alternative ways to use these attributes or avoided using subjective attributes at all. Regarding the subjective project classification principle – many of the participants' recent files, emails and web pages related to the same projects (indicating that they were working on the same project using different formats), and they had saved files of different format in the same project folders. However, as design does not suggest storing emails and web favorites with files, users avoid doing so. Regarding the subjective importance principle – users tended to retrieve their important information from highly visible and accessible locations offered by current design (e.g. by using the desktop), however since current systems offers no way to demote files of low subjective importance participants tended to use their own walk around ways for doing so (e.g. by moving them to a folder called "old" inside their original folder). Regarding the subjective context principle – participants tended to talk spontaneously about the context of their information items during the interview. These evidence imply that current PIM systems could possibly be improved if it would allow users to make more use of subjective attributes of their personal information. === Implementations === Each of the user-subjective design principles can be implemented in various ways. Moreover, as the approach is generative it offers PIM designers to use these principles in order to create their own user subjective designs. Below are design schemes that demonstrate an implementation of each of the principles. A more complete set of implementation examples can be found in the user-subjective website Archived 2011-02-01 at the Wayback Machine. The single hierarchy solution – addresses the project fragmentation problem (the current situation where the users stores and retrieve their project-related files, emails and web favorites at different hierarchies) and implements the subjective classification principle by offering the user a single folder hierarchy for all information items. At the operation system level the users would navigate to a folder and find there all project related files, emails, web favorites, tasks, contacts and notes. This would allow them to retrieve all their project-related information items from a single location regardless of their formats. When looking at these folders at their mail box the users would see only their emails and only web favorites through their browser. The single hierarchy design scheme has not been evaluated yet. GrayArea – implements the demotion principle by allowing users to move subjectively unimportant files to a gray area at the bottom end of their folders. This clears the upper part of the folder from file that are unlikely to be retrieved while allowing the users to retrieve these unimportant file in their original context in case they are needed after all. GrayArea design scheme was positively evaluated (see next section). ItemHistory – is an implementation of the subjective context principle. It allows users to reach all information items that were previously retrieved while that information item was open. This design scheme has not been evaluated to date. == Specific design evaluation == The evaluation of specific designs is the third and final step of the approach development. It had begun with the assessment of GrayArea. === GrayArea evaluation === GrayArea was evaluated by using a prototype that simulated the participants' folders but included a gray area where they could drag & drop their subjectively unimportant files. In the study 96 participants were asked to clean up their folders from unimportant files once with GrayArea and once without it. Results show that the use of GrayArea reduced the clutter in folders, that it was easier for participants to demote files than to delete them and that they would use it if provided in their next operating system. These results encourage commercial implementation of GrayArea and the development and testing of other user-subjective designs. == Chronological development == The user-subjective approach was developed by
Library history
Library history is a subdiscipline within library science and library and information science focusing on the history of libraries and their role in societies and cultures. Some see the field as a subset of information history. Library history is an academic discipline and should not be confused with its object of study (history of libraries): the discipline is much younger than the libraries it studies. Library history begins in ancient societies through contemporary issues facing libraries today. Topics include recording mediums, cataloguing systems, scholars, scribes, library supporters and librarians. == Earliest libraries == The earliest records of a library institution as it is presently understood can be dated back to around 5,000 years ago in the Southwest Asian regions of the world. One of the oldest libraries found is that of the ancient library at Ebla (circa 2500 BCE) in present-day Syria. In the 1970s, the excavation at Ebla's library unearthed over 20,000 clay tablets written in cuneiform script. === Library in Mesopotamia === The Assyrian King Assurbanipal created one of the greatest libraries in Nineveh in the seventh century BCE. The collection consisted of over 30,000 tablets written in a variety of languages. The collection was cataloged both by the shape of the tablet and by the subject of the content. The library had separate rooms for the different topics: government, history, law, astronomy, geography, and so on. The tablets also contained myths, hymns, and even jokes. Assurbanipal would send scribes to visit every corner of his kingdom to copy the content of other libraries. His library contained many of the most important literary works of the day, including the epic of Gilgamesh. Assurbanipal's Royal Library also had one of the first library catalogs. Unfortunately, Nineveh was eventually destroyed, and the library was lost in a fire. === Libraries in Ancient Greece === The Greek government was the first to sponsor public libraries. By 500 BCE both Athens and Samos had begun creating libraries for the public, though as most of the population was illiterate these spaces were serving a small, educated portion of the community. Athens developed a city archive at the Metroon in 405 BCE, where documents were stored in sealed jars. These would have saved the documents, but they would have been difficult to consult regularly. In Paros, around the same time, contracts were placed in the temple for safe keeping, and a book curse was placed for extra protection. === Library of Alexandria === The Library at Alexandria, Egypt, was renowned in the third century BCE while kings Ptolemy I Soter and Ptolemy II Philadelphus reigned. The library included a museum, garden, meeting areas and of course reading rooms. The Great Library, as it is known, was one of many in Alexandria. From its inception around the second century BCE, Alexandria was a well-known center for learning. It earned renown as the intellectual capital of the Western world up through the third century CE. The librarians at Alexandria collected, copied, and organized scrolls from across the known world. According to a primary source, every ship that came to Alexandria was required to hand over their books to be copied, and the copies would be returned to the owner, the library keeping the original. The Library of Alexandria was damaged by various disasters over time, including fire, invasion, and earthquake. Scholars believe the collection slowly diminished over time due to theft and efforts to remove it ahead of invading armies. While there are popular stories about how the library was ultimately destroyed, most of these are more myth than fact. === Libraries in Rome === Julius Caesar and his successor Augustus were the first to establish public libraries in ancient Rome, including the library of Apollo on the Palatine Hill. Several emperors followed suit over the next four centuries, including Hadrian, Tiberius, and Vespasian. Roman aristocrats also had personal libraries, which usually contained works in both Greek and Latin. A valuable example of this has been found at Herculaneum near Pompeii. Papyrus manuscripts in Herculaneum's Villa of the Papyri were encased in ash after the eruption of Vesuvius in 79 CE. Modern archaeology is now able to scan these artifacts and discern their contents, including many writings from Philodemus. The average Roman would not have been familiar with books beyond what they might hear read aloud in the forum. Public figures would pay for particular passages to be read aloud to the public from the steps of a public library. === Libraries in the Middle Ages === In the European Middle Ages, libraries began to become more prevalent, despite a widespread reduction in new writing beyond religious themes. Most libraries were initially connected to monasteries or religious institutions. Scriptoriums copied Christian religious texts to share with other religious centers or to be read aloud to their own parishioners. The Holy Roman Emperor Charlemagne (r. 786-814) had a large impact on the advancement of written culture in the Medieval Christian world, acquiring as many written works as he could, and employing many scribes to copy and recirculate vernacular versions of religious works. Most of the text held in small personal libraries was still religious in nature. == Early modern libraries == === Libraries of the Renaissance === During the Renaissance era the merchant middle class grew, and more people found benefits in education. They relied on libraries as a place to study and gain knowledge. Libraries provided a valuable resource, enriching the culture of those who were educated. Universities that had been started in the Middle Ages, founded their own libraries. Books in these libraries could not be borrowed from these libraries and were generally chained to the shelves to prevent theft. As more of the population became literate, new ideas like Humanism and Natural Law spawned an increase personal libraries, although they remained small. Gutenberg's invention of the printing press in 1456 opened the door to the modern era for libraries. == Oldest working libraries == According to the German librarian Michael Knoche, it is not possible to determine which library is the “oldest”: "Precise year dates are a construct, especially in the case of very old libraries. When a collection of books deserves to be called a library depends very much on the point of view of the observer." Various libraries are referred to as the “oldest”: The library founded in the 6th century of the Saint Catherine's Monastery in Sinai is "reputedly the oldest continuously run library in existence today", according to the Library of Congress. Its collection of religious and secular manuscripts is ranging from Bibles, liturgies and prayer books to legal documents such as deeds, court cases and fatwahs (legal opinions). The Al Qarawiyyin Library was founded in 859 by Fatima al-Fihri and is often regarded as the oldest working library in the world. It is in Fez, Morocco and is part of the oldest continually operating university in the world, the University of al-Qarawiyyin. The library houses approximately 4,000 ancient Islamic manuscripts. These manuscripts include 9th century Qurans and the oldest known accounts of the Islamic prophet Muhammed. The Malatestiana Library (Italian: Biblioteca Malatestiana) is a public library in the city of Cesena in northern Italy. Opened in 1454 it is significant for being the first civic library in Europe open to the general public. == Library history reports and writings of the early 19th and 20th century == In the early 19th and 20th century, representative titles were created reporting library history in the United States and the United Kingdom. American titles include Public Libraries in the United States of America, Their History, Condition, and Management (1876), Memorial History of Boston (1881) by Justin Winsor, Public Libraries in America (1894) by William I. Fletcher, and History of the New York Public Library (1923) by Henry M. Lydenberg. British titles include Old English Libraries (1911) by Earnest A. Savage and The Chained Library: A Survey of Four Centuries in the Evolution of the English Library by Burnett Hillman Streeter. In the beginning of the 20th century, library historians began applying scientific research methodologies to examine the library as a social agency. Two works that demonstrate this argument are Geschichte der Bibliotheken (1925) by Alfred Hessel and the Library Quarterly article from 1931, “The Sociological Beginnings of the Library Movement in America” by Arnold Borden. With the establishment of library schools, master's theses and doctoral dissertations represented the shift in serious research regarding libraries and library history. Two published doctoral dissertations that mark this trend are Foundations of the Public Library: The Origins of the American Public Library Movement in Ne
Australian Geoscience Data Cube
The Australian Geoscience Data Cube (AGDC) is an approach to storing, processing and analyzing large collections of Earth observation data. The technology is designed to meet challenges of national interest by being agile and flexible with vast amounts of layered grid data. The AGDC reduces processing time of traditional image analysis by calibrating, pre-computing known extents, pixel alignment and storing metadata in a cell lattice structure. The temporal-pixel aligned data can often be analysed faster across space and time dimensions than previous scene based techniques. This allows the AGDC to be flexible in tackling future challenges and improve analysis times on every-increasing data repositories of earth observation. The AGDC has also been used internationally to allow countries to maintain ecologically sustainable programs and reduce the difficulty curve of utilizing Remote Sensing data. == Background == The AGDC was originally conceived by Geoscience Australia but is now maintained in a partnership between Geoscience Australia, Commonwealth Scientific and Industrial Research Organisation (CSIRO) and National Computational Infrastructure National Facility (Australia) (NCI). This is made possible by the funding from the partnership and a number of organisations such as National Collaborative Research Infrastructure Strategy (NCRIS). == Analysis ready data, ingestion and indexing == The data processed in the cube is made analysis ready before being ingested and indexed into the AGDC. Analysis ready data is pre-processed data that has applied corrections for instrument calibration (gains and offsets), geolocation (spatial alignment) and radiometry (solar illumination, incidence angle, topography, atmospheric interference). The ingestion process manages the translation of datasets into the storage units while maintaining a database index. The data within the storage and index can be accessed via API calls often compiled within code such as Python (programming language). Example: s2a_l1c = dc.load(product='s2a_level1c_granule',x=(147.36, 147.41), y=(-35.1, -35.15), measurements=['04','03','02'], output_crs='EPSG:4326', resolution=(-0.00025,0.00025)) === Datasets currently stored === Geoscience Australia Landsat Surface Reflectance (1987 to present) Landsat Pixel Quality Landsat Fractional Cover Landsat NDVI === Datasets that have been piloted === USGS Landsat Surface Reflectance SRTM DEM Himawari 8 MODIS Sentinel-2 L1C / S2A Australian Gridded Climate Data == Open source == The AGDC code base is situated in GitHub as an open repository. The core code base moved to the Open Data Cube in early 2017 as part of an international collaboration. Whilst the code base is the Open Data Cube, individual cubes exist as their own right such as the AGDC on the National Computational Infrastructure National Facility (Australia) (NCI) using the High-Performance Computing Cluster HPCC. The core code can be installed on personal computers or public computers (using git) and has many unit tests. Documentation for the code base exists on Read the Docs. == Challenges of the AGDC == The AGDC is designed to meet nationally significant challenges such as the following. Sustainability Environment Water resource management Disaster assist Policy development Community planning Forest preservation Carbon measurement == International awards == The AGDC won the 2016 Content Platform of the Year award from Geospatial World Forum.
TeaOnHer
TeaOnHer is a male-oriented dating surveillance mobile app that allows men to anonymously rate and comment on women they are dating. It was set up in response to the existence of Tea, a female-oriented dating app that allowed women to rate and comment on men. In 2025, Cosmopolitian magazine described it as America's second most popular mobile app, with it being the second most popular app in the lifestyle section of Apple's App Store. The TeaOnHer app has fewer features than the rival Tea app, focusing instead on anonymous commenting. It is listed as having been developed by a company called Newville Media Corporation. TechCrunch reported in 2025 that TeaOnHer had leaked credentials of some of its users.
Sieve of Pritchard
In mathematics, the sieve of Pritchard is an algorithm for finding all prime numbers up to a specified bound. Like the ancient sieve of Eratosthenes, it has a simple conceptual basis in number theory. It is especially suited to quick hand computation for small bounds. Whereas the sieve of Eratosthenes marks off each non-prime for each of its prime factors, the sieve of Pritchard avoids considering almost all non-prime numbers by building progressively larger wheels, which represent the pattern of numbers not divisible by any of the primes processed thus far. It thereby achieves a better asymptotic complexity, and was the first sieve with a running time sublinear in the specified bound. Its asymptotic running-time has not been improved on, and it deletes fewer composites than any other known sieve. It was created in 1979 by Paul Pritchard. Since Pritchard has created a number of other sieve algorithms for finding prime numbers, the sieve of Pritchard is sometimes singled out by being called the wheel sieve (by Pritchard himself) or the dynamic wheel sieve. == Overview == A prime number is a natural number that has no natural number divisors other than the number 1 and itself. To find all the prime numbers less than or equal to a given integer N, a sieve algorithm examines a set of candidates in the range 2, 3, …, N, and eliminates those that are not prime, leaving the primes at the end. The sieve of Eratosthenes examines all of the range, first removing all multiples of the first prime 2, then of the next prime 3, and so on. The sieve of Pritchard instead examines a subset of the range consisting of numbers that occur on successive wheels, which represent the pattern of numbers left after each successive prime is processed by the sieve of Eratosthenes. For i > 0, the ith wheel Wi represents this pattern. It is the set of numbers between 1 and the product Pi = p1 · p2 ⋯ pi of the first i prime numbers that are not divisible by any of these prime numbers (and is said to have an associated length Pi). This is because adding Pi to a number does not change whether it is divisible by one of the first i prime numbers, since the remainder on division by any one of these primes is unchanged. So W1 = {1} with length P1 = 2 represents the pattern of odd numbers; W2 = {1,5} with length P2 = 6 represents the pattern of numbers not divisible by 2 or 3; etc. Wheels are so-called because Wi can be usefully visualized as a circle of circumference Pi with its members marked at their corresponding distances from an origin. Then rolling the wheel along the number line marks points corresponding to successive numbers not divisible by one of the first i prime numbers. The animation shows W2 being rolled up to 30. It is useful to define Wi → n for n > 0 to be the result of rolling Wi up to n. Then the animation generates W2 → 30 = {1,5,7,11,13,17,19,23,25,29}. Note that up to 52 − 1 = 24, this consists only of 1 and the primes between 5 and 25. The sieve of Pritchard is derived from the observation that this holds generally: for all i > 0, the values in Wi → (p2i+1 − 1) are 1 and the primes between pi+1 and p2i+1. It even holds for i = 0, where the wheel has length 1 and contains just 1 (representing all the natural numbers). So the sieve of Pritchard starts with the trivial wheel W0 and builds successive wheels until the square of the wheel's first member after 1 is at least N. Wheels grow very quickly, but only their values up to N are needed and generated. It remains to find a method for generating the next wheel. Note in the animation that W3 = {1,5,7,11,13,17,19,23,25,29} − {5 · 1 , 5 · 5} can be obtained by rolling W2 up to 30 and then removing 5 times each member of W2.This also holds generally: for all i ≥ 0, Wi+1 = (Wi → Pi+1) − {pi+1 · w | w ∈ Wi}. Rolling Wi past Pi just adds values to Wi, so the current wheel is first extended by getting each successive member starting with w = 1, adding Pi to it, and inserting the result in the set. Then the multiples of pi+1 are deleted. Care must be taken to avoid a number being deleted that itself needs to be multiplied by pi+1. The sieve of Pritchard as originally presented does so by first skipping past successive members until finding the maximum one needed, and then doing the deletions in reverse order by working back through the set. This is the method used in the first animation above. A simpler approach is just to gather the multiples of pi+1 in a list, and then delete them. Another approach is given by Gries and Misra. If the main loop terminates with a wheel whose length is less than N, it is extended up to N to generate the remaining primes. The algorithm, for finding all primes up to N, is therefore as follows: Start with a set W = {1} and length = 1 representing wheel 0, and prime p = 2. As long as p2 ≤ N, do the following: if length < N, then extend W by repeatedly getting successive members w of W starting with 1 and inserting length + w into W as long as it does not exceed p · length or N; increase length to the minimum of p · length and N. repeatedly delete p times each member of W by first finding the largest ≤ length and then working backwards. note the prime p, then set p to the next member of W after 1 (or 3 if p was 2). if length < N, then extend W to N by repeatedly getting successive members w of W starting with 1 and inserting length + w into W as long as it does not exceed N; On termination, the rest of the primes up to N are the members of W after 1. === Example === To find all the prime numbers less than or equal to 150, proceed as follows. Start with wheel 0 with length 1, representing all natural numbers 1, 2, 3...: 1 The first number after 1 for wheel 0 (when rolled) is 2; note it as a prime. Now form wheel 1 with length 2 × 1 = 2 by first extending wheel 0 up to 2 and then deleting 2 times each number in wheel 0, to get: 1 2 The first number after 1 for wheel 1 (when rolled) is 3; note it as a prime. Now form wheel 2 with length 3 × 2 = 6 by first extending wheel 1 up to 6 and then deleting 3 times each number in wheel 1, to get 1 2 3 5 The first number after 1 for wheel 2 is 5; note it as a prime. Now form wheel 3 with length 5 × 6 = 30 by first extending wheel 2 up to 30 and then deleting 5 times each number in wheel 2 (in reverse order), to get 1 2 3 5 7 11 13 17 19 23 25 29 The first number after 1 for wheel 3 is 7; note it as a prime. Now wheel 4 has length 7 × 30 = 210, so we only extend wheel 3 up to our limit 150. (No further extending will be done now that the limit has been reached.) We then delete 7 times each number in wheel 3 until we exceed our limit 150, to get the elements in wheel 4 up to 150: 1 2 3 5 7 11 13 17 19 23 25 29 31 37 41 43 47 49 53 59 61 67 71 73 77 79 83 89 91 97 101 103 107 109 113 119 121 127 131 133 137 139 143 149 The first number after 1 for this partial wheel 4 is 11; note it as a prime. Since we have finished with rolling, we delete 11 times each number in the partial wheel 4 until we exceed our limit 150, to get the elements in wheel 5 up to 150: 1 2 3 5 7 11 13 17 19 23 25 29 31 37 41 43 47 49 53 59 61 67 71 73 77 79 83 89 91 97 101 103 107 109 113 119 121 127 131 133 137 139 143 149 The first number after 1 for this partial wheel 5 is 13. Since 13 squared is at least our limit 150, we stop. The remaining numbers (other than 1) are the rest of the primes up to our limit 150. Just 8 composite numbers are removed, once each. The rest of the numbers considered (other than 1) are prime. In comparison, the natural version of Eratosthenes sieve (stopping at the same point) removes composite numbers 184 times. == Pseudocode == The sieve of Pritchard can be expressed in pseudocode, as follows: algorithm Sieve of Pritchard is input: an integer N >= 2. output: the set of prime numbers in {1,2,...,N}. let W and Pr be sets of integer values, and all other variables integer values. k, W, length, p, Pr := 1, {1}, 2, 3, {2}; {invariant: p = pk+1 and W = Wk ∩ {\displaystyle \cap } {1,2,...,N} and length = minimum of Pk,N and Pr = the primes up to pk} while p2 <= N do if (length < N) then Extend W,length to minimum of plength,N; Delete multiples of p from W; Insert p into Pr; k, p := k+1, next(W, 1) if (length < N) then Extend W,length to N; return Pr ∪ {\displaystyle \cup } W - {1}; where next(W, w) is the next value in the ordered set W after w. procedure Extend W,length to n is {in: W = Wk and length = Pk and n > length} {out: W = Wk → {\displaystyle \rightarrow } n and length = n} integer w, x; w, x := 1, length+1; while x <= n do Insert x into W; w := next(W,w); x := length + w; length := n; procedure Delete multiples of p from W,length is integer w; w := p; while pw <= length do w := next(W,w); while w > 1 do w := prev(W,w); Remove pw from W; where prev(W, w) is the previous value in the ordered set W before w. The algorithm can be initialized with W0 instead of W1 at the minor complication of making next(W, 1) a special case when k = 0. This a