In mathematics, a tuple is a finite sequence (or ordered list) of numbers. More generally, it is a sequence of mathematical objects, called the elements of the tuple. An n-tuple is a tuple of n elements, where n is a non-negative integer. There is only one 0-tuple, called the empty tuple. A 1-tuple and a 2-tuple are commonly called a singleton and an ordered pair, respectively. The term "infinite tuple" is occasionally used for "infinite sequences". Tuples are usually written by listing the elements within parentheses "( )" and separated by commas; for example, (2, 7, 4, 1, 7) denotes a 5-tuple. Other types of brackets are sometimes used, although they may have a different meaning. An n-tuple can be formally defined as the image of a function that has the set of the first n natural numbers as its domain (1, 2, ..., n). Tuples may be also defined from ordered pairs by a recurrence starting from an ordered pair; indeed, an n-tuple can be identified with the ordered pair of its (n − 1) first elements and its nth element, for example, ( ( ( 1 , 2 ) , 3 ) , 4 ) = ( 1 , 2 , 3 , 4 ) {\displaystyle \left(\left(\left(1,2\right),3\right),4\right)=\left(1,2,3,4\right)} . In computer science, tuples come in many forms. Most typed functional programming languages implement tuples directly as product types, tightly associated with algebraic data types, pattern matching, and destructuring assignment. Many programming languages offer an alternative to tuples, known as record types, featuring unordered elements accessed by label. A few programming languages combine ordered tuple product types and unordered record types into a single construct, as in C structs and Haskell records. Relational databases may formally identify their rows (records) as tuples. Tuples also occur in relational algebra; when programming the semantic web with the Resource Description Framework (RDF); in linguistics; and in philosophy. == Etymology == The term originated as an abstraction of the sequence: single, couple/double, triple, quadruple, quintuple, sextuple, septuple, octuple, ..., n‑tuple, ..., where the prefixes are taken from the Latin names of the numerals. The unique 0-tuple is called the null tuple or empty tuple. A 1‑tuple is called a single (or singleton), a 2‑tuple is called an ordered pair or couple, and a 3‑tuple is called a triple (or triplet). The number n can be any nonnegative integer. For example, a complex number can be represented as a 2‑tuple of reals, a quaternion can be represented as a 4‑tuple, an octonion can be represented as an 8‑tuple, and a sedenion can be represented as a 16‑tuple. Although these uses treat ‑tuple as the suffix, the original suffix was ‑ple as in "triple" (three-fold) or "decuple" (ten‑fold). This originates from medieval Latin plus (meaning "more") related to Greek ‑πλοῦς, which replaced the classical and late antique ‑plex (meaning "folded"), as in "duplex". == Properties == The general rule for the identity of two n-tuples is ( a 1 , a 2 , … , a n ) = ( b 1 , b 2 , … , b n ) {\displaystyle (a_{1},a_{2},\ldots ,a_{n})=(b_{1},b_{2},\ldots ,b_{n})} if and only if a 1 = b 1 , a 2 = b 2 , … , a n = b n {\displaystyle a_{1}=b_{1},{\text{ }}a_{2}=b_{2},{\text{ }}\ldots ,{\text{ }}a_{n}=b_{n}} . Thus a tuple has properties that distinguish it from a set: A tuple may contain multiple instances of the same element, so tuple ( 1 , 2 , 2 , 3 ) ≠ ( 1 , 2 , 3 ) {\displaystyle (1,2,2,3)\neq (1,2,3)} ; but set { 1 , 2 , 2 , 3 } = { 1 , 2 , 3 } {\displaystyle \{1,2,2,3\}=\{1,2,3\}} . Tuple elements are ordered: tuple ( 1 , 2 , 3 ) ≠ ( 3 , 2 , 1 ) {\displaystyle (1,2,3)\neq (3,2,1)} , but set { 1 , 2 , 3 } = { 3 , 2 , 1 } {\displaystyle \{1,2,3\}=\{3,2,1\}} . A tuple has a finite number of elements, while a set or a multiset may have an infinite number of elements. == Definitions == There are several definitions of tuples that give them the properties described in the previous section. === Tuples as functions === The 0 {\displaystyle 0} -tuple may be identified as the empty function. For n ≥ 1 , {\displaystyle n\geq 1,} the n {\displaystyle n} -tuple ( a 1 , … , a n ) {\displaystyle \left(a_{1},\ldots ,a_{n}\right)} may be identified with the surjective function F : { 1 , … , n } → { a 1 , … , a n } {\displaystyle F~:~\left\{1,\ldots ,n\right\}~\to ~\left\{a_{1},\ldots ,a_{n}\right\}} with domain domain F = { 1 , … , n } = { i ∈ N : 1 ≤ i ≤ n } {\displaystyle \operatorname {domain} F=\left\{1,\ldots ,n\right\}=\left\{i\in \mathbb {N} :1\leq i\leq n\right\}} and with codomain codomain F = { a 1 , … , a n } , {\displaystyle \operatorname {codomain} F=\left\{a_{1},\ldots ,a_{n}\right\},} that is defined at i ∈ domain F = { 1 , … , n } {\displaystyle i\in \operatorname {domain} F=\left\{1,\ldots ,n\right\}} by F ( i ) := a i . {\displaystyle F(i):=a_{i}.} That is, F {\displaystyle F} is the function defined by 1 ↦ a 1 ⋮ n ↦ a n {\displaystyle {\begin{alignedat}{3}1\;&\mapsto &&\;a_{1}\\\;&\;\;\vdots &&\;\\n\;&\mapsto &&\;a_{n}\\\end{alignedat}}} in which case the equality ( a 1 , a 2 , … , a n ) = ( F ( 1 ) , F ( 2 ) , … , F ( n ) ) {\displaystyle \left(a_{1},a_{2},\dots ,a_{n}\right)=\left(F(1),F(2),\dots ,F(n)\right)} necessarily holds. Tuples as sets of ordered pairs Functions are commonly identified with their graphs, which is a certain set of ordered pairs. Indeed, many authors use graphs as the definition of a function. Using this definition of "function", the above function F {\displaystyle F} can be defined as: F := { ( 1 , a 1 ) , … , ( n , a n ) } . {\displaystyle F~:=~\left\{\left(1,a_{1}\right),\ldots ,\left(n,a_{n}\right)\right\}.} === Tuples as nested ordered pairs === Another way of modeling tuples in set theory is as nested ordered pairs. This approach assumes that the notion of ordered pair has already been defined. The 0-tuple (i.e. the empty tuple) is represented by the empty set ∅ {\displaystyle \emptyset } . An n-tuple, with n > 0, can be defined as an ordered pair of its first entry and an (n − 1)-tuple (which contains the remaining entries when n > 1): ( a 1 , a 2 , a 3 , … , a n ) = ( a 1 , ( a 2 , a 3 , … , a n ) ) {\displaystyle (a_{1},a_{2},a_{3},\ldots ,a_{n})=(a_{1},(a_{2},a_{3},\ldots ,a_{n}))} This definition can be applied recursively to the (n − 1)-tuple: ( a 1 , a 2 , a 3 , … , a n ) = ( a 1 , ( a 2 , ( a 3 , ( … , ( a n , ∅ ) … ) ) ) ) {\displaystyle (a_{1},a_{2},a_{3},\ldots ,a_{n})=(a_{1},(a_{2},(a_{3},(\ldots ,(a_{n},\emptyset )\ldots ))))} Thus, for example: ( 1 , 2 , 3 ) = ( 1 , ( 2 , ( 3 , ∅ ) ) ) ( 1 , 2 , 3 , 4 ) = ( 1 , ( 2 , ( 3 , ( 4 , ∅ ) ) ) ) {\displaystyle {\begin{aligned}(1,2,3)&=(1,(2,(3,\emptyset )))\\(1,2,3,4)&=(1,(2,(3,(4,\emptyset ))))\\\end{aligned}}} A variant of this definition starts "peeling off" elements from the other end: The 0-tuple is the empty set ∅ {\displaystyle \emptyset } . For n > 0: ( a 1 , a 2 , a 3 , … , a n ) = ( ( a 1 , a 2 , a 3 , … , a n − 1 ) , a n ) {\displaystyle (a_{1},a_{2},a_{3},\ldots ,a_{n})=((a_{1},a_{2},a_{3},\ldots ,a_{n-1}),a_{n})} This definition can be applied recursively: ( a 1 , a 2 , a 3 , … , a n ) = ( ( … ( ( ( ∅ , a 1 ) , a 2 ) , a 3 ) , … ) , a n ) {\displaystyle (a_{1},a_{2},a_{3},\ldots ,a_{n})=((\ldots (((\emptyset ,a_{1}),a_{2}),a_{3}),\ldots ),a_{n})} Thus, for example: ( 1 , 2 , 3 ) = ( ( ( ∅ , 1 ) , 2 ) , 3 ) ( 1 , 2 , 3 , 4 ) = ( ( ( ( ∅ , 1 ) , 2 ) , 3 ) , 4 ) {\displaystyle {\begin{aligned}(1,2,3)&=(((\emptyset ,1),2),3)\\(1,2,3,4)&=((((\emptyset ,1),2),3),4)\\\end{aligned}}} === Tuples as nested sets === Using Kuratowski's representation for an ordered pair, the second definition above can be reformulated in terms of pure set theory: The 0-tuple (i.e. the empty tuple) is represented by the empty set ∅ {\displaystyle \emptyset } ; Let x {\displaystyle x} be an n-tuple ( a 1 , a 2 , … , a n ) {\displaystyle (a_{1},a_{2},\ldots ,a_{n})} , and let x → b ≡ ( a 1 , a 2 , … , a n , b ) {\displaystyle x\rightarrow b\equiv (a_{1},a_{2},\ldots ,a_{n},b)} . Then, x → b ≡ { { x } , { x , b } } {\displaystyle x\rightarrow b\equiv \{\{x\},\{x,b\}\}} . (The right arrow, → {\displaystyle \rightarrow } , could be read as "adjoined with".) In this formulation: ( ) = ∅ ( 1 ) = ( ) → 1 = { { ( ) } , { ( ) , 1 } } = { { ∅ } , { ∅ , 1 } } ( 1 , 2 ) = ( 1 ) → 2 = { { ( 1 ) } , { ( 1 ) , 2 } } = { { { { ∅ } , { ∅ , 1 } } } , { { { ∅ } , { ∅ , 1 } } , 2 } } ( 1 , 2 , 3 ) = ( 1 , 2 ) → 3 = { { ( 1 , 2 ) } , { ( 1 , 2 ) , 3 } } = { { { { { { ∅ } , { ∅ , 1 } } } , { { { ∅ } , { ∅ , 1 } } , 2 } } } , { { { { { ∅ } , { ∅ , 1 } } } , { { { ∅ } , { ∅ , 1 } } , 2 } } , 3 } } {\displaystyle {\begin{array}{lclcl}()&&&=&\emptyset \\&&&&\\(1)&=&()\rightarrow 1&=&\{\{()\},\{(),1\}\}\\&&&=&\{\{\emptyset \},\{\emptyset ,1\}\}\\&&&&\\(1,2)&=&(1)\rightarrow 2&=&\{\{(1)\},\{(1),2\}\}\\&&&=&\{\{\{\{\emptyset \},\{\emptyset ,1\}\}\},\\&&&&\{\{\{\emptyset \},\{\emptyset ,1\}\},2\}\}\\&&&&\\(1,2,3)&=&(1,2)\rightarrow 3&=&\{\{(1,2)\},\{(1,2),3\}\}\\&&&=&\{\{\{\{\{\{\empty
Artificial intelligence and elections
As artificial intelligence (AI) has become more mainstream, there is growing concern about how this will influence elections. Potential targets of AI include election processes, election offices, election officials and election vendors. There are also global efforts to improve elections using AI. == Tactics == Generative AI capabilities allow creation of misleading content. Examples of this include text-to-video, deepfake videos, text-to-image, AI-altered images, text-to-speech, voice cloning, and text-to-text. In the context of an election, a deepfake video of a candidate may propagate information that the candidate does not endorse. Chatbots could spread misinformation related to election locations, times or voting methods. In contrast to malicious actors in the past, these techniques require little technical skill and can spread rapidly. LLM-generated messages have the capacity to persuade humans on political issues. Researchers have begun to investigate how people rate messages that LLMs generate for how persuasive they are. When it came to policy issues, the LLM-generated messages received a 2.91 compared to a 2.80 when it came to smartness between the AI and humans. The LLM-generated messages were often more technical and analytical than human-generated messages. Generative AI has been used to micro-target people during tight political elections. The generation of targeted large language models has triggered concern that they will be used to leverage readily scale microtargeting. Rephrasing inputs have been used to generate fraudulent emails and phishing websites. Rephrasing inputs in a microtargeting does not violate the terms of OpenAI usage. There are no safeguards to prevent the use of rephrasing and creation of fraudulent emails. Political campaign managers have access to this allowing for them to create targeted content. == Usage by country == === Argentina === ==== 2023 elections ==== During the 2023 Argentine primary elections, Javier Milei's team distributed AI generated images including a fabricated image of his rival Sergio Massa and drew 3 million views. The team also created an unofficial Instagram account entitled "AI for the Homeland." Sergio Massa's team also distributed AI generated images and videos. === Bangladesh === ==== 2024 elections ==== In the run up to the 2024 Bangladeshi general election, deepfake videos of female opposition politicians appeared. Rumin Farhana was pictured in a bikini while Nipun Ray was shown in a swimming pool. === Canada === ==== 2025 elections ==== In the run up to the 2025 Canadian federal election, the use of AI tools is likely to figure prominently. India, Pakistan and Iran are all expected to make efforts to subvert the national vote using disinformation campaigns to deceive voters and sway diaspora communities. In a report by the Canadian Centre for Cyber Security called "Cyber Threats to Canada's Democratic Process: 2025 Update", it states that malicious actors including China and Russia: "are most likely to use generative AI as a means of creating and spreading disinformation, designed to sow division among Canadians and push narratives conducive to the interests of foreign states". === France === ==== 2024 elections ==== In the 2024 French legislative election, deepfake videos appeared claiming: i) That they showed the family of Marine le Pen. In the videos, young women, supposedly Le Pen's nieces, are seen skiing, dancing and at the beach "while making fun of France’s racial minorities": However, the family members don't exist. On social media there were over 2 million views. ii) In a video seen on social media, a deepfake video of a France24 broadcast appeared to report that the Ukrainian leadership had "tried to lure French president Emmanuel Macron to Ukraine to assassinate him and then blame his death on Russia". === Ghana === ==== 2024 elections ==== During the months before the December 2024 Ghanaian general election, a network of at least 171 fake accounts has been used to spam social media. Posts have been used by a group identified as "@TheTPatriots" to promote the New Patriotic Party, although it is not known whether the two are connected. All the networks' posts were "highly likely" to have been generated by ChatGPT and appear to be the "first secretly partisan network using AI to influence elections in Ghana". The opposition National Democratic Congress was also criticized with its leader John Mahama being called a drunkard. === India === ==== 2024 elections ==== In the 2024 Indian general election, politicians used deepfakes in their campaign materials. These deepfakes included politicians who had died prior to the election. Mathuvel Karunanidhi's party posted with his likeness even though he had died 2018. A video The All-India Anna Dravidian Progressive Federation party posted showed an audio clip of Jayaram Jayalalithaa even though she had died in 2016. The Deepfakes Analysis Unit (DAU) is an open source platform created in March 2024 for the public to share misleading content and assess if it had been AI-generated. AI was also used to translate political speeches in real time. This translating ability was widely used to reach more voters. === Indonesia === ==== 2024 elections ==== In the 2024 Indonesian presidential election, Prabowo Subianto made extensive use of AI-generated art in his campaign, which ranged from images of himself as an adorable child to various child portrayals in his advertisements. The Indonesian Children's Protection Commission condemned these ads, labeling them as a form of misuse. Other candidates, Anies Baswedan and Ganjar Pranowo, also incorporated AI art into their campaigns. Throughout the election period, all presidential candidates faced attacks from deepfakes, both in video and audio formats. === Ireland === ==== 2024 elections ==== In the last weeks of the 2024 Irish general election a spoof election poster appeared in Dublin featuring "an AI-generated candidate with three arms". The candidate is called Aidan Irwin, but no-one stood in the election with that name. A slogan on the poster says "put matters into artificial intelligence’s hands". The convincing election poster shows a man that "has six fingers on one hand, three arms, and a distorted thumb". === New Zealand === ==== 2023 elections ==== In May 2023, ahead of the 2023 New Zealand general election in October 2023, the New Zealand National Party published a "series of AI-generated political advertisements" on its Instagram account. After confirming that the images were faked, a party spokesperson said that it was "an innovative way to drive our social media". === Pakistan === ==== 2024 elections ==== AI has been used by the imprisoned ex-Prime Minister Imran Khan and his media team in the 2024 Pakistani general election: i) An AI generated audio of his voice was added to a video clip and was broadcast at a virtual rally. ii) An op-ed in The Economist written by Khan was later claimed by himself to have been written by AI which was later denied by his team. The article was liked and shared on social media by thousands of users. === South Africa === ==== 2024 elections ==== In the 2024 South African general election, there were several uses of AI content: i) A deepfaked video of Joe Biden emerged on social media showing him saying that "The U.S. would place sanctions on SA and declare it an enemy state if the African National Congress (ANC) won". ii) In a deepfake video, Donald Trump was shown endorsing the uMkhonto weSizwe party. It was posted to social media and was viewed more than 158,000 times. iii) Less than 3 months before the elections, a deepfake video showed U.S. rapper Eminem endorsing the Economic Freedom Fighters party while criticizing the ANC. The deepfake was viewed on social media more than 173,000 times. === South Korea === ==== 2022 elections ==== In the 2022 South Korean presidential election, a committee for one presidential candidate Yoon Suk Yeol released an AI avatar 'Al Yoon Seok-yeol' that would campaign in places the candidate could not go. The other presidential candidate Lee Jae-myung introduced a chatbot that provided information about the candidate's pledges. ==== 2024 elections ==== Deepfakes were used to spread misinformation before the 2024 South Korean legislative election with one source reporting 129 deepfake violations of election laws within a two week period. Seoul hosted the 2024 Summit for Democracy, a virtual gathering of world leaders initiated by US President Joe Biden in 2021. The focus of the summit was on digital threats to democracy including artificial intelligence and deepfakes. === Taiwan === ==== 2024 elections ==== AI-generated content was used during the 2024 Taiwanese presidential election. Among the media were: i) A deepfake video of General Secretary of the Chinese Communist Party Xi Jinping which showed him supporting the presidential elections. Created on social media, the video was "widely circulated
AirPair
AirPair is a service and eponymous company that connects people who need help with programming issues (usually, programmers at small technology companies or at finance companies that use technology products) and people who can help them. Unlike services such as oDesk and Elance, AirPair is not a service for outsourcing programming tasks, but rather a service that facilitates one-off knowledge transfers from people with highly specialized knowledge of particular technology stacks or programming issues to people who are in need of specialized help. == History == AirPair launched in March 2013, with founder Jonathon Kresner, who hails from Australia, working full-time, and it soon hired three other part-time developers to work alongside him. Kresner had previously founded two other startups: Preparty, a social invitation and event-booking service based in Australia, and ClimbFind, an online rock-climbing community that reached a million users. Kresner was inspired to work on AirPair because he saw the need for outside expert assistance with programming issues arise regularly at these startups. In November 2013, founder Kresner describes the company's initial success at bootstrapping itself to "Ramen profitability" in a blog post. In December 2013, AirPair was accepted into the Winter 2014 Y Combinator batch. In March 2014, AirPair announced it would launch partnerships with Stripe, Twilio, and other companies that had their own application programming interfaces, allowing developers having trouble with the APIs to seek help over AirPair from experts on the APIs. AirPair presented at the Y Combinator Winter 2014 Demo Day on March 25, 2014, and successfully raised over $1 million within the next 48 hours. == Reception == A review of AirPair by Will Lam stressed that because payment was based on time rather than results, it was important to use it for clearly thought-out questions where one had high confidence that the session would help. Dennis Beatty, who met AirPair founder Jonathon Kresner in March 2014, wrote in April 2014 a glowing review of AirPair's vision of connecting people and its business success. AirPair has been compared with other peer-to-peer coding help sites such as Codementor and HackHands.
SAP StreamWork
SAP StreamWork is an enterprise collaboration tool from SAP SE released in March 2010, and discontinued in December 2015. StreamWork allowed real-time collaboration like Google Wave, but focused on business activities such as analyzing data, planning meetings, and making decisions. It incorporated technology from Box.net and Evernote to allow users to connect to online files and documents, and document-reader technology from Scribd allowed users to view documents directly within its environment. StreamWork supported the OpenSocial set of application programming interfaces (APIs), allowing it to connect to tools built by third-party developers, such as Google Docs. A version of StreamWork intended for large enterprises used a virtual appliance based on Novell's SUSE Linux Enterprise to connect it to business systems, including those from SAP.
Differentiable imaging
Differentiable imaging is a method within computational imaging that incorporates differentiable programming to design imaging systems. It treats the entire imaging process - from light passing through optical components to the numerical reconstruction—as a differentiable programming problem. This approach links optical hardware with numerical reconstruction, enabling joint optimization of both parts through differentiable programming. Differentiable imaging additionally extends the scope of computational imaging beyond image reconstruction, such as by aiding in characterization of optical components. == Background == Computational imaging combines optical hardware and computational algorithms to capture and reconstruct information that conventional imaging system cannot. This is achieved from a combination of the imaging system and the software used in the image reconstruction. Since the captured information may not directly show the image of the target, these systems often rely on numerical models that describe how light encodes the target. In practice, such models may deviate from the physical systems due to uncertainties such as noise, misalignments, manufacturing imperfections, environmental variations, etc. These uncertainties can cause a mismatch between the physical system and its numerical model, which may degrade reconstruction quality and limit the effectiveness of the hardware–software co-design. Uncertainty quantification is also studied in other hybrid physical–numerical systems, such as digital twin. While numerical modeling imaging systems date back to the several decades, such as the multislice method in electron microscopy or X-Ray nanotomography, differentiable imaging emphasizes jointly modeling uncertainties and solving inverse problems with image reconstruction simultaneously. Differentiable imaging transforms the traditional encoding model y = f ( x ) {\textstyle y=f(x)} into a more comprehensive formulation y = f ( x , θ ) {\textstyle y=f(x,\theta )} , where θ {\displaystyle \theta } represents a parameter set of mismatches between physical systems and numerical models. The forward model captures the entire imaging pipeline through a series of interconnected component functions: y = f ( x , θ ) , f = f n o i s e ∘ f c ∘ f o c ∘ f x ∘ f o i ∘ f i , {\displaystyle y=f(x,\theta ),\qquad f=f_{noise}\circ f_{c}\circ f_{oc}\circ f_{x}\circ f_{oi}\circ f_{i},} where the function composition operator ∘ {\displaystyle \circ } connects each system component, and θ = { θ c , θ o c , … } {\displaystyle \theta =\{\theta _{c},\theta _{oc},\ldots \}} encompasses uncertainty system parameters. Each component corresponds to specific physical processes within the imaging system, from illumination through object interactions to sensor behavior and noises. This forward model enables the formulation of an inverse problem that simultaneously optimizes system parameters while reconstructing images: x ∗ , θ ∗ = argmin x , θ L ( f ( x , θ ) , y ) + ∑ n = 1 N β n R n ( x ) {\displaystyle x^{},\theta ^{}={\text{argmin}}_{x,\theta }{\mathcal {L}}(f(x,\theta ),y)+\sum _{n=1}^{N}\beta _{n}{\mathcal {R}}_{n}(x)} s . t . x ∈ Ω x , θ ∈ Ω θ {\displaystyle s.t.\quad x\in \Omega _{x},\theta \in \Omega _{\theta }} Here, L ( f ( x , θ ) , y ) {\displaystyle {\mathcal {L}}(f(x,\theta ),y)} represents the fidelity term that quantifies the discrepancy between the model predictions and measured data. The whole process of the y = f ( x , θ ) {\displaystyle y=f(x,\theta )} is constructed as a computer graph based on differentiable programming, and the inverse problem is solved with gradient based algorithm, while the gradient is calculated with automatic differentiation. == Applications == One application of differentiable imaging is uncertainty management, which seeks to quantify and mitigate the impact of factors induce reality-numerical mismatch. Explicitly accounting for uncertainties can improve reconstruction accuracy and system robustness. Examples include: Model-related uncertainties: unknown or unmeasurable variables—for instance, optical system quantities that differ from the design specifications Data and system uncertainties: artifacts introduced during image acquisition, such as low-quality data, noise, or hardware imperfections Manufacturing uncertainties: variability in the production of imaging hardware—such as slight deviations in lens curvature or sensor alignment—that alters the physical system's behavior
CMU Pronouncing Dictionary
The CMU Pronouncing Dictionary (also known as CMUdict) is an open-source pronouncing dictionary originally created by the Speech Group at Carnegie Mellon University (CMU) for use in speech recognition research. CMUdict provides a mapping orthographic/phonetic for English words in their North American pronunciations. It is commonly used to generate representations for speech recognition (ASR), e.g. the CMU Sphinx system, and speech synthesis (TTS), e.g. the Festival system. CMUdict can be used as a training corpus for building statistical grapheme-to-phoneme (g2p) models that will generate pronunciations for words not yet included in the dictionary. The most recent release is 0.7b; it contains over 134,000 entries. An interactive lookup version is available. == Database format == The database is distributed as a plain text file with one entry to a line in the format "WORD
Curve (tonality)
In image editing, a curve is a remapping of image tonality, specified as a function from input level to output level, used as a way to emphasize colours or other elements in a picture. Curves can usually be applied to all channels together in an image, or to each channel individually. Applying a curve to all channels typically changes the brightness in part of the spectrum. Light parts of a picture can be easily made lighter and dark parts darker to increase contrast. Applying a curve to individual channels can be used to stress a colour. This is particularly efficient in the Lab colour space due to the separation of luminance and chromaticity, but it can also be used in RGB, CMYK or whatever other colour models the software supports.