AI Headshot Generator

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Open information extraction

In natural language processing, open information extraction (OIE) is the task of generating a structured, machine-readable representation of the information in text, usually in the form of triples or n-ary propositions. == Overview == A proposition can be understood as truth-bearer, a textual expression of a potential fact (e.g., "Dante wrote the Divine Comedy"), represented in an amenable structure for computers [e.g., ("Dante", "wrote", "Divine Comedy")]. An OIE extraction normally consists of a relation and a set of arguments. For instance, ("Dante", "passed away in" "Ravenna") is a proposition formed by the relation "passed away in" and the arguments "Dante" and "Ravenna". The first argument is usually referred as the subject while the second is considered to be the object. The extraction is said to be a textual representation of a potential fact because its elements are not linked to a knowledge base. Furthermore, the factual nature of the proposition has not yet been established. In the above example, transforming the extraction into a full fledged fact would first require linking, if possible, the relation and the arguments to a knowledge base. Second, the truth of the extraction would need to be determined. In computer science transforming OIE extractions into ontological facts is known as relation extraction. In fact, OIE can be seen as the first step to a wide range of deeper text understanding tasks such as relation extraction, knowledge-base construction, question answering, semantic role labeling. The extracted propositions can also be directly used for end-user applications such as structured search (e.g., retrieve all propositions with "Dante" as subject). OIE was first introduced by TextRunner developed at the University of Washington Turing Center headed by Oren Etzioni. Other methods introduced later such as Reverb, OLLIE, ClausIE or CSD helped to shape the OIE task by characterizing some of its aspects. At a high level, all of these approaches make use of a set of patterns to generate the extractions. Depending on the particular approach, these patterns are either hand-crafted or learned. == OIE systems and contributions == Reverb suggested the necessity to produce meaningful relations to more accurately capture the information in the input text. For instance, given the sentence "Faust made a pact with the devil", it would be erroneous to just produce the extraction ("Faust", "made", "a pact") since it would not be adequately informative. A more precise extraction would be ("Faust", "made a pact with", "the devil"). Reverb also argued against the generation of overspecific relations. OLLIE stressed two important aspects for OIE. First, it pointed to the lack of factuality of the propositions. For instance, in a sentence like "If John studies hard, he will pass the exam", it would be inaccurate to consider ("John", "will pass", "the exam") as a fact. Additionally, the authors indicated that an OIE system should be able to extract non-verb mediated relations, which account for significant portion of the information expressed in natural language text. For instance, in the sentence "Obama, the former US president, was born in Hawaii", an OIE system should be able to recognize a proposition ("Obama", "is", "former US president"). ClausIE introduced the connection between grammatical clauses, propositions, and OIE extractions. The authors stated that as each grammatical clause expresses a proposition, each verb mediated proposition can be identified by solely recognizing the set of clauses expressed in each sentence. This implies that to correctly recognize the set of propositions in an input sentence, it is necessary to understand its grammatical structure. The authors studied the case in the English language that only admits seven clause types, meaning that the identification of each proposition only requires defining seven grammatical patterns. The finding also established a separation between the recognition of the propositions and its materialization. In a first step, the proposition can be identified without any consideration of its final form, in a domain-independent and unsupervised way, mostly based on linguistic principles. In a second step, the information can be represented according to the requirements of the underlying application, without conditioning the identification phase. Consider the sentence "Albert Einstein was born in Ulm and died in Princeton". The first step will recognize the two propositions ("Albert Einstein", "was born", "in Ulm") and ("Albert Einstein", "died", "in Princeton"). Once the information has been correctly identified, the propositions can take the particular form required by the underlying application [e.g., ("Albert Einstein", "was born in", "Ulm") and ("Albert Einstein", "died in", "Princeton")]. CSD introduced the idea of minimality in OIE. It considers that computers can make better use of the extractions if they are expressed in a compact way. This is especially important in sentences with subordinate clauses. In these cases, CSD suggests the generation of nested extractions. For example, consider the sentence "The Embassy said that 6,700 Americans were in Pakistan". CSD generates two extractions [i] ("6,700 Americans", "were", "in Pakistan") and [ii] ("The Embassy", "said", "that [i]"). This is usually known as reification.
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AdBlock

AdBlock is an ad-blocking browser extension for Google Chrome, Apple Safari (desktop and mobile), Firefox, Samsung Internet, Microsoft Edge and Opera. AdBlock allows users to prevent page elements, such as advertisements, from being displayed. It is free to download and use, and it includes optional donations to the developers. The AdBlock extension was created on December 8, 2009, which is the day that supports for extensions was added to Google Chrome. It was one of the first Google Chrome extensions that was made. Since 2016, AdBlock has been based on the Adblock Plus source code. In July 2018, AdBlock acquired uBlock, a commercial ad-blocker owned by uBlock LLC and based on uBlock Origin. In April 2021, eyeo GmbH (developer of Adblock Plus) announced its purchase of AdBlock, Inc (formerly BetaFish, Inc). == Crowdfunding == Gundlach launched a crowdfunding campaign on Crowdtilt in August 2013 in order to fund an ad campaign to raise awareness of ad-blocking and to rent a billboard at Times Square. After the one-month campaign, it raised $55,000. == Sales and acceptable ads == AdBlock was sold to an anonymous buyer in 2015 and on October 15, 2015, Gundlach's name was taken down from the site. In the terms of the deal, the original developer Michael Gundlach left operations to Adblock's continuing director, Gabriel Cubbage, and as of October 2, 2015, AdBlock began participating in the Acceptable Ads program. Acceptable Ads identifies "non-annoying" ads, which AdBlock shows by default. The intent is to allow non-invasive advertising, to either maintain support for websites that rely on advertising as a main source of revenue or for websites that have an agreement with the program. == Filters == AdBlock uses EasyList, the same filter syntax as Adblock Plus for Firefox, and natively supports the use of a number of filter lists. == Partnership with Amnesty International == On March 12, 2016, in support of World Day Against Cyber Censorship, and in partnership with Amnesty International, instead of blocking ads, AdBlock replaced ads with banners linked to articles on Amnesty's website, written by prominent free speech advocates such as Edward Snowden, to raise awareness of government-imposed online censorship and digital privacy issues around the world. The campaign was met with both praise and criticism, with AdBlock's CEO, Gabriel Cubbage, defending the decision in an essay on AdBlock's website, saying "We’re showing you Amnesty banners, just for today, because we believe users should be part of the conversation about online privacy. Tomorrow, those spaces will be vacant again. But take a moment to consider that in an increasingly information-driven world, when your right to digital privacy is threatened, so is your right to free expression." Meanwhile, Simon Sharwood of The Register characterized Cubbage's position as "'You should control your computer except when we feel political', says AdBlock CEO". == AdBlock for Firefox == On September 13, 2014, the AdBlock team released a version for Firefox users, ported from the code for Google Chrome, released under the same free software license as the original Adblock. The extension was removed on April 2, 2015, by an administrator on Mozilla Add-ons. On December 7, 2015, the official AdBlock site's knowledge base article stated that with version 44 or higher of Firefox desktop and Firefox Mobile, AdBlock will not be supported. The last version of Adblock for those platforms will work on older versions of Firefox. AdBlock was released again on Mozilla Add-ons on November 17, 2016. On April 1, 2012, Adblock developer Michael Gundlach tweaked the code to display LOLcats instead of simply blocking ads. Initially developed as a short-lived April Fools joke, the response was so positive that CatBlock was continued to be offered as an optional add-on supported by a monthly subscription. On October 23, 2014, the developer decided to end official support for CatBlock, and made it open-source, under GPLv3 licensing, as the original extension.
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Level set (data structures)

In computer science, a level set is a data structure designed to represent discretely sampled dynamic level sets of functions. A common use of this form of data structure is in efficient image rendering. The underlying method constructs a signed distance field that extends from the boundary, and can be used to solve the motion of the boundary in this field. == Chronological developments == The powerful level-set method is due to Osher and Sethian 1988. However, the straightforward implementation via a dense d-dimensional array of values, results in both time and storage complexity of O ( n d ) {\displaystyle O(n^{d})} , where n {\displaystyle n} is the cross sectional resolution of the spatial extents of the domain and d {\displaystyle d} is the number of spatial dimensions of the domain. === Narrow band === The narrow band level set method, introduced in 1995 by Adalsteinsson and Sethian, restricted most computations to a thin band of active voxels immediately surrounding the interface, thus reducing the time complexity in three dimensions to O ( n 2 ) {\displaystyle O(n^{2})} for most operations. Periodic updates of the narrowband structure, to rebuild the list of active voxels, were required which entailed an O ( n 3 ) {\displaystyle O(n^{3})} operation in which voxels over the entire volume were accessed. The storage complexity for this narrowband scheme was still O ( n 3 ) . {\displaystyle O(n^{3}).} Differential constructions over the narrow band domain edge require careful interpolation and domain alteration schemes to stabilise the solution. === Sparse field === This O ( n 3 ) {\displaystyle O(n^{3})} time complexity was eliminated in the approximate "sparse field" level set method introduced by Whitaker in 1998. The sparse field level set method employs a set of linked lists to track the active voxels around the interface. This allows incremental extension of the active region as needed without incurring any significant overhead. While consistently O ( n 2 ) {\displaystyle O(n^{2})} efficient in time, O ( n 3 ) {\displaystyle O(n^{3})} storage space is still required by the sparse field level set method. See for implementation details. === Sparse block grid === The sparse block grid method, introduced by Bridson in 2003, divides the entire bounding volume of size n 3 {\displaystyle n^{3}} into small cubic blocks of m 3 {\displaystyle m^{3}} voxels each. A coarse grid of size ( n / m ) 3 {\displaystyle (n/m)^{3}} then stores pointers only to those blocks that intersect the narrow band of the level set. Block allocation and deallocation occur as the surface propagates to accommodate to the deformations. This method has a suboptimal storage complexity of O ( ( n m ) 3 + m 3 n 2 ) {\displaystyle O\left((nm)3+m^{3}n^{2}\right)} , but retains the constant time access inherent to dense grids. === Octree === The octree level set method, introduced by Strain in 1999 and refined by Losasso, Gibou and Fedkiw, and more recently by Min and Gibou uses a tree of nested cubes of which the leaf nodes contain signed distance values. Octree level sets currently require uniform refinement along the interface (i.e. the narrow band) in order to obtain sufficient precision. This representation is efficient in terms of storage, O ( n 2 ) , {\displaystyle O(n^{2}),} and relatively efficient in terms of access queries, O ( log n ) . {\displaystyle O(\log \,n).} An advantage of the level method on octree data structures is that one can solve the partial differential equations associated with typical free boundary problems that use the level set method. The CASL research group has developed this line of work in computational materials, computational fluid dynamics, electrokinetics, image-guided surgery and controls. === Run-length encoded === The run-length encoding (RLE) level set method, introduced in 2004, applies the RLE scheme to compress regions away from the narrow band to just their sign representation while storing with full precision the narrow band. The sequential traversal of the narrow band is optimal and storage efficiency is further improved over the octree level set. The addition of an acceleration lookup table allows for fast O ( log ⁡ r ) {\displaystyle O(\log r)} random access, where r is the number of runs per cross section. Additional efficiency is gained by applying the RLE scheme in a dimensional recursive fashion, a technique introduced by Nielsen & Museth's similar DT-Grid. === Hash Table Local Level Set === The Hash Table Local Level Set method was introduced in 2011 by Eyiyurekli and Breen and extended in 2012 by Brun, Guittet, and Gibou, only computes the level set data in a band around the interface, as in the Narrow Band Level-Set Method, but also only stores the data in that same band. A hash table data structure is used, which provides an O ( 1 ) {\displaystyle O(1)} access to the data. However, Brun et al. conclude that their method, while being easier to implement, performs worse than a quadtree implementation. They find that as it is, [...] a quadtree data structure seems more adapted than the hash table data structure for level-set algorithms. Three main reasons for worse efficiency are listed: to obtain accurate results, a rather large band is required close to the interface, which counterbalances the absence of grid nodes far from the interface; the performances are deteriorated by extrapolation procedures on the outer edges of the local grid and the width of the band restricts the time step and slows down the method. === Point-based === Corbett in 2005 introduced the point-based level set method. Instead of using a uniform sampling of the level set, the continuous level set function is reconstructed from a set of unorganized point samples via moving least squares.
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ViEWER

ViEWER, the Virtual Environment Workbench for Education and Research, is a proprietary, freeware computer program for Microsoft Windows written by researchers at the University of Idaho for the study of visual perception and complex immersive three-dimensional environments. It was created using C++ and OpenGL, and has been used by Dr. Brian Dyre, Dr. Steffen Werner, Dr. Ernesto Bustamante, Dr. Ben Barton, and their undergraduate and graduate researchers in visual perception, signal detection, and child-safety experiments.
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IDMS

The Integrated Database Management System (IDMS) is a network model (CODASYL) database management system for mainframes. It was first developed at BFGoodrich and later marketed by Cullinane Database Systems (renamed Cullinet in 1983). Since 1989 the product has been owned by Computer Associates (now CA Technologies), who renamed it Advantage CA-IDMS and later simply to CA IDMS. In 2018 Broadcom acquired CA Technologies, renaming it back to IDMS. == History == The roots of IDMS go back to the pioneering database management system called Integrated Data Store (IDS), developed at General Electric by a team led by Charles Bachman and first released in 1964. In the early 1960s IDS was taken from its original form, by the computer group of the BFGoodrich Chemical Division, and re-written in a language called Intermediate System Language (ISL). ISL was designed as a portable system programming language able to produce code for a variety of target machines. Since ISL was actually written in ISL, it was able to be ported to other machine architectures with relative ease, and then to produce code that would execute on them. The Chemical Division computer group had given some thought to selling copies of IDMS to other companies, but was told by management that they were not in the software products business. Eventually, a deal was struck with John Cullinane to buy the rights and market the product. Because Cullinane was required to remit royalties back to B.F. Goodrich, all add-on products were listed and billed as separate products – even if they were mandatory for the core IDMS product to work. This sometimes confused customers. The original platforms were the GE 235 computer and GE DATANET-30 message switching computer: later the product was ported to IBM mainframes and to DEC and ICL hardware. The IBM-ported version runs on IBM mainframe systems (System/360, System/370, System/390, zSeries, System z9). In the mid-1980s, it was claimed that some 2,500 IDMS licenses had been sold. Users included the Strategic Air Command, Ford of Canada, Ford of Europe, Jaguar Cars, Clarks Shoes UK, Axa/PPP, MAPFRE, Royal Insurance, Tesco, Manulife, Hudson's Bay Company, Cleveland Clinic, Bank of Canada, General Electric, Aetna and BT in the UK. A version for use on the Digital Equipment Corporation PDP-11 series of computers was sold to DEC and was marketed as DBMS-11. In 1976 the source code was licensed to ICL, who ported the software to run on their 2900 series mainframes, and subsequently also on the older 1900 range. ICL continued development of the software independently of Cullinane, selling the original ported product under the name ICL 2900 IDMS and an enhanced version as IDMSX. In this form it was used by many large UK users, an example being the Pay-As-You-Earn system operated by Inland Revenue. Many of these IDMSX systems for UK Government were still running in 2013. In the early to mid-1980s, relational database management systems started to become more popular, encouraged by increasing hardware power and the move to minicomputers and client–server architecture. Relational databases offered improved development productivity over CODASYL systems, and the traditional objections based on poor performance were slowly diminishing. Cullinet attempted to continue competing against IBM's DB2 and other relational databases by developing a relational front-end and a range of productivity tools. These included Automatic System Facility (ASF), which made use of a pre-existing IDMS feature called LRF (Logical Record Facility). ASF was a fill-in-the-blanks database generator that would also develop a mini-application to maintain the tables. It is difficult to judge whether such features may have been successful in extending the selling life of the product, but they made little impact in the long term. Those users who stayed with IDMS were primarily interested in its high performance, not in its relational capabilities. It was widely recognized (helped by a high-profile campaign by E. F. Codd, the father of the relational model) that there was a significant difference between a relational database and a network database with a relational veneer. In 1989 Computer Associates continued after Cullinet acquisition with the development and released Release 12.0 with full SQL in 1992–93. CA Technologies continued to market and support the CA IDMS and enhanced IDMS in subsequent releases by TCP/IP support, two phase commit support, XML publishing, zIIP specialty processor support, Web-enabled access in combination with CA IDMS Server, SQL Option and GUI database administration via CA IDMS Visual DBA tool. CA-IDMS systems are today still running businesses worldwide. Many customers have opted to web-enable their applications via the CA-IDMS SQL Option which is part of CA Technologies' Dual Database Strategy. == Integrated Data Dictionary == One of the sophisticated features of IDMS was its built-in Integrated data dictionary (IDD). The IDD was primarily developed to maintain database definitions. It was itself an IDMS database. DBAs (database administrators) and other users interfaced with the IDD using a language called Data Dictionary Definition Language (DDDL). IDD was also used to store definitions and code for other products in the IDMS family such as ADS/Online and IDMS-DC. IDD's power was that it was extensible and could be used to create definitions of just about anything. Some companies used it to develop in-house documentation. == Overview == === Logical Data Model === The data model offered to users is the CODASYL network model. The main structuring concepts in this model are records and sets. Records essentially follow the COBOL pattern, consisting of fields of different types: this allows complex internal structure such as repeating items and repeating groups. The most distinctive structuring concept in the Codasyl model is the set. Not to be confused with a mathematical set, a Codasyl set represents a one-to-many relationship between records: one owner, many members. The fact that a record can be a member in many different sets is the key factor that distinguishes the network model from the earlier hierarchical model. As with records, each set belongs to a named set type (different set types model different logical relationships). Sets are in fact ordered, and the sequence of records in a set can be used to convey information. A record can participate as an owner and member of any number of sets. Records have identity, the identity being represented by a value known as a database key. In IDMS, as in most other Codasyl implementations, the database key is directly related to the physical address of the record on disk. Database keys are also used as pointers to implement sets in the form of linked lists and trees. This close correspondence between the logical model and the physical implementation (which is not a strictly necessary part of the Codasyl model, but was a characteristic of all successful implementations) is responsible for the efficiency of database retrieval, but also makes operations such as database loading and restructuring rather expensive. Records can be accessed directly by database key, by following set relationships, or by direct access using key values. Initially the only direct access was through hashing, a mechanism known in the Codasyl model as CALC access. In IDMS, CALC access is implemented through an internal set, linking all records that share the same hash value to an owner record that occupies the first few bytes of every disk page. In subsequent years, some versions of IDMS added the ability to access records using BTree-like indexes. === Storage === IDMS organizes its databases as a series of files. These files are mapped and pre-formatted into so-called areas. The areas are subdivided into pages which correspond to physical blocks on the disk. The database records are stored within these blocks. The DBA allocates a fixed number of pages in a file for each area. The DBA then defines which records are to be stored in each area, and details of how they are to be stored. IDMS intersperses special space-allocation pages throughout the database. These pages are used to keep track of the free space available in each page in the database. To reduce I/O requirements, the free space is only tracked for all pages when the free space for the area falls below 30%. Four methods are available for storing records in an IDMS database: Direct, Sequential, CALC, and VIA. The Fujitsu/ICL IDMSX version extends this with two more methods, Page Direct, and Random. In direct mode the target database key is specified by the user and is stored as close as possible to that DB key, with the actual DB key on which the record is stored being returned to the application program. Sequential placement (not to be confused with indexed sequential), simply places each new record at the end of the area. This option is rarely used. CALC uses a hashing algo
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Tensor operator

In pure and applied mathematics, quantum mechanics and computer graphics, a tensor operator generalizes the notion of operators which are scalars and vectors. A special class of these are spherical tensor operators which apply the notion of the spherical basis and spherical harmonics. The spherical basis closely relates to the description of angular momentum in quantum mechanics and spherical harmonic functions. The coordinate-free generalization of a tensor operator is known as a representation operator. == The general notion of scalar, vector, and tensor operators == In quantum mechanics, physical observables that are scalars, vectors, and tensors, must be represented by scalar, vector, and tensor operators, respectively. Whether something is a scalar, vector, or tensor depends on how it is viewed by two observers whose coordinate frames are related to each other by a rotation. Alternatively, one may ask how, for a single observer, a physical quantity transforms if the state of the system is rotated. Consider, for example, a system consisting of a molecule of mass M {\displaystyle M} , traveling with a definite center of mass momentum, p z ^ {\displaystyle p{\mathbf {\hat {z}} }} , in the z {\displaystyle z} direction. If we rotate the system by 90 ∘ {\displaystyle 90^{\circ }} about the y {\displaystyle y} axis, the momentum will change to p x ^ {\displaystyle p{\mathbf {\hat {x}} }} , which is in the x {\displaystyle x} direction. The center-of-mass kinetic energy of the molecule will, however, be unchanged at p 2 / 2 M {\displaystyle p^{2}/2M} . The kinetic energy is a scalar and the momentum is a vector, and these two quantities must be represented by a scalar and a vector operator, respectively. By the latter in particular, we mean an operator whose expected values in the initial and the rotated states are p z ^ {\displaystyle p{\mathbf {\hat {z}} }} and p x ^ {\displaystyle p{\mathbf {\hat {x}} }} . The kinetic energy on the other hand must be represented by a scalar operator, whose expected value must be the same in the initial and the rotated states. In the same way, tensor quantities must be represented by tensor operators. An example of a tensor quantity (of rank two) is the electrical quadrupole moment of the above molecule. Likewise, the octupole and hexadecapole moments would be tensors of rank three and four, respectively. Other examples of scalar operators are the total energy operator (more commonly called the Hamiltonian), the potential energy, and the dipole-dipole interaction energy of two atoms. Examples of vector operators are the momentum, the position, the orbital angular momentum, L {\displaystyle {\mathbf {L} }} , and the spin angular momentum, S {\displaystyle {\mathbf {S} }} . (Fine print: Angular momentum is a vector as far as rotations are concerned, but unlike position or momentum it does not change sign under space inversion, and when one wishes to provide this information, it is said to be a pseudovector.) Scalar, vector and tensor operators can also be formed by products of operators. For example, the scalar product L ⋅ S {\displaystyle {\mathbf {L} }\cdot {\mathbf {S} }} of the two vector operators, L {\displaystyle {\mathbf {L} }} and S {\displaystyle {\mathbf {S} }} , is a scalar operator, which figures prominently in discussions of the spin–orbit interaction. Similarly, the quadrupole moment tensor of our example molecule has the nine components Q i j = ∑ α q α ( 3 r α , i r α , j − r α 2 δ i j ) . {\displaystyle Q_{ij}=\sum _{\alpha }q_{\alpha }\left(3r_{\alpha ,i}r_{\alpha ,j}-r_{\alpha }^{2}\delta _{ij}\right).} Here, the indices i {\displaystyle i} and j {\displaystyle j} can independently take on the values 1, 2, and 3 (or x {\displaystyle x} , y {\displaystyle y} , and z {\displaystyle z} ) corresponding to the three Cartesian axes, the index α {\displaystyle \alpha } runs over all particles (electrons and nuclei) in the molecule, q α {\displaystyle q_{\alpha }} is the charge on particle α {\displaystyle \alpha } , and r α , i {\displaystyle r_{\alpha ,i}} is the i {\displaystyle i} -th component of the position of this particle. Each term in the sum is a tensor operator. In particular, the nine products r α , i r α , j {\displaystyle r_{\alpha ,i}r_{\alpha ,j}} together form a second rank tensor, formed by taking the outer product of the vector operator r α {\displaystyle {\mathbf {r} }_{\alpha }} with itself. == Rotations of quantum states == === Quantum rotation operator === The rotation operator about the unit vector n (defining the axis of rotation) through angle θ is U [ R ( θ , n ^ ) ] = exp ⁡ ( − i θ ℏ n ^ ⋅ J ) {\displaystyle U[R(\theta ,{\hat {\mathbf {n} }})]=\exp \left(-{\frac {i\theta }{\hbar }}{\hat {\mathbf {n} }}\cdot \mathbf {J} \right)} where J = (Jx, Jy, Jz) are the rotation generators (also the angular momentum matrices): J x = ℏ 2 ( 0 1 0 1 0 1 0 1 0 ) J y = ℏ 2 ( 0 i 0 − i 0 i 0 − i 0 ) J z = ℏ ( − 1 0 0 0 0 0 0 0 1 ) {\displaystyle J_{x}={\frac {\hbar }{\sqrt {2}}}{\begin{pmatrix}0&1&0\\1&0&1\\0&1&0\end{pmatrix}}\,\quad J_{y}={\frac {\hbar }{\sqrt {2}}}{\begin{pmatrix}0&i&0\\-i&0&i\\0&-i&0\end{pmatrix}}\,\quad J_{z}=\hbar {\begin{pmatrix}-1&0&0\\0&0&0\\0&0&1\end{pmatrix}}} and let R ^ = R ^ ( θ , n ^ ) {\displaystyle {\widehat {R}}={\widehat {R}}(\theta ,{\hat {\mathbf {n} }})} be a rotation matrix. According to the Rodrigues' rotation formula, the rotation operator then amounts to U [ R ( θ , n ^ ) ] = 1 1 − i sin ⁡ θ ℏ n ^ ⋅ J − 1 − cos ⁡ θ ℏ 2 ( n ^ ⋅ J ) 2 . {\displaystyle U[R(\theta ,{\hat {\mathbf {n} }})]=1\!\!1-{\frac {i\sin \theta }{\hbar }}{\hat {\mathbf {n} }}\cdot \mathbf {J} -{\frac {1-\cos \theta }{\hbar ^{2}}}({\hat {\mathbf {n} }}\cdot \mathbf {J} )^{2}.} An operator Ω ^ {\displaystyle {\widehat {\Omega }}} is invariant under a unitary transformation U if Ω ^ = U † Ω ^ U ; {\displaystyle {\widehat {\Omega }}={U}^{\dagger }{\widehat {\Omega }}U;} in this case for the rotation U ^ ( R ) {\displaystyle {\widehat {U}}(R)} , Ω ^ = U ( R ) † Ω ^ U ( R ) = exp ⁡ ( i θ ℏ n ^ ⋅ J ) Ω ^ exp ⁡ ( − i θ ℏ n ^ ⋅ J ) . {\displaystyle {\widehat {\Omega }}={U(R)}^{\dagger }{\widehat {\Omega }}U(R)=\exp \left({\frac {i\theta }{\hbar }}{\hat {\mathbf {n} }}\cdot \mathbf {J} \right){\widehat {\Omega }}\exp \left(-{\frac {i\theta }{\hbar }}{\hat {\mathbf {n} }}\cdot \mathbf {J} \right).} === Angular momentum eigenkets === The orthonormal basis set for total angular momentum is | j , m ⟩ {\displaystyle |j,m\rangle } , where j is the total angular momentum quantum number and m is the magnetic angular momentum quantum number, which takes values −j, −j + 1, ..., j − 1, j. A general state within the j subspace | ψ ⟩ = ∑ m c j m | j , m ⟩ {\displaystyle |\psi \rangle =\sum _{m}c_{jm}|j,m\rangle } rotates to a new state by: | ψ ¯ ⟩ = U ( R ) | ψ ⟩ = ∑ m c j m U ( R ) | j , m ⟩ {\displaystyle |{\bar {\psi }}\rangle =U(R)|\psi \rangle =\sum _{m}c_{jm}U(R)|j,m\rangle } Using the completeness condition: I = ∑ m ′ | j , m ′ ⟩ ⟨ j , m ′ | {\displaystyle I=\sum _{m'}|j,m'\rangle \langle j,m'|} we have | ψ ¯ ⟩ = I U ( R ) | ψ ⟩ = ∑ m m ′ c j m | j , m ′ ⟩ ⟨ j , m ′ | U ( R ) | j , m ⟩ {\displaystyle |{\bar {\psi }}\rangle =IU(R)|\psi \rangle =\sum _{mm'}c_{jm}|j,m'\rangle \langle j,m'|U(R)|j,m\rangle } Introducing the Wigner D matrix elements: D ( R ) m ′ m ( j ) = ⟨ j , m ′ | U ( R ) | j , m ⟩ {\displaystyle {D(R)}_{m'm}^{(j)}=\langle j,m'|U(R)|j,m\rangle } gives the matrix multiplication: | ψ ¯ ⟩ = ∑ m m ′ c j m D m ′ m ( j ) | j , m ′ ⟩ ⇒ | ψ ¯ ⟩ = D ( j ) | ψ ⟩ {\displaystyle |{\bar {\psi }}\rangle =\sum _{mm'}c_{jm}D_{m'm}^{(j)}|j,m'\rangle \quad \Rightarrow \quad |{\bar {\psi }}\rangle =D^{(j)}|\psi \rangle } For one basis ket: | j , m ¯ ⟩ = ∑ m ′ D ( R ) m ′ m ( j ) | j , m ′ ⟩ {\displaystyle |{\overline {j,m}}\rangle =\sum _{m'}{D(R)}_{m'm}^{(j)}|j,m'\rangle } For the case of orbital angular momentum, the eigenstates | ℓ , m ⟩ {\displaystyle |\ell ,m\rangle } of the orbital angular momentum operator L and solutions of Laplace's equation on a 3d sphere are spherical harmonics: Y ℓ m ( θ , ϕ ) = ⟨ θ , ϕ | ℓ , m ⟩ = ( 2 ℓ + 1 ) 4 π ( ℓ − m ) ! ( ℓ + m ) ! P ℓ m ( cos ⁡ θ ) e i m ϕ {\displaystyle Y_{\ell }^{m}(\theta ,\phi )=\langle \theta ,\phi |\ell ,m\rangle ={\sqrt {{(2\ell +1) \over 4\pi }{(\ell -m)! \over (\ell +m)!}}}\,P_{\ell }^{m}(\cos {\theta })\,e^{im\phi }} where Pℓm is an associated Legendre polynomial, ℓ is the orbital angular momentum quantum number, and m is the orbital magnetic quantum number which takes the values −ℓ, −ℓ + 1, ... ℓ − 1, ℓ The formalism of spherical harmonics have wide applications in applied mathematics, and are closely related to the formalism of spherical tensors, as shown below. Spherical harmonics are functions of the polar and azimuthal angles, ϕ and θ respectively, which can be conveniently collected into a unit vector n(θ, ϕ) pointing in the direction of those angles, in the Cartesian basis it is: n ^ ( θ , ϕ ) = cos ⁡ ϕ sin ⁡ θ e x + s
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PNGOUT

PNGOUT is a freeware command line optimizer for PNG images written by Ken Silverman. The transformation is lossless, meaning that the resulting image is visually identical to the source image. According to its author, this program can often get higher compression than other optimizers by 5–10%. It is possible to compress some inflated PNGs to a size below 1% of the original file. PNGOUT was also available as a plug-in for the freeware image viewer IrfanView and can be enabled as an option when saving files. It allows editing of various PNGOUT settings via a dialog box. PNGOUT integration was removed in IrfanView version 4.58 in favour of OptiPNG. In 2006, a commercial version of PNGOUT with a graphical user interface, known as PNGOUTWin, was released by Ardfry Imaging, a small company Silverman co-founded in 2005. There is also a freeware GUI frontend to PNGOUT available, known as PNGGauntlet. == Main operation == The main function of PNGOUT is to reduce the size of image data contained in the IDAT chunk. This chunk is compressed using the deflate algorithm. Deflate algorithms can vary in speed and compression ratio, with higher compression ratios generally implying lower speed. Ken Silverman wrote a deflate compressor for PNGOUT that is slower than the ones used in most graphics software, but produces smaller files. PNGOUT also performs automatic bit depth, color, and palette reduction where appropriate.
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ViEWER

ViEWER, the Virtual Environment Workbench for Education and Research, is a proprietary, freeware computer program for Microsoft Windows written by researchers at the University of Idaho for the study of visual perception and complex immersive three-dimensional environments. It was created using C++ and OpenGL, and has been used by Dr. Brian Dyre, Dr. Steffen Werner, Dr. Ernesto Bustamante, Dr. Ben Barton, and their undergraduate and graduate researchers in visual perception, signal detection, and child-safety experiments.
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Powerset (company)

Powerset was an American company based in San Francisco, California, that, in 2006, was developing a natural language search engine for the Internet. On July 1, 2008, Powerset was acquired by Microsoft for an estimated $100 million (~$143 million in 2024). Powerset was working on building a natural language search engine that could find targeted answers to user questions (as opposed to keyword based search). For example, when confronted with a question like "Which U.S. state has the highest income tax?", conventional search engines ignore the question phrasing and instead do a search on the keywords "state", "highest", "income", and "tax". Powerset on the other hand, attempts to use natural language processing to understand the nature of the question and return pages containing the answer. The company was in the process of "building a natural language search engine that reads and understands every sentence on the Web". The company has licensed natural language technology from PARC, the former Xerox Palo Alto Research Center. On May 11, 2008, the company unveiled a tool for searching a fixed subset of English Wikipedia using conversational phrases rather than keywords. Acquisition by Microsoft: One significant milestone in Powerset's history was its acquisition by Microsoft on July 1, 2008, for an estimated $100 million. This acquisition was part of Microsoft's broader strategy to enhance its search capabilities and compete more effectively with other search engine providers, particularly Google. Natural Language Search Engine: Powerset's primary focus was on developing a natural language search engine capable of understanding and interpreting user queries in a more human-like manner. Instead of simply matching keywords, Powerset aimed to comprehend the meaning behind the words, allowing for more accurate and contextually relevant search results. Technology and Partnerships: Powerset had licensed natural language technology from PARC, the Xerox Palo Alto Research Center. This technology likely played a crucial role in the development of Powerset's NLP capabilities. Wikipedia Search Tool: In May 2008, Powerset unveiled a search tool that allowed users to search a fixed subset of English Wikipedia using conversational phrases rather than traditional keywords. This demonstrated the potential of Powerset's NLP technology in providing more precise and relevant search results. == Powerlabs == In a form of beta testing, Powerset opened an online community called Powerlabs on September 17, 2007. Business Week said: "The company hopes the site will marshal thousands of people to help build and improve its search engine before it goes public next year." Said The New York Times: "[Powerset Labs] goes far beyond the 'alpha' or 'beta' testing involved in most software projects, when users put a new product through rigorous testing to find its flaws. Powerset doesn’t have a product yet, but rather a collection of promising natural language technologies, which are the fruit of years of research at Xerox PARC." Powerlabs' initial search results are taken from Wikipedia. == Notable people == Barney Pell (born March 18, 1968, in Hollywood, California) was co-founder and CEO of Powerset. Pell received his Bachelor of Science degree in symbolic systems from Stanford University in 1989, where he graduated Phi Beta Kappa and was a National Merit Scholar. Pell received a PhD in computer science from Cambridge University in 1993, where he was a Marshall Scholar. He has worked at NASA, as chief strategist and vice president of business development at StockMaster.com (acquired by Red Herring in March, 2000) and at Whizbang! Labs. Prior to joining Powerset, Pell was an Entrepreneur-in-Residence at Mayfield Fund, a venture capital firm in Silicon Valley. Pell is also a founder of Moon Express, Inc., a U.S. company awarded a $10M commercial lunar contract by NASA and a competitor in the Google Lunar X PRIZE. Steve Newcomb was the COO and co-founder of Powerset. Prior to joining Powerset, he was a co-founder of Loudfire, General Manager at Promptu, and was on the board of directors at Jaxtr. He left Powerset in October 2007 to form Virgance, a social startup incubator. Lorenzo Thione (born in Como, Italy) was the product architect and co-founder of Powerset. Prior to joining Powerset, he worked at FXPAL in natural language processing and related research fields. Thione earned his master's degree in software engineering from the University of Texas at Austin. Ronald Kaplan, former manager of research in Natural Language Theory and Technology at PARC, served as the company's CTO and CSO. Ryan Ferrier is a member of the founding team of Powerset. He managed personnel and internal operations. After 2008 he went on to co-found Serious Business, which made Facebook applications and was later bought by Zynga. Another Powerset alumnus, Alex Le, became CTO of Serious Business and went on to become an executive producer at Zynga when it bought the company. Siqi Chen founded a stealth startup in mobile computing after leaving Powerset. Tom Preston-Werner worked at Powerset and left after the acquisition to found GitHub. == Investors == Powerset attracted a wide range of investors, many of whom had considerable experience in the venture capital field. The company received $12.5 million (~$18.2 million in 2024) in Series A funding during November 2007, co-led by the venture capital firms Foundation Capital and The Founders Fund. Among the better-known investors: Esther Dyson, founding chairman of ICANN, founder of the newsletter Release 1.0 and editor at Cnet Peter Thiel, founder and former CEO of PayPal Luke Nosek, founder of PayPal Todd Parker. Managing Partner, Hidden River Ventures Reid Hoffman, executive vice president of PayPal and founder of LinkedIn First Round Capital, seed-stage venture firm
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Showbox.com

Showbox is an online video streaming platform that enables users to stream and download many videos, commonly movies and TV shows, for free. == History == The company opened the platforms to users who registered from its beta in late 2015. The platform was officially launched in February 2016, enabling any visitor to sign up and create videos online. In April 2016, Showbox was featured on the Product Hunt website, coming to the top of the website's lists for that day and week with over 1400 upvotes from the Product Hunt community. Also in April 2016, Showbox partnered with YouTube's leading multi-channel networks, including Fullscreen, BroadbandTV, StyleHaul, AwesomenessTV, and BuzzMyVideos, to enable their communities of creators to access the platform. In June 2016, the company launched Showbox For Brands, a business-oriented video creation platform, enabling companies to create video content in-house and with their communities and influencers. In March 2017, the company launched Showbox Engage, a use case of its B2B product launched in 2016, enabling companies to launch user-generated content campaigns with their communities. In April 2017, Showbox and the United Nations announced a partnership around the 70th anniversary of the declaration of human rights, with an annual, ongoing global campaign in 135 languages, inviting people worldwide to create their part of the declaration in a video from anywhere around the world. In November 2017, Showbox partnered with the Ad:tech and Digital Marketing World Forum conferences (DMWF) in New York to provide their users and communities with a User Generated Content video solution. == Technology == Showbox's video creation technology includes an online green screen feature, proprietary computer vision algorithms, deep learning technology to support the automatic creation of videos in the cloud, and advanced video composition, including special effects. == Coverage and awards == In March 2015, Showbox was nominated as one of the 10 Israeli startups to take over our TV screens this year. In July 2016, Showbox won the Publicis90 award as part of Publicis' "global initiative to foster digital entrepreneurship". In March 2017, Showbox was chosen as one of The Culture Trip's 10 startups to watch for in 2017.
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Voice activity detection

Voice activity detection (VAD), also known as speech activity detection or speech detection, is the detection of the presence or absence of human speech, used in speech processing. The main uses of VAD are in speaker diarization, speech coding and speech recognition. It can facilitate speech processing, and can also be used to deactivate some processes during non-speech section of an audio session: it can avoid unnecessary coding/transmission of silence packets in Voice over Internet Protocol (VoIP) applications, saving on computation and on network bandwidth. VAD is an important enabling technology for a variety of speech-based applications. Therefore, various VAD algorithms have been developed that provide varying features and compromises between latency, sensitivity, accuracy and computational cost. Some VAD algorithms also provide further analysis, for example whether the speech is voiced, unvoiced or sustained. Voice activity detection is usually independent of language. It was first investigated for use on time-assignment speech interpolation (TASI) systems. == Algorithm overview == The typical design of a VAD algorithm is as follows: There may first be a noise reduction stage, e.g. via spectral subtraction. Then some features or quantities are calculated from a section of the input signal. A classification rule is applied to classify the section as speech or non-speech – often this classification rule finds when a value exceeds a certain threshold. There may be some feedback in this sequence, in which the VAD decision is used to improve the noise estimate in the noise reduction stage, or to adaptively vary the threshold(s). These feedback operations improve the VAD performance in non-stationary noise (i.e. when the noise varies a lot). A representative set of recently published VAD methods formulates the decision rule on a frame by frame basis using instantaneous measures of the divergence distance between speech and noise. The different measures which are used in VAD methods include spectral slope, correlation coefficients, log likelihood ratio, cepstral, weighted cepstral, and modified distance measures. Independently from the choice of VAD algorithm, a compromise must be made between having voice detected as noise, or noise detected as voice (between false positive and false negative). A VAD operating in a mobile phone must be able to detect speech in the presence of a range of very diverse types of acoustic background noise. In these difficult detection conditions it is often preferable that a VAD should fail-safe, indicating speech detected when the decision is in doubt, to lower the chance of losing speech segments. The biggest difficulty in the detection of speech in this environment is the very low signal-to-noise ratios (SNRs) that are encountered. It may be impossible to distinguish between speech and noise using simple level detection techniques when parts of the speech utterance are buried below the noise. == Applications == VAD is an integral part of different speech communication systems such as audio conferencing, echo cancellation, speech recognition, speech encoding, speaker recognition and hands-free telephony. In the field of multimedia applications, VAD allows simultaneous voice and data applications. Similarly, in Universal Mobile Telecommunications Systems (UMTS), it controls and reduces the average bit rate and enhances overall coding quality of speech. In cellular radio systems (for instance GSM and CDMA systems) based on Discontinuous Transmission (DTX) mode, VAD is essential for enhancing system capacity by reducing co-channel interference and power consumption in portable digital devices. In speech processing applications, voice activity detection plays an important role since non-speech frames are often discarded. For a wide range of applications such as digital mobile radio, Digital Simultaneous Voice and Data (DSVD) or speech storage, it is desirable to provide a discontinuous transmission of speech-coding parameters. Advantages can include lower average power consumption in mobile handsets, higher average bit rate for simultaneous services like data transmission, or a higher capacity on storage chips. However, the improvement depends mainly on the percentage of pauses during speech and the reliability of the VAD used to detect these intervals. On the one hand, it is advantageous to have a low percentage of speech activity. On the other hand, clipping, that is the loss of milliseconds of active speech, should be minimized to preserve quality. This is the crucial problem for a VAD algorithm under heavy noise conditions. === Use in telemarketing === One controversial application of VAD is in conjunction with predictive dialers used by telemarketing firms. In order to maximize agent productivity, telemarketing firms set up predictive dialers to call more numbers than they have agents available, knowing most calls will end up in either "Ring – No Answer" or answering machines. When a person answers, they typically speak briefly ("Hello", "Good evening", etc.) and then there is a brief period of silence. Answering machine messages are usually 3–15 seconds of continuous speech. By setting VAD parameters correctly, dialers can determine whether a person or a machine answered the call and, if it's a person, transfer the call to an available agent. If it detects an answering machine message, the dialer hangs up. Often, even when the system correctly detects a person answering the call, no agent may be available, resulting in a "silent call". Call screening with a multi-second message like "please say who you are, and I may pick up the phone" will frustrate such automated calls. == Performance evaluation == To evaluate a VAD, its output using test recordings is compared with those of an "ideal" VAD – created by hand-annotating the presence or absence of voice in the recordings. The performance of a VAD is commonly evaluated on the basis of the following four parameters: FEC (Front End Clipping): clipping introduced in passing from noise to speech activity; MSC (Mid Speech Clipping): clipping due to speech misclassified as noise; OVER: noise interpreted as speech due to the VAD flag remaining active in passing from speech activity to noise; NDS (Noise Detected as Speech): noise interpreted as speech within a silence period. Although the method described above provides useful objective information concerning the performance of a VAD, it is only an approximate measure of the subjective effect. For example, the effects of speech signal clipping can at times be hidden by the presence of background noise, depending on the model chosen for the comfort noise synthesis, so some of the clipping measured with objective tests is in reality not audible. It is therefore important to carry out subjective tests on VADs, the main aim of which is to ensure that the clipping perceived is acceptable. In VoIP applications, front-end clipping can be reduced by rewinding to shortly before the detection and sending very slightly delayed data. This kind of test requires a certain number of listeners to judge recordings containing the processing results of the VADs being tested, giving marks to several speech sequences on the following features: Quality; Comprehension difficulty; Audibility of clipping. These marks are then used to calculate average results for each of the features listed above, thus providing a global estimate of the behavior of the VAD being tested. To conclude, whereas objective methods are very useful in an initial stage to evaluate the quality of a VAD, subjective methods are more significant. As they require the participation of several people for a few days, increasing cost, they are generally only used when a proposal is about to be standardized. == Implementations == One early standard VAD is that developed by British Telecom for use in the Pan-European digital cellular mobile telephone service in 1991. It uses inverse filtering trained on non-speech segments to filter out background noise, so that it can then more reliably use a simple power-threshold to decide if a voice is present. The G.729 standard calculates the following features for its VAD: line spectral frequencies, full-band energy, low-band energy (<1 kHz), and zero-crossing rate. It applies a simple classification using a fixed decision boundary in the space defined by these features, and then applies smoothing and adaptive correction to improve the estimate. The GSM standard includes two VAD options developed by ETSI. Option 1 computes the SNR in nine bands and applies a threshold to these values. Option 2 calculates different parameters: channel power, voice metrics, and noise power. It then thresholds the voice metrics using a threshold that varies according to the estimated SNR. The Speex audio compression library uses a procedure named Improved Minima Controlled Recursive Averaging, which uses a smoothed representation of spectral pow
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Digital sculpting

Digital sculpting, also known as sculpt modeling or 3D sculpting, is the use of software that offers tools to push, pull, smooth, grab, pinch or otherwise manipulate a digital object as if it were made of a real-life substance such as clay. == Sculpting technology == The geometry used in digital sculpting programs to represent the model can vary; each offers different benefits and limitations. The majority of digital sculpting tools on the market use mesh-based geometry, in which an object is represented by an interconnected surface mesh of polygons that can be pushed and pulled around. This is somewhat similar to the physical process of beating copper plates to sculpt a scene in relief. Other digital sculpting tools use voxel-based geometry, in which the volume of the object is the basic element. Material can be added and removed, much like sculpting in clay. Still other tools make use of more than one basic geometry representation. A benefit of mesh-based programs is that they support sculpting at multiple resolutions on a single model. Areas of the model that are finely detailed can have very small polygons while other areas can have larger polygons. In many mesh-based programs, the mesh can be edited at different levels of detail, and the changes at one level will propagate to higher and lower levels of model detail. A limitation of mesh-based sculpting is the fixed topology of the mesh; the specific arrangement of the polygons can limit the ways in which detail can be added or manipulated. A benefit of voxel-based sculpting is that voxels allow complete freedom over form. The topology of a model can be altered continually during the sculpting process as material is added and subtracted, which frees the sculptor from considering the layout of polygons on the model's surface. After sculpting, it may be necessary to retopologize the model to obtain a clean mesh for use in animation or real-time rendering. Voxels, however, are more limited in handling multiple levels of detail. Unlike mesh-based modeling, broad changes made to voxels at a low level of detail may completely destroy finer details. == Uses == Sculpting can often introduce details to meshes that would otherwise have been difficult or impossible to create using traditional 3D modeling techniques. This makes it preferable for achieving photorealistic and hyperrealistic results, though, many stylized results are achieved as well. Sculpting is primarily used in high poly organic modeling (the creation of 3D models which consist mainly of curves or irregular surfaces, as opposed to hard surface modeling). It is also used by auto manufacturers in their design of new cars. It can create the source meshes for low poly game models used in video games. In conjunction with other 3D modeling and texturing techniques and Displacement and Normal mapping, it can greatly enhance the appearance of game meshes often to the point of photorealism. Some sculpting programs like 3D-Coat, Zbrush, and Mudbox offer ways to integrate their workflows with traditional 3D modeling and rendering programs. Conversely, 3D modeling applications like 3ds Max, Maya and MODO are now incorporating sculpting capability as well, though these are usually less advanced than tools found in sculpting-specific applications. High poly sculpts are also extensively used in CG artwork for movies, industrial design, art, photorealistic illustrations, and for prototyping in 3D printing. == 3D print == Sculptors and digital artists use digital sculpting to create a model (or Digital Twin) to be materialized through CNC technologies including 3D printing. The final sculptures are often called Digital Sculpture or 3D printed art. While digital technologies have emerged in many art disciplines (painting, photography), this is less the case for digital sculpture due to the higher complexity and technology limitations to produce the final sculpture. == Sculpting Process == The best way to learn sculpture is by understanding primary, secondary and tertiary forms. First, break down the object you want to make down its basic shapes, such as a sphere or cube. Focus on making the large, overall shape of the object. After that, work on the bigger shapes on top of or inside the object. These can be protrusions or cut outs. Then, do a final detail pass, such as pores or lines to break up the shape. == Sculpting programs == There are a number of digital sculpting tools available. Some popular tools for creating are: Traditional 3D modeling suites are also beginning to include sculpting capability. 3D modeling programs which currently feature some form of sculpting include the following:
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Application Lifecycle Framework

The Application Lifecycle Framework (ALF) was a project by the Eclipse Foundation that aimed to create a standardized, open-source system to allow different application lifecycle management (ALM) tools to work together more easily. The goal was to provide common protocols and integration services that would let software development tools from different vendors communicate and share data. However, the project failed to gain sufficient support from major industry players and was terminated in 2008.
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Shape factor (image analysis and microscopy)

Shape factors are dimensionless quantities used in image analysis and microscopy that numerically describe the shape of a particle, independent of its size. Shape factors are calculated from measured dimensions, such as diameter, chord lengths, area, perimeter, centroid, moments, etc. The dimensions of the particles are usually measured from two-dimensional cross-sections or projections, as in a microscope field, but shape factors also apply to three-dimensional objects. The particles could be the grains in a metallurgical or ceramic microstructure, or the microorganisms in a culture, for example. The dimensionless quantities often represent the degree of deviation from an ideal shape, such as a circle, sphere or equilateral polyhedron. Shape factors are often normalized, that is, the value ranges from zero to one. A shape factor equal to one usually represents an ideal case or maximum symmetry, such as a circle, sphere, square or cube. == Aspect ratio == The most common shape factor is the aspect ratio, a function of the largest diameter and the smallest diameter orthogonal to it: A R = d min d max {\displaystyle A_{R}={\frac {d_{\min }}{d_{\max }}}} The normalized aspect ratio varies from approaching zero for a very elongated particle, such as a grain in a cold-worked metal, to near unity for an equiaxed grain. The reciprocal of the right side of the above equation is also used, such that the AR varies from one to approaching infinity. == Circularity == Another very common shape factor is the circularity (or isoperimetric quotient), a function of the perimeter P and the area A: f circ = 4 π A P 2 {\displaystyle f_{\text{circ}}={\frac {4\pi A}{P^{2}}}} The circularity of a circle is 1, and much less than one for a starfish footprint. The reciprocal of the circularity equation is also used, such that fcirc varies from one for a circle to infinity. == Elongation shape factor == The less-common elongation shape factor is defined as the square root of the ratio of the two second moments in of the particle around its principal axes. f elong = i 2 i 1 {\displaystyle f_{\text{elong}}={\sqrt {\frac {i_{2}}{i_{1}}}}} == Compactness shape factor == The compactness shape factor is a function of the polar second moment in of a particle and a circle of equal area A. f comp = A 2 2 π i 1 2 + i 2 2 {\displaystyle f_{\text{comp}}={\frac {A^{2}}{2\pi {\sqrt {{i_{1}}^{2}+{i_{2}}^{2}}}}}} The fcomp of a circle is one, and much less than one for the cross-section of an I-beam. == Waviness shape factor == The waviness shape factor of the perimeter is a function of the convex portion Pcvx of the perimeter to the total. f wav = P cvx P {\displaystyle f_{\text{wav}}={\frac {P_{\text{cvx}}}{P}}} Some properties of metals and ceramics, such as fracture toughness, have been linked to grain shapes. == An application of shape factors == Greenland, the largest island in the world, has an area of 2,166,086 km2; a coastline (perimeter) of 39,330 km; a north–south length of 2670 km; and an east–west length of 1290 km. The aspect ratio of Greenland is A R = 1290 2670 = 0.483 {\displaystyle A_{R}={\frac {1290}{2670}}=0.483} The circularity of Greenland is f circ = 4 π ( 2166086 ) 39330 2 = 0.0176. {\displaystyle f_{\text{circ}}={\frac {4\pi (2166086)}{39330^{2}}}=0.0176.} The aspect ratio is agreeable with an eyeball-estimate on a globe. Such an estimate on a typical flat map, using the Mercator projection, would be less accurate due to the distorted scale at high latitudes. The circularity is deceptively low, due to the fjords that give Greenland a very jagged coastline (see the coastline paradox). A low value of circularity does not necessarily indicate a lack of symmetry, and shape factors are not limited to microscopic objects.
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KoalaPad

The KoalaPad is a graphics tablet, released in 1983 by US company Koala Technologies Corporation, for the Apple II, TRS-80 Color Computer (as the TRS-80 Touch Pad), Atari 8-bit computers, Commodore 64, and IBM PC compatibles. Originally designed by Dr. David Thornburg as a low-cost computer drawing tool for schools, the Koala Pad and the bundled drawing program, KoalaPainter, was popular with home users as well. KoalaPainter was called KoalaPaint in some versions for the Apple II, and PC Design for the IBM PC. A program called Graphics Exhibitor was included for creating slideshow presentations from KoalaPainter drawings. == Description == The pad was four inches square (i.e. roughly 10×10 cm) and mounted on a slightly inclined base with the back of the pad higher than the front. At the top, "behind" the pad, were two buttons. The pad hooked into the computer using the analog signals of the joystick ports (the so-called paddle inputs), which meant that it had a low resolution and tended to jostle the cursor if moved during use. As an alternative to the drawing stylus, the pad could as easily be operated by the user's fingers for tasks that demanded less precision, such as selecting between menu items (thus using the pad as a kind of "indirect touch screen"). The top-mounted buttons tended to be somewhat frustrating to use, as the user had to "reach around" the stylus to push the buttons in order to start or stop drawing. A similar tablet from Atari, the Atari CX77 Touch Tablet, addressed this with a built-in button on the stylus, which some enterprising users adapted for use with their KoalaPad. == KoalaPainter == The pad shipped with a simple bitmap graphics editor developed by Audio Light called KoalaPainter, PC Design or Micro Illustrator depending on the target machine (see release history). Although bundled with the pad, KoalaPainter could also be operated using an ordinary digital joystick. One unique feature of the program, for its time, was that it held two pictures in the computer's memory, allowing the user to flip from one to the other—a function commonly used in order to study the differences between an original and a modified picture, and to copy and paste between two different pictures. Some third-party bitmap editors could also be used with the KoalaPad, such as Broderbund's Dazzle Draw for the Apple II. === Release history === KoalaPainter for Commodore 64 (1983) and Atari 8-bit computers (1983) PC Design for the IBM PC (1983) Micro Illustrator for the Apple II (1983), Atari 8-bit computers (1983) and Commodore Plus/4 (1984) KoalaPainter II for Commodore 64 (1984) === Reception === Ahoy! called KoalaPainter "a very powerful and effective color drawing package", and concluded that it and the KoalaPad were "excellent in ease of use, a fine choice for a beginner as well as young children". BYTE's reviewer stated in December 1984 that he made far fewer errors when using an Apple Mouse with MousePaint than with a KoalaPad and its software. He found that MousePaint was easier to use and more efficient, predicting that the mouse would receive more software support than the pad. Cassie Stahl in InfoWorld's Essential Guide to Atari Computers praised the tablet and its documentation, rating it "Excellent" among all categories and stating that "Playing with the KoalaPad becomes addictive. It does everything it claims to, and it does it well". She also liked Micro Illustrator, rating it "Excellent" except for "Good" for Performance. While criticizing the limited erase function, Stahl reported an undocumented feature enabling exporting pictures to other software. === File format === The Commodore 64 version of KoalaPainter used a fairly simple file format corresponding directly to the way bitmapped graphics are handled on the computer: A two-byte load address, followed immediately by 8,000 bytes of raw bitmap data, 1,000 bytes of raw "Video Matrix" data, 1,000 bytes of raw "Color RAM" data, and a one-byte Background Color field. == KoalaWare == Koala Technologies offered more software beyond the bundled KoalaPainter and Graphics Exhibitor for use with the pad. Among these applications, marketed under the moniker KoalaWare (like KoalaPainter itself), was educational software for use with customized keypads and overlays, such as spelling tools, music programs, and mathematics instruction software, as well as software for "translating" graphical designs into Logo programs.
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