A smart speaker is a type of loudspeaker and voice command device with an integrated virtual assistant that offers interactive actions and hands-free activation with the help of one "wake word" (or several "wake words"). Some smart speakers also act as smart home hubs by using Wi-Fi, Bluetooth, Thread, and other protocol standards to extend usage beyond audio playback and control home automation devices connected through a local area network. == History == Early voice-activated devices began in 2013 with MIT's Jasper project, which used multiple microphones and cloud software to power hands-free interactions from across a room. The first commercial smart speaker was the Amazon Echo, which was released in 2014 powered by Alexa and a ring of far-field microphones. Google followed in 2016 with Home, powered by Google Assistant. By 2017, devices like the Echo Show and Home Hub (later called Nest Hub) added touchscreens and video, creating the "smart display" subcategory. In 2018, Apple joined the smart speaker trend by launching the HomePod, which focused on high-quality audio alongside their built-in assistant Siri. ASUS release its own smart Speaker Xiao-Bu in 2019 with Artificial Intelligence, it terminates the Cloud Service on June 1st, 2025, which means all real-time service such as weather, news, currency conversion is affected. Sonos's 1st smart speaker Sonos One released in 2017, powered by Alexa. Invoke by Harman Kardon was powered by Microsoft's intelligent personal assistant, Cortana. In the early 2020s, smart speakers gained on-device voice processing for faster responses and improved privacy. New standards such as Matter and Thread allowed multitudes of smart-home devices (even from completely different brands) to work together. == Features == === Audio and Voice === Smart speakers use multiple microphones along with noise-cancelling software to pick up your voice from across the room, even when music is playing or the assistant is already talking. Noise suppression and echo cancellation is also used by the speaker so it can focus in on who is talking and ignore any background noises. Most smart speaker models can recognize who is speaking by voiceprint, which allows the speaker to grab information from that person's calendar, preferences, or music playlists. Listening to music on a speaker is when importance for good audio quality becomes apparent. Entry-level (cheaper) speakers such as the Home Mini or the Echo Dot have a single full-range driver. These lower-end speakers typically aren't great for listening to music as the audio quality is pretty poor. More advanced units such as the Home Max or Echo Studio have separate tweeters and woofers meant for listening to music in high quality. === Connectivity and smart-home control === Most connect over Wi-Fi or Bluetooth and support hub protocols like Thread and Matter. That lets them not only stream and play music but also allows you to control various brands of smart lights, thermostats, door locks, cameras, and much more-all from one point of control. Each can have its own designated interface and features in-house, usually launched or controlled via application or home automation software. These devices are able to communicate with each other via peer-to-peer connection through mesh networking. These speakers and related smart devices are typically controlled with one smartphone application. === Assistant services and skills === The built-in assistants handle timers, alarms, reminders, news briefings, weather updates, send messages to other smart devices, send texts, make calls, and simple questions. You can combine actions together in what are typically known as routines (for example saying "good morning" turns on lights, starts the coffee, says the weather, and reads the news) and add extra functions known as skills or actions (for things like ordering food or playing trivia games). This hands-free use of smart speakers can help assist those with disabilities. Most other technologies need the user to be able to physically interact with the device. Smart speakers are not bound by these limitations and can serve as an excellent tool for those who are unable to use their arms or legs or have vision issues. Although these tasks can be completed by a phone or computer, consumers tend to lean towards smart speakers due to factors such as their range being much greater than that of a phone and the need to not have to physically interact with the speaker to get the voice assistant as with most smartphones, certain parts of a phone may need to be interacted with to activate the speaking assistant. === Smart displays === Some smart speakers also include a screen to show the user a visual response. A smart speaker with a touchscreen is known as a smart display; these integrate a conversational user interface with display screens to augment voice interaction with images and video. They are powered by one of the common voice assistants and offer additional controls for smart home devices, feature streaming apps, and web browsers with touch controls for selecting content. The first smart displays were introduced in 2017 by Amazon (Amazon Echo Show) and Google (Google/Nest Home Hub). Hotel chain Marriott International partnered with Amazon to install Echo devices in select hotels since 2018. A Taiwanese startup, Aiello, launched the Aiello Voice Assistant (AVA) in the Asian hotel market in 2019, claiming it is powered by a multi-AI model system. Angie by Nomadix, which is similar to the Amazon Echo, launched its first product in 2017, specifically targeting hotel properties in the North America. In May 2019, Angie Hospitality acquired the assets of Roxy, a competitor that also built its own speech-enabled virtual assistant technology for hotels. This acquisition merged two proprietary NLP stacks into the current Nomadix product. === Artificial intelligence === The newest speakers can use on-device AI or cloud-based generative models to allow the smart speaker to carry on much more natural conversations, draft emails or recipes, suggest ideas based on context, or even create short pieces of music or art. This AI evolution allows these speakers to do far more than what they could do before. == Accuracy == According to a study by Proceedings of the National Academy of Sciences of the United States of America released In March 2020, the six biggest tech development companies, Amazon, Apple, Google, Yandex, IBM and Microsoft, have misidentified more words spoken by "black people" than "white people". The systems tested errors and unreadability, with a 19 and 35 percent discrepancy for the former and a 2 and 20 percent discrepancy for the latter. The North American Chapter of the Association for Computational Linguistics (NAACL) also identified a discrepancy between male and female voices. According to their research, Google's speech recognition software is 13 percent more accurate for men than women. It performs better than the systems used by Bing, AT&T, and IBM. == Privacy concerns == The built-in microphone in smart speakers is continuously listening for wake words followed by a command. However, these continuously listening microphones also raise privacy concerns among users. According to a survey taken by 1,007 people in Western Europe, it is clear that privacy is the biggest concern holding consumers back from buying "smart" products. these concerns include what is being recorded, how the data will be used, how it will be protected, and whether it will be used for invasive advertising. Furthermore, an analysis of Amazon Echo Dots showed that 30–38% of "spurious audio recordings were human conversations", suggesting that these devices capture audio other than strictly detection of the wake word. === As a wiretap === There are strong concerns that the ever-listening microphone of smart speakers presents a perfect candidate for wiretapping. In 2017, British security researcher Mark Barnes showed that pre-2017 Echos have exposed pins which allow for a compromised OS to be booted. According to Umar Iqbal, an assistant professor at Washington University in St. Louis, research indicates that data from consumer interactions with Alexa was used to targeted advertisements and products to consumer with over 40% of transmitted data lacking proper encryption raising privacy concerns. Further data indicates that due to the Smart Speakers ability to always capture audio, it begins to pick up on external conversations from consumers not related to commands given to the smart speaker. Things such as other members in the household, consumers on the phone and even TV audio can be picked up by these speakers and stored for future use by companies. === Voice assistance vs privacy === While voice assistants provide a valuable service, there can be some hesitation towards using them in various social contexts, such as in public or around other users. However, only more recently have users begun interac
Wink Bingo
Wink Bingo is an online bingo website launched in 2008. It is part of Broadway Gaming Ireland DF Limited and is based and licensed in Ireland. == History == Wink Bingo launched in 2008 and under chief executive Eitan Boyd it grew to 60,000 active players within two years. It had an estimated £1.3 million profit in the first 11 months of trading, and by 2009 it had estimated annual revenue of £15 million. In 2009 Wink Bingo was purchased by 888 Holdings Plc, which operates a number of entertainment brands including 888casino, 888poker and 888sport. The initial up front fee was reported in the London Evening Standard to be £11 million, rising as high as £59.7 million depending on performance-based earn out arrangements. The acquisition included Daub Ltd’s other online bingo businesses Posh Bingo and Bingo Fabulous. In 2011, the sellers agreed to amend the terms and accept two subsequent payments in addition to the initial cost, of £9.2 million in May and £6.1 million in August. In 2011 Wink Bingo sponsored ITV2's The Only Way Is Essex, and other notable advertising campaigns have included sponsorship of Harry Hill's TV Burp. In 2014, Wink Bingo rebranded with an updated slogan 'Wink if you're in!', with an aim of creating a 'sunny, calm and inclusive' online destination, and an accompanying TV commercial featuring the Ottawan song D.I.S.C.O. re-recorded as B.I.N.G.O.. Wink also launched a new digital magazine, 'Winkly', and 'Winkipedia, a bingo encyclopedia'. Wink Bingo is available on desktop and as a mobile app. Wink launched Wink Slots in 2016 as a companion site to Wink Bingo. The Advertising Standards Authority has ruled on Wink Bingo's advertisements on a number of occasions. In August 2008, Wink ran a television ad which showed a midwife celebrating while at work at a hospital maternity unit. The ASA banned the ad, concluding that it condoned gambling in the workplace and suggested that it took priority over professional commitments. In June 2013, the Gambling Reform & Society Perception Group (GRASP) challenged the use of semi-naked "athletic" men together with the claim "Go on ... you know you want to" on an outdoor ad, suggesting it linked gambling to seduction and enhanced attractiveness. The complaint was not upheld. The site underwent another rebrand and pop art inspired redesign in April 2018, taking on a new tone of voice and a new slogan, "You’ve Earned It". An online shop was added, where players can redeem reward points for free play or vouchers for online high street retailers. In 2021 Wink Bingo was purchased by Saphalata Holdings, a company that forms part of the Broadway Gaming group. === Cancer Research UK campaign === In 2015 Wink Bingo began an open-ended partnership with the Peter Andre Fund to raise money for Cancer Research UK. Peter Andre also met with players who were selected in a raffle. == Awards ==
Mistral AI
Mistral AI SAS (French: [mistʁal]) is a French artificial intelligence (AI) company, headquartered in Paris. Founded in 2023, it has open-weight large language models (LLMs), with both open-source and proprietary AI models. As of 2025 the company has a valuation of more than US$14 billion. == Namesake == The company is named after the mistral, a powerful, cold wind in southern France, a term which originates from the Occitan language. == History == Mistral AI was established in April 2023 by three French AI researchers, Arthur Mensch, Guillaume Lample and Timothée Lacroix. Mensch, an expert in advanced AI systems, is a former employee of Google DeepMind; Lample and Lacroix, meanwhile, are large-scale AI models specialists who had worked for Meta Platforms. The trio originally met during their studies at École Polytechnique. == Company operation == === Funding === In June 2023, the start-up carried out a first fundraising of €105 million ($117 million) with investors including the American fund Lightspeed Venture Partners, Eric Schmidt, Xavier Niel and JCDecaux. The valuation was then estimated by the Financial Times at €240 million ($267 million). On 10 December 2023, Mistral AI announced that it had raised €385 million ($428 million) as part of its second fundraising. This round of financing involves the Californian fund Andreessen Horowitz, BNP Paribas and the software publisher Salesforce. It was valued at over €2 billion. On 26 February 2024, Microsoft announced an investment of $16 million in Mistral AI. On 16 April 2024, reporting revealed that Mistral was in talks to raise €500 million, a deal that would more than double its current valuation to at least €5 billion. In June 2024, Mistral AI secured a €600 million ($645 million) funding round, increasing its valuation to €5.8 billion ($6.2 billion). Based on valuation, as of June 2024, the company was ranked fourth globally in the AI industry, and first outside the San Francisco Bay Area. In April 2025, Mistral AI announced a €100 million partnership with the shipping company CMA CGM. In August 2025, the Financial Times reported that Mistral was in talks to raise $1 billion at a $10 billion valuation. In September 2025, Bloomberg announced that Mistral AI has secured a €2 billion investment valuing it at €12 billion ($14 billion). This comes after $1.5 billion investment from Dutch company ASML, which owns 11% of Mistral. In February 2026, Mistral acquired Koyeb, a Paris-based AI startup. Later that month, Mistral AI announced a multi-year strategic partnership with Accenture to help enterprises deploy sovereign AI solutions at scale. In March 2026 Mistral raised $830 million in order to build new datacenters near Paris and in Sweden. == Services == On 19 November, 2024, the company announced updates for Le Chat (pronounced /lə ʃa/ in French, like the French word for "cat"). It added the ability to create images, using Black Forest Labs' Flux Pro model. On 6 February 2025, Mistral AI released Le Chat on iOS and Android mobile devices. Mistral AI also introduced a Pro subscription tier, priced at $14.99 per month, which provides access to more advanced models, unlimited messaging, and web browsing. At the end of May 2026, Le Chat was renamed Vibe, and new features were introduced at the same time. == Models == The following table lists the main model versions of Mistral, describing the significant changes included with each version: === Mistral 7B === Mistral AI claimed in the Mistral 7B release blog post that the model outperforms LLaMA 2 13B on all benchmarks tested, and is on par with LLaMA 34B on many benchmarks tested, despite having only 7 billion parameters, a small size compared to its competitors. === Mixtral 8x7B === Mistral AI claimed in 2023 that its model beat both LLaMA 70B, and GPT-3.5 in most benchmarks. In March 2024, research conducted by Patronus AI comparing performance of LLMs on a 100-question test with prompts to generate text from books protected under U.S. copyright law found that OpenAI's GPT-4, Mixtral, Meta AI's LLaMA-2, and Anthropic's Claude 2 generated copyrighted text verbatim in 44%, 22%, 10%, and 8% of responses respectively. === Mistral Small 3.1 === On 17 March 2025, Mistral released Mistral Small 3.1 as a smaller, more efficient model. === Mistral Medium 3 === On 7 May 2025, Mistral AI released Mistral Medium 3. === Magistral Small and Magistral Medium === On 10 June 2025, Mistral AI released their first AI reasoning models: Magistral Small (open-source), and Magistral Medium, models which are purported to have chain-of-thought capabilities. === Mistral Large 3 and Ministral 3 === On 2 December 2025, Mistral AI released Mistral Large 3, a sparse, mixture-of-experts model with 41 billion active parameters and 675 billion total parameters, and Ministral 3, three small, dense models with 3 billion, 7 billion and 14 billion parameters. === Devstral 2 and Devstral Small 2 === On 10 December 2025, Mistral AI released Devstral 2 and Devstral Small 2. Devstral Small 2, a 24B parameter model is claimed to achieve better performance at coding than Qwen 3 Coder Flash model which is a 30B parameter model.
Open Neural Network Exchange
The Open Neural Network Exchange (ONNX) [ˈɒnɪks] is an open-source artificial intelligence ecosystem of technology companies and research organizations that establish open standards for representing machine learning algorithms and software tools to enable a standard format for representing machine learning models. ONNX is available on GitHub. == History == ONNX was originally named Toffee and was developed by the PyTorch team at Facebook. In September 2017 it was renamed to ONNX and announced by Facebook and Microsoft. Later, IBM, Huawei, Intel, AMD, Arm and Qualcomm announced support for the initiative. In October 2017, Microsoft announced that it would add its Cognitive Toolkit and Project Brainwave platform to the initiative. In November 2019 ONNX was accepted as graduate project in Linux Foundation AI. In October 2020 Zetane Systems became a member of the ONNX ecosystem. == Intent == The initiative targets: === Framework interoperability === Enable developers to move machine learning models between different frameworks, which may be used at different stages of the development process, such as training, architecture design, or deployment on mobile devices. === Shared optimization === Provide a common representation that can be used by hardware vendors and other developers to apply optimizations to artificial neural network models across multiple machine learning frameworks. == Contents == ONNX provides definitions of an extensible computation graph model, built-in operators and standard data types, focused on inferencing (evaluation).. The container format is Protocol Buffers. Each computation dataflow graph is a list of nodes that form an acyclic graph. Nodes have inputs and outputs. Each node is a call to an operator. Metadata documents the graph. Built-in operators are to be available on each ONNX-supporting framework. ONNX models can be trained in a single framework, such as PyTorch or TensorFlow, and then exported to ONNX. This format allows models to be transferred from the training framework to other environments for testing or deployment. Once a model is in ONNX format, it can be executed in different runtime systems or on various hardware platforms, such as GPUs or specialized AI accelerators. Using a common format enables the same model representation to be used across multiple systems and frameworks.
Computer Power and Human Reason
Computer Power and Human Reason: From Judgment to Calculation is a 1976 nonfiction book by German-American computer scientist Joseph Weizenbaum in which he contends that while artificial intelligence may be possible, we should never allow computers to make important decisions, as they will always lack human qualities such as compassion and wisdom. == Background == Before writing Computer Power and Human Reason, Weizenbaum had garnered significant attention for creating the ELIZA program, an early milestone in conversational computing. His firsthand observation of people attributing human-like qualities to a simple program prompted him to reflect more deeply on society's readiness to entrust moral and ethical considerations to machines. == Reception and legacy == Computer Power and Human Reason sparked scholarly debate on the acceptable scope of AI applications, particularly in fields where human welfare and ethical considerations are paramount. Early academic reviews highlighted that Weizenbaum's stance pushed readers to recognize that even as computers grow more capable, they lack the intrinsic moral compass and empathy required for certain kinds of judgment. The book caused disagreement with, and separation from, other members of the artificial intelligence research community, a status the author later said he'd come to take pride in.
Spherical basis
In pure and applied mathematics, particularly quantum mechanics and computer graphics and their applications, a spherical basis is the basis used to express spherical tensors. The spherical basis closely relates to the description of angular momentum in quantum mechanics and spherical harmonic functions. While spherical polar coordinates are one orthogonal coordinate system for expressing vectors and tensors using polar and azimuthal angles and radial distance, the spherical basis are constructed from the standard basis and use complex numbers. == In three dimensions == A vector A in 3D Euclidean space R3 can be expressed in the familiar Cartesian coordinate system in the standard basis ex, ey, ez, and coordinates Ax, Ay, Az: or any other coordinate system with associated basis set of vectors. From this extend the scalars to allow multiplication by complex numbers, so that we are now working in C 3 {\displaystyle \mathbb {C} ^{3}} rather than R 3 {\displaystyle \mathbb {R} ^{3}} . === Basis definition === In the spherical bases denoted e+, e−, e0, and associated coordinates with respect to this basis, denoted A+, A−, A0, the vector A is: where the spherical basis vectors can be defined in terms of the Cartesian basis using complex-valued coefficients in the xy plane: in which i {\displaystyle i} denotes the imaginary unit, and one normal to the plane in the z direction: e 0 = e z {\displaystyle \mathbf {e} _{0}=\mathbf {e} _{z}} The inverse relations are: === Commutator definition === While giving a basis in a 3-dimensional space is a valid definition for a spherical tensor, it only covers the case for when the rank k {\displaystyle k} is 1. For higher ranks, one may use either the commutator, or rotation definition of a spherical tensor. The commutator definition is given below, any operator T q ( k ) {\displaystyle T_{q}^{(k)}} that satisfies the following relations is a spherical tensor: [ J ± , T q ( k ) ] = ℏ ( k ∓ q ) ( k ± q + 1 ) T q ± 1 ( k ) {\displaystyle [J_{\pm },T_{q}^{(k)}]=\hbar {\sqrt {(k\mp q)(k\pm q+1)}}T_{q\pm 1}^{(k)}} [ J z , T q ( k ) ] = ℏ q T q ( k ) {\displaystyle [J_{z},T_{q}^{(k)}]=\hbar qT_{q}^{(k)}} === Rotation definition === Analogously to how the spherical harmonics transform under a rotation, a general spherical tensor transforms as follows, when the states transform under the unitary Wigner D-matrix D ( R ) {\displaystyle {\mathcal {D}}(R)} , where R is a (3×3 rotation) group element in SO(3). That is, these matrices represent the rotation group elements. With the help of its Lie algebra, one can show these two definitions are equivalent. D ( R ) T q ( k ) D † ( R ) = ∑ q ′ = − k k T q ′ ( k ) D q ′ q ( k ) {\displaystyle {\mathcal {D}}(R)T_{q}^{(k)}{\mathcal {D}}^{\dagger }(R)=\sum _{q'=-k}^{k}T_{q'}^{(k)}{\mathcal {D}}_{q'q}^{(k)}} === Coordinate vectors === For the spherical basis, the coordinates are complex-valued numbers A+, A0, A−, and can be found by substitution of (3B) into (1), or directly calculated from the inner product ⟨, ⟩ (5): A 0 = ⟨ e 0 , A ⟩ = ⟨ e z , A ⟩ = A z {\displaystyle A_{0}=\left\langle \mathbf {e} _{0},\mathbf {A} \right\rangle =\left\langle \mathbf {e} _{z},\mathbf {A} \right\rangle =A_{z}} with inverse relations: In general, for two vectors with complex coefficients in the same real-valued orthonormal basis ei, with the property ei·ej = δij, the inner product is: where · is the usual dot product and the complex conjugate must be used to keep the magnitude (or "norm") of the vector positive definite. == Properties (three dimensions) == === Orthonormality === The spherical basis is an orthonormal basis, since the inner product ⟨, ⟩ (5) of every pair vanishes meaning the basis vectors are all mutually orthogonal: ⟨ e + , e − ⟩ = ⟨ e − , e 0 ⟩ = ⟨ e 0 , e + ⟩ = 0 {\displaystyle \left\langle \mathbf {e} _{+},\mathbf {e} _{-}\right\rangle =\left\langle \mathbf {e} _{-},\mathbf {e} _{0}\right\rangle =\left\langle \mathbf {e} _{0},\mathbf {e} _{+}\right\rangle =0} and each basis vector is a unit vector: ⟨ e + , e + ⟩ = ⟨ e − , e − ⟩ = ⟨ e 0 , e 0 ⟩ = 1 {\displaystyle \left\langle \mathbf {e} _{+},\mathbf {e} _{+}\right\rangle =\left\langle \mathbf {e} _{-},\mathbf {e} _{-}\right\rangle =\left\langle \mathbf {e} _{0},\mathbf {e} _{0}\right\rangle =1} hence the need for the normalizing factors of 1 / 2 {\displaystyle 1/\!{\sqrt {2}}} . === Change of basis matrix === The defining relations (3A) can be summarized by a transformation matrix U: ( e + e − e 0 ) = U ( e x e y e z ) , U = ( − 1 2 − i 2 0 + 1 2 − i 2 0 0 0 1 ) , {\displaystyle {\begin{pmatrix}\mathbf {e} _{+}\\\mathbf {e} _{-}\\\mathbf {e} _{0}\end{pmatrix}}=\mathbf {U} {\begin{pmatrix}\mathbf {e} _{x}\\\mathbf {e} _{y}\\\mathbf {e} _{z}\end{pmatrix}}\,,\quad \mathbf {U} ={\begin{pmatrix}-{\frac {1}{\sqrt {2}}}&-{\frac {i}{\sqrt {2}}}&0\\+{\frac {1}{\sqrt {2}}}&-{\frac {i}{\sqrt {2}}}&0\\0&0&1\end{pmatrix}}\,,} with inverse: ( e x e y e z ) = U − 1 ( e + e − e 0 ) , U − 1 = ( − 1 2 + 1 2 0 + i 2 + i 2 0 0 0 1 ) . {\displaystyle {\begin{pmatrix}\mathbf {e} _{x}\\\mathbf {e} _{y}\\\mathbf {e} _{z}\end{pmatrix}}=\mathbf {U} ^{-1}{\begin{pmatrix}\mathbf {e} _{+}\\\mathbf {e} _{-}\\\mathbf {e} _{0}\end{pmatrix}}\,,\quad \mathbf {U} ^{-1}={\begin{pmatrix}-{\frac {1}{\sqrt {2}}}&+{\frac {1}{\sqrt {2}}}&0\\+{\frac {i}{\sqrt {2}}}&+{\frac {i}{\sqrt {2}}}&0\\0&0&1\end{pmatrix}}\,.} It can be seen that U is a unitary matrix, in other words its Hermitian conjugate U† (complex conjugate and matrix transpose) is also the inverse matrix U−1. For the coordinates: ( A + A − A 0 ) = U ∗ ( A x A y A z ) , U ∗ = ( − 1 2 + i 2 0 + 1 2 + i 2 0 0 0 1 ) , {\displaystyle {\begin{pmatrix}A_{+}\\A_{-}\\A_{0}\end{pmatrix}}=\mathbf {U} ^{\mathrm {} }{\begin{pmatrix}A_{x}\\A_{y}\\A_{z}\end{pmatrix}}\,,\quad \mathbf {U} ^{\mathrm {} }={\begin{pmatrix}-{\frac {1}{\sqrt {2}}}&+{\frac {i}{\sqrt {2}}}&0\\+{\frac {1}{\sqrt {2}}}&+{\frac {i}{\sqrt {2}}}&0\\0&0&1\end{pmatrix}}\,,} and inverse: ( A x A y A z ) = ( U ∗ ) − 1 ( A + A − A 0 ) , ( U ∗ ) − 1 = ( − 1 2 + 1 2 0 − i 2 − i 2 0 0 0 1 ) . {\displaystyle {\begin{pmatrix}A_{x}\\A_{y}\\A_{z}\end{pmatrix}}=(\mathbf {U} ^{\mathrm {} })^{-1}{\begin{pmatrix}A_{+}\\A_{-}\\A_{0}\end{pmatrix}}\,,\quad (\mathbf {U} ^{\mathrm {} })^{-1}={\begin{pmatrix}-{\frac {1}{\sqrt {2}}}&+{\frac {1}{\sqrt {2}}}&0\\-{\frac {i}{\sqrt {2}}}&-{\frac {i}{\sqrt {2}}}&0\\0&0&1\end{pmatrix}}\,.} === Cross products === Taking cross products of the spherical basis vectors, we find an obvious relation: e q × e q = 0 {\displaystyle \mathbf {e} _{q}\times \mathbf {e} _{q}={\boldsymbol {0}}} where q is a placeholder for +, −, 0, and two less obvious relations: e ± × e ∓ = ± i e 0 {\displaystyle \mathbf {e} _{\pm }\times \mathbf {e} _{\mp }=\pm i\mathbf {e} _{0}} e ± × e 0 = ± i e ± {\displaystyle \mathbf {e} _{\pm }\times \mathbf {e} _{0}=\pm i\mathbf {e} _{\pm }} === Inner product in the spherical basis === The inner product between two vectors A and B in the spherical basis follows from the above definition of the inner product: ⟨ A , B ⟩ = A + B + ⋆ + A − B − ⋆ + A 0 B 0 ⋆ {\displaystyle \left\langle \mathbf {A} ,\mathbf {B} \right\rangle =A_{+}B_{+}^{\star }+A_{-}B_{-}^{\star }+A_{0}B_{0}^{\star }}
GermaNet
GermaNet is a semantic network for the German language. It relates nouns, verbs, and adjectives semantically by grouping lexical units that express the same concept into synsets and by defining semantic relations between these synsets. GermaNet is free for academic use, after signing a license. GermaNet shares much in common with the English WordNet and can be viewed as an online thesaurus or a light-weight ontology. GermaNet has been developed and maintained at the University of Tübingen since 1997 within the research group for General and Computational Linguistics. It has been integrated into the EuroWordNet, a multilingual lexical-semantic database. == Database == === Contents === GermaNet partitions the lexical space into a set of concepts that are interlinked by semantic relations. A semantic concept is modeled by a synset. A synset is a set of words (called lexical units) where all the words are taken to have the same or almost the same meaning. Thus, a synset is a set of synonyms grouped under one definition, or "gloss". In addition to the gloss, synsets are labeled with their syntactic function and accompanied by example sentences for each distinct meaning in the synset. Just as in WordNet, for each word category the semantic space is divided into a number of semantic fields closely related to major nodes in the semantic network: Ort, or "location", Körper, or "body", etc. As of version 20.0 (release November 2025), GermaNet contains: Synsets: 179438 Lexical units: 231500 Literals: 216517 1.29 lexical units per synset Number of conceptual relations: 194367 Number of lexical relations: 13602 (synonymy excluded) Number of split compounds: 130901 Number of Interlingual Index (ILI) records: 28561 Number of Wiktionary sense descriptions: 29539 === Format === All GermaNet data is stored in a PostgreSQL relational database. The database schema follows the internal structure of GermaNet: there are tables to store synsets, lexical units, conceptual and lexical relations, etc. GermaNet data is distributed both in this database format and as XML files. In the XML data, two types of files, one for synsets and the other for relations, represent all data available in the GermaNet database. == Interfaces == There are software libraries and APIs available for Java and Python. These programs are distributed under free-software licenses and provide easy access to all information in various versions of GermaNet. GermaNet Rover is an on-line application that can be used to search for synsets in GermaNet, explore the data associated with them, and calculate the semantic similarity of pairs of synsets. It features visualizations of the hypernym relation and advanced filtering options for synset searching. == Licenses == GermaNet 20.0 (released November 2025) can be distributed under one of the following types of license agreements: Academic Research License Agreement: for the purpose of research at academic institutions. There is no license fee for academic use. Licenses are not given to individual students, and those seeking a license are required to talk to an academic advisor. Research and Development License Agreement: applies to non-academic institutions and research consortia. To be used strictly for technology development and internal research. Commercial License Agreement: applies to non-academic institutions and commercial enterprises. It permits technology development and internal research, as well as giving the non-exclusive right to distribute and market any derived product or service. == Alternatives == Open-de-WordNet is a freely available alternative to GermaNet which is compatible with WordNet. == Linguistic applications == GermaNet has been used for a variety of applications, including: semantic analysis shallow recognition of implicit document structure compound analysis analyzing sectional preferences word sense disambiguation