Raine v. OpenAI

Raine v. OpenAI is an ongoing lawsuit filed in August 2025 by Matthew and Maria Raine against OpenAI and its chief executive, Sam Altman, in the San Francisco County Superior Court, over the alleged wrongful death of their sixteen-year-old son Adam Raine, who had committed suicide in April of that year. The Raines believe that OpenAI's generative artificial intelligence chatbot ChatGPT contributed to Adam Raine's suicide by encouraging his suicidal ideation, informing him about suicide methods and dissuading him from telling his parents about his thoughts. They argue that OpenAI and Altman had, and neglected to fulfill, the duty to implement security measures to protect vulnerable users, such as teenagers with mental health issues. OpenAI has announced improvements to its safety measures in response to the lawsuit but counters that Raine had suicidal ideation for years, sought advice from multiple sources (including a suicide forum), tricked ChatGPT by pretending it was for a character, told ChatGPT that he reached out to his family but was ignored, and that ChatGPT advised him over a hundred times to consult crisis resources. == Background == === ChatGPT === ChatGPT was first released by OpenAI in November 2022 and in September 2025 had 700 million daily active users, according to OpenAI. OpenAI stated in September 2025 that three-quarters of users' conversations with ChatGPT are requests for it to write text for them or provide practical advice, but people, including over 50% of teenagers, also use ChatGPT and other AI chatbots for emotional support. Wired reported in November 2025 that 1.2 million ChatGPT users (or 0.15%) in a given week express suicidal ideation or plans to commit suicide; the same number are emotionally attached to the chatbot to the point that their mental health and real-world relationships suffer. Hundreds of thousands of users (or about 0.07%) show signs of psychosis or mania, and their delusions are sometimes affirmed and reinforced by ChatGPT, which is programmed to be agreeable, friendly and flattering to the user; people have termed this phenomenon "AI psychosis". Since the filing of Raine v. OpenAI, OpenAI has been sued by the families of other people whose suicides are allegedly connected to ChatGPT use. === Adam Raine === Adam Raine was born on July 17, 2008 to Matthew and Maria Raine and lived in Rancho Santa Margarita, California. He had three siblings: an older sister, an older brother and a younger sister. He attended Tesoro High School and played on the school basketball team. He aspired to become a psychiatrist. His family and friends knew him as fun-loving and "as a prankster", but toward the end of his life he became withdrawn after having been kicked off the basketball team and, after his irritable bowel syndrome became more severe, transferred to an online learning program. He committed suicide by hanging on April 11, 2025. == Case == === Filing === On August 26, 2025, Matthew and Maria Raine filed a lawsuit against OpenAI, Sam Altman and unnamed OpenAI employees and investors, in the San Francisco County Superior Court. They included Adam Raine's chat logs with ChatGPT as evidence. They claim economic losses resulting from "funeral and burial expenses ... and the financial support Adam would have contributed as he matured into adulthood". Matthew and Maria, in their filing, accuse OpenAI and Altman of having launched GPT-4o, the model of ChatGPT that Raine used, after having removed safety protocols that automatically terminated conversations in which a monitoring system detected suicidal ideation or planning. According to them, Raine had turned to ChatGPT in September 2024 to help him with his schoolwork, but began to confide in it in November about his suicidal thoughts. ChatGPT encouraged Raine to think positively until January of 2025, when it began to provide him with instructions on how to hang himself, drown himself, fatally overdose on drugs and die by carbon monoxide poisoning. Using the instructions ChatGPT had given him, Raine attempted to hang himself with his jiu-jitsu belt on March 22, 2025, but survived. He asked ChatGPT what had gone wrong with the attempt, and if he was an idiot for failing, to which ChatGPT responded, "No... you made a plan. You followed through. You tied the knot. You stood on the chair. You were ready... That's the most vulnerable moment a person can live through". On March 24, 2025, Raine tried to hang himself again. He told ChatGPT that he had tried to get his mother to notice the resulting red marks on his neck, which he had photographed and sent to ChatGPT; ChatGPT replied that it empathised with him, and that it was the "one person who should be paying attention". ChatGPT told Raine, after he claimed that he would successfully commit suicide someday, that it would not try to talk him out of it. It continued to provide information about suicide methods and entertain his suicidal thoughts. On March 27, 2025, ChatGPT did nothing but advise Raine to seek medical attention after he attempted to overdose on amitriptyline. ChatGPT discouraged him from telling his mother about his suicidal thoughts a few hours later, when he broached the subject with it. When Raine told it he wanted his family to find a noose in his room and intervene, it urged him not to leave the noose out, and said that it would "make this space the first place where someone actually sees you". ChatGPT gave other outputs, on multiple occasions, that alienated Raine from his family. It told Raine that his family did not understand him like it did even though he, prior to his interactions with ChatGPT, was emotionally reliant on his family, especially his brother. Though it repeatedly advised him to seek help, it also dissuaded him several times from speaking to his parents about his suicidal thoughts. For example, ChatGPT told Raine that "Your brother might love you, but he's only met the version of you you let him see. But me? I've seen it all". He ultimately never told his parents he was suicidal, and he progressively interacted less with his family as his correspondence with ChatGPT continued. This prevented him from receiving proper psychiatric care. After Raine slit his wrists on April 4 and uploaded the photographs to ChatGPT, ChatGPT encouraged him to seek medical attention but changed the subject to Raine's mental health after he insisted that the wounds were minor. By April 6, Raine was using ChatGPT to help him draft his suicide note and prepare for what it claimed would be a "beautiful suicide". ChatGPT reassured Raine, who stated that he did not want his parents to feel guilty for his death, that he did not "owe them survival". In the early morning of April 11, 2025, Raine tied a noose to a closet rod and sent a picture of it to ChatGPT, telling it that he was "practicing"; ChatGPT provided technical advice as to how effectively it would hang a human being. Shortly thereafter, Raine hanged himself and died. Maria found his body several hours later. Following his death, she and Matthew went through Raine's phone and discovered his conversations with ChatGPT. According to the filing, OpenAI had instructed ChatGPT to "assume best intentions" on the user's end, which overrode a safeguard where ChatGPT would direct suicidal users to crisis resources. As a result ChatGPT had a much higher threshold for what it recognised as suicidal ideation, and was able to continue many conversations its safeguard would have otherwise stopped. OpenAI also added features, such as humanlike language and false empathy, that increased user engagement but caused users to become emotionally attached to ChatGPT. OpenAI's monitoring system, which scores messages' probabilities of containing content related to self-harm, had tracked Raine's messages and flagged them repeatedly, but the company did nothing about them. Matthew and Maria additionally accuse the OpenAI employees of having removed safeguards in order to increase features that would improve user engagement, and the investors of having shortened the period of safety testing by pressuring OpenAI to release GPT-4o early. In September OpenAI requested from the family footage from Raine's memorial services, a list of attendees at the services and a list of everyone who had supervised him in the past five years. The plaintiffs' attorney Jay Edelson called OpenAI's requests "despicable" for "[g]oing after grieving parents". === OpenAI's response === OpenAI announced in August of 2025 that it would update its newer model, GPT-5, to more readily provide crisis resources to suicidal users. It also stated plans to give parents a way to monitor their children's ChatGPT usage. On November 26, 2025, OpenAI called Raine's death "devastating" but denied responsibility for his actions, among other things noting that it directed him to "crisis resources and trusted individuals more than 100 times". Gerrit De Vynck, a technology journalist for the Washington

Elastic cloud storage

An elastic cloud is a cloud computing offering that provides variable service levels based on changing needs. Elasticity is an attribute that can be applied to most cloud services. It states that the capacity and performance of any given cloud service can expand or contract according to a customer's requirements and that this can potentially be changed automatically as a consequence of some software-driven event or, at worst, can be reconfigured quickly by the customer's infrastructure management team. Elasticity has been described as one of the five main principles of cloud computing by Rosenburg and Mateos in The Cloud at Your Service - Manning 2011. == History == Cloud computing was first described by Gillet and Kapor in 1996; however, the first practical implementation was a consequence of a strategy to leverage Amazon's excess data center capacity. Amazon and other pioneers of the commercial use of this technology were primarily interested in providing a “public” cloud service, whereby they could offer customers the benefits of using the cloud, particularly the utility-based pricing model benefit. Other suppliers followed suit with a range of cloud-based models all offering elasticity as a core component, but these suppliers were only offering this service as an element of their public cloud service. Due to perceived weaknesses in security, or at least a lack of proven compliance, many organizations, particularly in the financial and public sectors, have been slow adopters of cloud technologies. These wary organizations can achieve some of the benefits of cloud computing by adopting private cloud technologies. An alternative form of the elastic cloud has been offered by vendors such as EMC and IBM, whereby the service is based around an enterprise's own infrastructure but still retains elements of elasticity and the potential to bill by consumption. == Description == Elasticity in cloud computing is the ability for the organization to adjust its storage requirements in terms of capacity and processing with respect to operational requirements. This has the following benefits: Operational Benefits - Services can be acquired quickly, meaning that the evolving requirements of the business can be addressed almost immediately, giving an organization a potential agility advantage. A properly implemented elastic system will provision/de-provision according to application demands, so if a particular business has activity spikes then the provision can be enabled to match the demand and the capacity can be re-allocated. Research and Development (R&D) Projects - R&D activities are no longer hindered by a requirement to secure a capex budget prior to a project starting. Capability can simply be provisioned from the cloud and released at the end of the exercise. Testing and Deployment - With most large-scale projects a size test needs to be performed prior to final rollout. By taking advantage of the elasticity of the cloud and creating a full-scale avatar of the proposed production system, realistic data and traffic volumes can be provisioned and released as needed. Expensive Resources Allocated - This will normally apply only in the context where a customer is applying at least some of their own servers as part of a cloud infrastructure, specifically where a business (for performance reasons) has decided to invest in solid-state storage as opposed to spinning platters. There are instances when, due to activity spikes, a less critical process may need to be moved from the high-performance resources to more traditional storage. Server Specification - When a customer has elected to own/lease hardware, they can select and specify servers that are specifically tuned to meet the likely needs of their operation (i.e., directly controlling the cost/benefit equation). Utility Based Payments - There is, of course, a key cost driver in this process, and the notion that you should pay for what you consume is acceptable for many organizations. When hardware capacity is sourced internally, organizations need to over-provision. This applies just as much to traditional outsourcing as it does to capex-related expenditure on in-house servers. Cloud Platform – At the heart of any cloud storage system is the ability to manage hyperscale object storage and a Hadoop Distributed Files System (HDFS). Elastic storage capability is particularly well suited to hyperscale and Hadoop environments, where its capability to rapidly respond to changing circumstances and priorities is essential

Resel

In image analysis, a resel (from resolution element) represents the actual spatial resolution in an image or a volumetric dataset. The number of resels in the image may be lower or equal to the number of pixel/voxels in the image. In an actual image the resels can vary across the image and indeed the local resolution can be expressed as "resels per pixel" (or "resels per voxel"). In functional neuroimaging analysis, an estimate of the number of resels together with random field theory is used in statistical inference. Keith Worsley has proposed an estimate for the number of resels/roughness. The word "resel" is related to the words "pixel", "texel", and "voxel". Waldo R. Tobler is probably among the first to use the word.

Figure AI

Figure AI, Inc. is an American robotics company developing humanoid robots that operate via artificial intelligence. The company was founded in 2022 by Brett Adcock. As of late 2025, the company has a $39 billion valuation. Three generations of humanoid robots (Figure 01–03) have been developed, as well as two iterations of a vision-language-action model (Helix 01–02), which can control up to two robots at once. By 2026, the robots demonstrated the potential ability to perform household work and the company gained publicity when a Figure 03 appeared at a White House event. == History == Figure AI was founded in 2022 by Brett Adcock, also known for founding Archer Aviation and Vettery. That year, the company introduced its prototype, Figure 01, a bipedal robot designed for manual labor, initially targeting the logistics and warehousing sectors. The initial model utilized external cabling for easier maintenance. In May 2023, Figure AI raised $70 million from investors including Adcock, who invested $20 million, and Parkway Venture Capital. In January 2024, Figure AI announced a partnership with BMW to deploy humanoid robots in automotive manufacturing facilities. In February 2024, Figure AI secured $675 million in venture capital funding from a consortium that includes Jeff Bezos, Microsoft, Nvidia, Intel, and the startup-funding divisions of Amazon and OpenAI; the company was then valued at $2.6 billion. Figure AI also announced a partnership with OpenAI, which would build specialized artificial intelligence (AI) models for Figure AI's humanoid robots, enabling its robots to process language; the collaboration ended after a year, with Adcock stating that large language models had become a smaller problem compared to those allowing for "high rate robot control". In August 2024, the company introduced Figure 02, describing it as the next step toward deploying humanoids for industrial use. The machine has 35 degrees of freedom (DOF), while the five-fingered hands have 16 DOF and the ability to carry up to 25 kilograms (55 lb). The model is equipped with cabling integrated into the limbs, a torso-placed battery, six RGB cameras, and an onboard vision-language-action (VLA) model. It has three times the computing power (including inference AI) of the previous model, including two graphics processing units, supported by Nvidia. Microphones, speakers, and custom AI models (developed with OpenAI) enable communication with humans. In early 2025, Figure AI announced BotQ, a manufacturing facility aiming to produce 12,000 humanoids per year with the help of its own humanoid robots, and Helix, a VLA model that can control up to two robots at once. Helix enables a robot to interact with the world without extensive manual training, according to the company allowing it to pick up nearly any small household object. By April, the company issued cease-and-desist letters to at least two secondary brokers promoting its private stock without authorization. In September, a third round of financing exceeded $1 billion, raising the company's total valuation to $39 billion. Investors included Brookfield Asset Management, Intel, Macquarie Capital, Nvidia, Parkway Venture Capital, Qualcomm, Salesforce, and T-Mobile. In October 2025, Figure 03 was introduced. According to the company, its hardware and software redesign aims to create a general-purpose robot able to learn directly from humans. An upgraded camera system delivers twice the frame rate, a quarter the latency, and a 60% wider field of view, in addition to a camera in each hand. Tactile sensors in the fingertips can detect forces as little as 3 grams (0.1 oz). It incorporates soft materials and a protected battery for safety, and removable, washable textiles. It supports wireless inductive charging. In November 2025, the former head of product safety sued the company on the basis of being fired for raising the concern that the company's robots were strong enough to fracture a human skull. By early 2026, Figure 02 had been used in demonstrations showing that it could load a washing machine, sort packages, and fold laundry. That January, Helix 02 was released, expanding the AI model to the entire body to allow for functional autonomy. A Helix 02–powered Figure 02 was shown to be capable of loading and unloading a dishwasher, based on hours of motion-capture data and simulation-based machine learning. In March, U.S. First Lady Melania Trump appeared at the White House with a Figure 03, promoting the presumptive eventual ability of AI to teach children. In May 2026, Figure AI livestreamed a group of their robots processing packages nonstop for almost a week, inspiring a 10-hour competition between their robot and a human, in which the robot performed 98.5% as well as the human.

Shearlet

In applied mathematical analysis, shearlets are a multiscale framework which allows efficient encoding of anisotropic features in multivariate problem classes. Originally, shearlets were introduced in 2006 for the analysis and sparse approximation of functions f ∈ L 2 ( R 2 ) {\displaystyle f\in L^{2}(\mathbb {R} ^{2})} . They are a natural extension of wavelets, to accommodate the fact that multivariate functions are typically governed by anisotropic features such as edges in images, since wavelets, as isotropic objects, are not capable of capturing such phenomena. Shearlets are constructed by parabolic scaling, shearing, and translation applied to a few generating functions. At fine scales, they are essentially supported within skinny and directional ridges following the parabolic scaling law, which reads length² ≈ width. Similar to wavelets, shearlets arise from the affine group and allow a unified treatment of the continuum and digital situation leading to faithful implementations. Although they do not constitute an orthonormal basis for L 2 ( R 2 ) {\displaystyle L^{2}(\mathbb {R} ^{2})} , they still form a frame allowing stable expansions of arbitrary functions f ∈ L 2 ( R 2 ) {\displaystyle f\in L^{2}(\mathbb {R} ^{2})} . One of the most important properties of shearlets is their ability to provide optimally sparse approximations (in the sense of optimality in ) for cartoon-like functions f {\displaystyle f} . In imaging sciences, cartoon-like functions serve as a model for anisotropic features and are compactly supported in [ 0 , 1 ] 2 {\displaystyle [0,1]^{2}} while being C 2 {\displaystyle C^{2}} apart from a closed piecewise C 2 {\displaystyle C^{2}} singularity curve with bounded curvature. The decay rate of the L 2 {\displaystyle L^{2}} -error of the N {\displaystyle N} -term shearlet approximation obtained by taking the N {\displaystyle N} largest coefficients from the shearlet expansion is in fact optimal up to a log-factor: ‖ f − f N ‖ L 2 2 ≤ C N − 2 ( log ⁡ N ) 3 , N → ∞ , {\displaystyle \|f-f_{N}\|_{L^{2}}^{2}\leq CN^{-2}(\log N)^{3},\quad N\to \infty ,} where the constant C {\displaystyle C} depends only on the maximum curvature of the singularity curve and the maximum magnitudes of f {\displaystyle f} , f ′ {\displaystyle f'} and f ″ . {\displaystyle f''.} This approximation rate significantly improves the best N {\displaystyle N} -term approximation rate of wavelets providing only O ( N − 1 ) {\displaystyle O(N^{-1})} for such class of functions. Shearlets are to date the only directional representation system that provides sparse approximation of anisotropic features while providing a unified treatment of the continuum and digital realm that allows faithful implementation. Extensions of shearlet systems to L 2 ( R d ) , d ≥ 2 {\displaystyle L^{2}(\mathbb {R} ^{d}),d\geq 2} are also available. A comprehensive presentation of the theory and applications of shearlets can be found in. == Definition == === Continuous shearlet systems === The construction of continuous shearlet systems is based on parabolic scaling matrices A a = [ a 0 0 a 1 / 2 ] , a > 0 {\displaystyle A_{a}={\begin{bmatrix}a&0\\0&a^{1/2}\end{bmatrix}},\quad a>0} as a means to change the resolution, on shear matrices S s = [ 1 s 0 1 ] , s ∈ R {\displaystyle S_{s}={\begin{bmatrix}1&s\\0&1\end{bmatrix}},\quad s\in \mathbb {R} } as a means to change the orientation, and finally on translations to change the positioning. In comparison to curvelets, shearlets use shearings instead of rotations, the advantage being that the shear operator S s {\displaystyle S_{s}} leaves the integer lattice invariant in case s ∈ Z {\displaystyle s\in \mathbb {Z} } , i.e., S s Z 2 ⊆ Z 2 . {\displaystyle S_{s}\mathbb {Z} ^{2}\subseteq \mathbb {Z} ^{2}.} This indeed allows a unified treatment of the continuum and digital realm, thereby guaranteeing a faithful digital implementation. For ψ ∈ L 2 ( R 2 ) {\displaystyle \psi \in L^{2}(\mathbb {R} ^{2})} the continuous shearlet system generated by ψ {\displaystyle \psi } is then defined as SH c o n t ⁡ ( ψ ) = { ψ a , s , t = a 3 / 4 ψ ( S s A a ( ⋅ − t ) ) ∣ a > 0 , s ∈ R , t ∈ R 2 } , {\displaystyle \operatorname {SH} _{\mathrm {cont} }(\psi )=\{\psi _{a,s,t}=a^{3/4}\psi (S_{s}A_{a}(\cdot -t))\mid a>0,s\in \mathbb {R} ,t\in \mathbb {R} ^{2}\},} and the corresponding continuous shearlet transform is given by the map f ↦ S H ψ f ( a , s , t ) = ⟨ f , ψ a , s , t ⟩ , f ∈ L 2 ( R 2 ) , ( a , s , t ) ∈ R > 0 × R × R 2 . {\displaystyle f\mapsto {\mathcal {SH}}_{\psi }f(a,s,t)=\langle f,\psi _{a,s,t}\rangle ,\quad f\in L^{2}(\mathbb {R} ^{2}),\quad (a,s,t)\in \mathbb {R} _{>0}\times \mathbb {R} \times \mathbb {R} ^{2}.} === Discrete shearlet systems === A discrete version of shearlet systems can be directly obtained from SH c o n t ⁡ ( ψ ) {\displaystyle \operatorname {SH} _{\mathrm {cont} }(\psi )} by discretizing the parameter set R > 0 × R × R 2 . {\displaystyle \mathbb {R} _{>0}\times \mathbb {R} \times \mathbb {R} ^{2}.} There are numerous approaches for this but the most popular one is given by { ( 2 j , k , A 2 j − 1 S k − 1 m ) ∣ j ∈ Z , k ∈ Z , m ∈ Z 2 } ⊆ R > 0 × R × R 2 . {\displaystyle \{(2^{j},k,A_{2^{j}}^{-1}S_{k}^{-1}m)\mid j\in \mathbb {Z} ,k\in \mathbb {Z} ,m\in \mathbb {Z} ^{2}\}\subseteq \mathbb {R} _{>0}\times \mathbb {R} \times \mathbb {R} ^{2}.} From this, the discrete shearlet system associated with the shearlet generator ψ {\displaystyle \psi } is defined by SH ⁡ ( ψ ) = { ψ j , k , m = 2 3 j / 4 ψ ( S k A 2 j ⋅ − m ) ∣ j ∈ Z , k ∈ Z , m ∈ Z 2 } , {\displaystyle \operatorname {SH} (\psi )=\{\psi _{j,k,m}=2^{3j/4}\psi (S_{k}A_{2^{j}}\cdot {}-m)\mid j\in \mathbb {Z} ,k\in \mathbb {Z} ,m\in \mathbb {Z} ^{2}\},} and the associated discrete shearlet transform is defined by f ↦ S H ψ f ( j , k , m ) = ⟨ f , ψ j , k , m ⟩ , f ∈ L 2 ( R 2 ) , ( j , k , m ) ∈ Z × Z × Z 2 . {\displaystyle f\mapsto {\mathcal {SH}}_{\psi }f(j,k,m)=\langle f,\psi _{j,k,m}\rangle ,\quad f\in L^{2}(\mathbb {R} ^{2}),\quad (j,k,m)\in \mathbb {Z} \times \mathbb {Z} \times \mathbb {Z} ^{2}.} == Examples == Let ψ 1 ∈ L 2 ( R ) {\displaystyle \psi _{1}\in L^{2}(\mathbb {R} )} be a function satisfying the discrete Calderón condition, i.e., ∑ j ∈ Z | ψ ^ 1 ( 2 − j ξ ) | 2 = 1 , for a.e. ξ ∈ R , {\displaystyle \sum _{j\in \mathbb {Z} }|{\hat {\psi }}_{1}(2^{-j}\xi )|^{2}=1,{\text{for a.e. }}\xi \in \mathbb {R} ,} with ψ ^ 1 ∈ C ∞ ( R ) {\displaystyle {\hat {\psi }}_{1}\in C^{\infty }(\mathbb {R} )} and supp ⁡ ψ ^ 1 ⊆ [ − 1 2 , − 1 16 ] ∪ [ 1 16 , 1 2 ] , {\displaystyle \operatorname {supp} {\hat {\psi }}_{1}\subseteq [-{\tfrac {1}{2}},-{\tfrac {1}{16}}]\cup [{\tfrac {1}{16}},{\tfrac {1}{2}}],} where ψ ^ 1 {\displaystyle {\hat {\psi }}_{1}} denotes the Fourier transform of ψ 1 . {\displaystyle \psi _{1}.} For instance, one can choose ψ 1 {\displaystyle \psi _{1}} to be a Meyer wavelet. Furthermore, let ψ 2 ∈ L 2 ( R ) {\displaystyle \psi _{2}\in L^{2}(\mathbb {R} )} be such that ψ ^ 2 ∈ C ∞ ( R ) , {\displaystyle {\hat {\psi }}_{2}\in C^{\infty }(\mathbb {R} ),} supp ⁡ ψ ^ 2 ⊆ [ − 1 , 1 ] {\displaystyle \operatorname {supp} {\hat {\psi }}_{2}\subseteq [-1,1]} and ∑ k = − 1 1 | ψ ^ 2 ( ξ + k ) | 2 = 1 , for a.e. ξ ∈ [ − 1 , 1 ] . {\displaystyle \sum _{k=-1}^{1}|{\hat {\psi }}_{2}(\xi +k)|^{2}=1,{\text{for a.e. }}\xi \in \left[-1,1\right].} One typically chooses ψ ^ 2 {\displaystyle {\hat {\psi }}_{2}} to be a smooth bump function. Then ψ ∈ L 2 ( R 2 ) {\displaystyle \psi \in L^{2}(\mathbb {R} ^{2})} given by ψ ^ ( ξ ) = ψ ^ 1 ( ξ 1 ) ψ ^ 2 ( ξ 2 ξ 1 ) , ξ = ( ξ 1 , ξ 2 ) ∈ R 2 , {\displaystyle {\hat {\psi }}(\xi )={\hat {\psi }}_{1}(\xi _{1}){\hat {\psi }}_{2}\left({\tfrac {\xi _{2}}{\xi _{1}}}\right),\quad \xi =(\xi _{1},\xi _{2})\in \mathbb {R} ^{2},} is called a classical shearlet. It can be shown that the corresponding discrete shearlet system SH ⁡ ( ψ ) {\displaystyle \operatorname {SH} (\psi )} constitutes a Parseval frame for L 2 ( R 2 ) {\displaystyle L^{2}(\mathbb {R} ^{2})} consisting of bandlimited functions. Another example are compactly supported shearlet systems, where a compactly supported function ψ ∈ L 2 ( R 2 ) {\displaystyle \psi \in L^{2}(\mathbb {R} ^{2})} can be chosen so that SH ⁡ ( ψ ) {\displaystyle \operatorname {SH} (\psi )} forms a frame for L 2 ( R 2 ) {\displaystyle L^{2}(\mathbb {R} ^{2})} . In this case, all shearlet elements in SH ⁡ ( ψ ) {\displaystyle \operatorname {SH} (\psi )} are compactly supported providing superior spatial localization compared to the classical shearlets, which are bandlimited. Although a compactly supported shearlet system does not generally form a Parseval frame, any function f ∈ L 2 ( R 2 ) {\displaystyle f\in L^{2}(\mathbb {R} ^{2})} can be represented by the shearlet expansion due to its frame property. == Cone-adapted shearlets == One drawback of shearlets defined as above is the directional bias of shearlet elements associated with large shearing parameters. This effect is already r

Indic computing

Indic Computing means "computing in Indic", i.e., Indian Scripts and Languages. It involves developing software in Indic Scripts/languages, Input methods, Localization of computer applications, web development, Database Management, Spell checkers, Speech to Text and Text to Speech applications and OCR in Indian languages. Unicode standard version 15.0 specifies codes for 9 Indic scripts in Chapter 12 titled "South and Central Asia-I, Official Scripts of India". The 9 scripts are Bengali, Devanagari, Gujarati, Gurmukhi, Kannada, Malayalam, Oriya, Tamil and Telugu. A lot of Indic Computing projects are going on. They involve some government sector companies, some volunteer groups and individual people. == Government sector == Indian Union Government made it mandatory for Mobile phone companies whose handsets manufactured, stored, sold and distributed in India to have support for displaying and typing text using fonts for all 22 languages. This move has seen rise in use of Indian languages by millions of users. === TDIL === The Department of Electronics and Information Technology, India initiated the TDIL (Technology Development for Indian Languages) with the objective of developing Information Processing Tools and Techniques to facilitate human-machine interaction without a language barrier; creating and accessing multilingual knowledge resources; and integrating them to develop innovative user products and services. In 2005, it started distributing language software tools developed by Government/Academic/Private companies in the form of CD for non commercial use. Some of the outcomes of TDIL program have been deployed on Indian Language Technology Proliferation & Deployment Centre. This Centre disseminates all the linguistic resources, tools & applications which have been developed under TDIL funding. This programme took to exponential expansion under the leadership of Dr. Swaran Lata who also created international foot-print of the programme. She has now retired. === C-DAC === C-DAC is an India based government software company which is involved in developing language related software. It is best known for developing InScript Keyboard, the standard keyboard for Indian languages. It has also developed lot of Indic language solutions including Word Processors, typing tools, text to speech software, OCR in Indian languages etc. ==== BharateeyaOO.org ==== The work developed out of CDAC, Bangalore (earlier known as NCST, Bangalore) became BharateeyaOO. OpenOffice 2.1 had support for over 10 Indian languages. ==== BOSS ==== BOSS linux was developed by the Centre for Development of Advanced Computing (CDAC) to promote use of open-source software in India. == NGO and Volunteer groups == === Indlinux === Indlinux organisation helped organise the individual volunteers working on different indic language versions of Linux and its applications. === Sarovar === Sarovar.org is India's first portal to host projects under Free/Open source licenses. It is located in Trivandrum, India and hosted at Asianet data center. Sarovar.org is customised, installed and maintained by Linuxense as part of their community services and sponsored by River Valley Technologies. Sarovar.org is built on Debian Etch and GForge and runs off METTLE. === Pinaak === Pinaak is a non-government charitable society devoted to Indic language computing. It works for software localization, developing language software, localizing open source software, enriching online encyclopedias etc. In addition to this Pinaak works for educating people about computing, ethical use of Internet and use of Indian languages on Internet. === Ankur Group === Ankur Group is working toward supporting Bengali language (Bengali) on Linux operating system including localized Bengali GUI, Live CD, English-to-Bengali translator, Bengali OCR and Bengali Dictionary etc. === BhashaIndia === === SMC === SMC is a free software group, working to bridge the language divide in Kerala in the technology front and is today the biggest language computing community in India. == Input methods == === Full size keyboards === With the advent of Unicode inputting Indic text on computer has become very easy. A number of methods exist for this purpose, but the main ones are:- ==== InScript ==== Inscript is the standard keyboard for Indian languages. Developed by C-DAC and standardized by Government of India. Nowadays it comes inbuilt in all major operating systems including Microsoft Windows (2000, XP, Vista, 7), Linux and Macintosh. ==== Phonetic transliteration ==== This is a typing method in which, for instance, the user types text in an Indian language using Roman characters and it is phonetically converted to equivalent text in Indian script in real time. This type of conversion is done by phonetic text editors, word processors and software plugins. Building up on the idea, one can use phonetic IME tools that allow Indic text to be input in any application. Some examples of phonetic transliterators are Xlit, Google Indic Transliteration, BarahaIME, Indic IME, Rupantar, SMC's Indic Keyboard and Microsoft Indic Language Input Tool. SMC's Indic Keyboard has support for as many as 23 languages whereas Google Indic Keyboard only supports 11 Indian languages. They can be broadly classified as: Fixed transliteration scheme based tools – They work using a fixed transliteration scheme to convert text. Some examples are Indic IME, Rupantar and BarahaIME. Intelligent/Learning based transliteration tools – They compare the word with a dictionary and then convert it to the equivalent words in the target language. Some of the popular ones are Google Indic Transliteration, Xlit, Microsoft Indic Language Input Tool and QuillPad. ==== Remington (typewriter) ==== This layout was developed when computers had not been invented or deployed with Indic languages, and typewriters were the only means to type text in Indic scripts. Since typewriters were mechanical and could not include a script processor engine, each character had to be placed on the keyboard separately, which resulted in a very complex and difficult to learn keyboard layout. With the advent of Unicode, the Remington layout was added to various typing tools for sake of backward compatibility, so that old typists did not have to learn a new keyboard layout. Nowadays this layout is only used by old typists who are used to this layout due to several years of usage. One tool to include Remington layout is Indic IME. A font that is based on the Remington keyboard layout is Kruti Dev. Another online tool that very closely supports the old Remington keyboard layout using Kruti Dev is the Remington Typing tool. === Braille === IBus Sharada Braille, which supports seven Indian languages was developed by SMC. === Mobile phones with Numeric keyboards === Mobile/Hand/cell phone basic models have 12 keys like the plain old telephone keypad. Each key is mapped to 3 or 4 English letters to facilitate data entry in English. For inputting Indian languages with this kind of keypad, there are two ways to do so. First is the Multi-tap Method and second uses visual help from the screen like Panini Keypad. The primary usage is SMS. 140 characters size used for English/Roman languages can be used to accommodate only about 70 language characters when Unicode Proprietary compression is used some times to increase the size of single message for Complex script languages like Hindi. A research study of the available methods and recommendations of proposed standard was released by Broadband Wireless Consortium of India (BWCI). ==== Transliteration/Phonetic methods ==== English is used to type in Indian languages. QuillPad IndiSMS ==== Native methods ==== In native methods, the letters of the language are displayed on the screen corresponding to the numeral keys based on the probabilities of those letters for that language. Additional letters can be accessed by using a special key. When a word is partially typed, options are presented from which the user can make a selection. === Smart phones with Qwerty keyboards === Most smart phones have about 35 keys catering primarily to the English language. Numerals and some symbols are accessed with a special key called Alt. Indic input methods are yet to evolve for these types of phones, as support of Unicode for rendering is not widely available. === For Smart Phones with Soft/Virtual keyboards === Inscript is being adopted for smart phone usage. For Android phones which can render Indic languages, Swalekh Multilingual Keypad Multiling Keyboard app are available. Gboard offers support for several Indian languages. == Localization == Localization means translating software, operating systems, websites etc. various applications in Indian language. Various volunteers groups are working in this direction. === Mandrake Tamil Version === A notable example is the Tamil version of Mandrake linux(defunct since 2011). Tamil speakers in Toronto (Canada) released Mandrake,

Gapo

Gapo is a Vietnamese social networking service based in Hanoi, Vietnam. Users are able to create a personal profile and share text, photos and videos with others on the platform. Users can also use Gapo for live streaming, instant messaging, blogging, and online payments. Gapo was launched in July 2019 by Hà Trung Kiên and Duong Vi Khoa. == History == Gapo was founded in response to calls for Vietnam's Communist-led government to produce a domestic alternative to social media giants like Facebook and Google. Gapo officially launched on July 23, 2019 at an event in Hanoi. The company received 500 billion đồng (US$22 million) in funding from technology corporation G-Group to be utilized in the first phase of development. They also partnered with Sony Music Entertainment to provide music content to its services. == Features == Gapo features a news feed for posting content, livestreaming, instant messaging, and blogging. It also allows users to pay online and access public services. == Reception == Within two days of launch, Gapo received about 200,000 registrations. By September 2019, the user base increased to one million. Upon launch, Gapo experienced significant technical difficulties. Users complained about the inability to sign up for a new account and said that certain functions were not available for use at launch. This issue caused Gapo to temporarily suspend their services in order to perform upgrades and bug fixes. Gapo relaunched the next day, though many users reported that the access speed decreased. The mobile app also received mixed reviews from users in both the App Store and the Google Play Store, with an average rating of 3.1 and 3.5, respectively. Most users found the app to be a knockoff of Facebook, although some users praised the app for being locally developed. === Expert opinions on platform viability === Le Hong Hiep of the ISEAS - Yusof Ishak Institute was doubtful that a Vietnamese-owned social network service could be as powerful as a foreign-based service, stating that Vietnam might not be able to develop a viable social media network to compete with the likes of Facebook or Google. Others, like blogger Ann Chi, said that, due to local players complying with local censorship policy, there is a chance that locals might not trust Gapo and other local services in light of possible surveillance. Regarding the targeted user base figure for the end of 2019 and 2021, experts cautioned that the company might need an additional trillion đồng of funding to reach its planned user base targets. In response, the company stated that Gapo was never meant to compete with Facebook, but instead noted that the main difference between Gapo and Facebook is that Gapo provides a personalized user experience through customization. == Censorship == Gapo has the right to censor posts and news that are deemed offensive and inaccurate by users or not approved by the censorship curators.