AI Headshot Magisk Module

AI Headshot Magisk Module — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

  • Seq2seq

    Seq2seq

    Seq2seq is a family of machine learning approaches used for natural language processing. Originally developed by Lê Viết Quốc, a Vietnamese computer scientist and a machine learning pioneer at Google Brain, this framework has become foundational in many modern AI systems. Applications include language translation, image captioning, conversational models, speech recognition, and text summarization. Seq2seq uses sequence transformation: it turns one sequence into another sequence. == History == One naturally wonders if the problem of translation could conceivably be treated as a problem in cryptography. When I look at an article in Russian, I say: 'This is really written in English, but it has been coded in some strange symbols. I will now proceed to decode. seq2seq is an approach to machine translation (or more generally, sequence transduction) with roots in information theory, where communication is understood as an encode-transmit-decode process, and machine translation can be studied as a special case of communication. This viewpoint was elaborated, for example, in the noisy channel model of machine translation. In practice, seq2seq maps an input sequence into a real-numerical vector by using a neural network (the encoder), and then maps it back to an output sequence using another neural network (the decoder). The idea of encoder-decoder sequence transduction had been developed in the early 2010s. The papers most commonly cited as the originators that produced seq2seq are two papers from 2014. In the seq2seq as proposed by them, both the encoder and the decoder were LSTMs. This had the "bottleneck" problem, since the encoding vector has a fixed size, so for long input sequences, information would tend to be lost, as they are difficult to fit into the fixed-length encoding vector. The attention mechanism, proposed in 2014, resolved the bottleneck problem. They called their model RNNsearch, as it "emulates searching through a source sentence during decoding a translation". A problem with seq2seq models at this point was that recurrent neural networks are difficult to parallelize. The 2017 publication of Transformers resolved the problem by replacing the encoding RNN with self-attention Transformer blocks ("encoder blocks"), and the decoding RNN with cross-attention causally-masked Transformer blocks ("decoder blocks"). === Priority dispute === One of the papers cited as the originator for seq2seq is (Sutskever et al 2014), published at Google Brain while they were on Google's machine translation project. The research allowed Google to overhaul Google Translate into Google Neural Machine Translation in 2016. Tomáš Mikolov claims to have developed the idea (before joining Google Brain) of using a "neural language model on pairs of sentences... and then [generating] translation after seeing the first sentence"—which he equates with seq2seq machine translation, and to have mentioned the idea to Ilya Sutskever and Quoc Le (while at Google Brain), who failed to acknowledge him in their paper. Mikolov had worked on RNNLM (using RNN for language modelling) for his PhD thesis, and is more notable for developing word2vec. == Architecture == The main reference for this section is. === Encoder === The encoder is responsible for processing the input sequence and capturing its essential information, which is stored as the hidden state of the network and, in a model with attention mechanism, a context vector. The context vector is the weighted sum of the input hidden states and is generated for every time instance in the output sequences. === Decoder === The decoder takes the context vector and hidden states from the encoder and generates the final output sequence. The decoder operates in an autoregressive manner, producing one element of the output sequence at a time. At each step, it considers the previously generated elements, the context vector, and the input sequence information to make predictions for the next element in the output sequence. Specifically, in a model with attention mechanism, the context vector and the hidden state are concatenated together to form an attention hidden vector, which is used as an input for the decoder. The seq2seq method developed in the early 2010s uses two neural networks: an encoder network converts an input sentence into numerical vectors, and a decoder network converts those vectors to sentences in the target language. The Attention mechanism was grafted onto this structure in 2014 and is shown below. Later it was refined into the encoder-decoder Transformer architecture of 2017. === Training vs prediction === There is a subtle difference between training and prediction. During training time, both the input and the output sequences are known. During prediction time, only the input sequence is known, and the output sequence must be decoded by the network itself. Specifically, consider an input sequence x 1 : n {\displaystyle x_{1:n}} and output sequence y 1 : m {\displaystyle y_{1:m}} . The encoder would process the input x 1 : n {\displaystyle x_{1:n}} step by step. After that, the decoder would take the output from the encoder, as well as the as input, and produce a prediction y ^ 1 {\displaystyle {\hat {y}}_{1}} . Now, the question is: what should be input to the decoder in the next step? A standard method for training is "teacher forcing". In teacher forcing, no matter what is output by the decoder, the next input to the decoder is always the reference. That is, even if y ^ 1 ≠ y 1 {\displaystyle {\hat {y}}_{1}\neq y_{1}} , the next input to the decoder is still y 1 {\displaystyle y_{1}} , and so on. During prediction time, the "teacher" y 1 : m {\displaystyle y_{1:m}} would be unavailable. Therefore, the input to the decoder must be y ^ 1 {\displaystyle {\hat {y}}_{1}} , then y ^ 2 {\displaystyle {\hat {y}}_{2}} , and so on. It is found that if a model is trained purely by teacher forcing, its performance would degrade during prediction time, since generation based on the model's own output is different from generation based on the teacher's output. This is called exposure bias or a train/test distribution shift. A 2015 paper recommends that, during training, randomly switch between teacher forcing and no teacher forcing. === Attention for seq2seq === The attention mechanism is an enhancement introduced by Bahdanau et al. in 2014 to address limitations in the basic Seq2Seq architecture where a longer input sequence results in the hidden state output of the encoder becoming irrelevant for the decoder. It enables the model to selectively focus on different parts of the input sequence during the decoding process. At each decoder step, an alignment model calculates the attention score using the current decoder state and all of the attention hidden vectors as input. An alignment model is another neural network model that is trained jointly with the seq2seq model used to calculate how well an input, represented by the hidden state, matches with the previous output, represented by attention hidden state. A softmax function is then applied to the attention score to get the attention weight. In some models, the encoder states are directly fed into an activation function, removing the need for alignment model. An activation function receives one decoder state and one encoder state and returns a scalar value of their relevance. Consider the seq2seq language English-to-French translation task. To be concrete, let us consider the translation of "the zone of international control ", which should translate to "la zone de contrôle international ". Here, we use the special token as a control character to delimit the end of input for both the encoder and the decoder. An input sequence of text x 0 , x 1 , … {\displaystyle x_{0},x_{1},\dots } is processed by a neural network (which can be an LSTM, a Transformer encoder, or some other network) into a sequence of real-valued vectors h 0 , h 1 , … {\displaystyle h_{0},h_{1},\dots } , where h {\displaystyle h} stands for "hidden vector". After the encoder has finished processing, the decoder starts operating over the hidden vectors, to produce an output sequence y 0 , y 1 , … {\displaystyle y_{0},y_{1},\dots } , autoregressively. That is, it always takes as input both the hidden vectors produced by the encoder, and what the decoder itself has produced before, to produce the next output word: ( h 0 , h 1 , … {\displaystyle h_{0},h_{1},\dots } , "") → "la" ( h 0 , h 1 , … {\displaystyle h_{0},h_{1},\dots } , " la") → "la zone" ( h 0 , h 1 , … {\displaystyle h_{0},h_{1},\dots } , " la zone") → "la zone de" ... ( h 0 , h 1 , … {\displaystyle h_{0},h_{1},\dots } , " la zone de contrôle international") → "la zone de contrôle international " Here, we use the special token as a control character to delimit the start of input for the decoder. The decoding terminates as soon as "" appears in the decoder output. ==

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  • Kuaishou

    Kuaishou

    Kuaishou Technology is a Chinese publicly traded partly state-owned holding company based in Haidian District, Beijing, that was founded in 2011 by Hua Su (Chinese: 宿华) and Cheng Yixiao (Chinese: 程一笑). The company, listed on the Hong Kong Stock Exchange, is known for developing a mobile app for sharing users' short videos, a social network, and video special effects editor. The app is known as Kwai in many countries outside of China. It is also known as Snack Video in India, Pakistan and Indonesia. == Ownership and governance == Kuaishou's overseas team is led by the former CEO of the application 99, and staff from Google, Facebook, Netflix, and TikTok were recruited to lead the company's international expansion. The China Internet Investment Fund, a state-owned enterprise controlled by the Cyberspace Administration of China, holds a golden share ownership stake in Kuaishou. == History == Kuaishou is China's first short video platform that was developed in 2011 by engineer Hua Su and Cheng Yixiao. Prior to co-founding Kuaishou, Su Hua had worked for both Google and Baidu as a software engineer. The company is headquartered in Haidian District, Beijing. Kuaishou's predecessor "GIF Kuaishou" was founded in March 2011. GIF Kuaishou was a mobile app with which users could make and share GIF pictures. In 2013, Kuaishou became a short-video social platform. By 2013, the app had reached 100 million daily users. By 2019, it had exceeded 200 million active daily users. In March 2017, Kuaishou closed a US$350 million investment round that was led by Tencent. In January 2018, Forbes estimated the company's valuation to be US$18 billion. In April 2018, Kuaishou's app was briefly banned from Chinese app stores after China Central Television (CCTV) reported on the platform popularizing videos of teenage mothers. In 2019, the company announced a partnership with the People's Daily, an official newspaper of the Central Committee of the Chinese Communist Party, to help it experiment with the use of artificial intelligence in news. In June 2020, following the start of the 2020–2021 China–India skirmishes, the Government of India banned Kwai along with 58 other apps, citing "data and privacy issues". In January 2021, Kuaishou announced it was planning an initial public offering (IPO) to raise approximately US$5 billion. Kuaishou's stock completed its first day of trading at $300 Hong Kong dollars (HKD) (US$38.70), more than doubling its initial offer price, and causing its market value to rise to over $1 trillion HKD (US$159 billion). In February 2021, Kuaishou made a debut on the Hong Kong Stock Exchange, with its shares soaring by 194% at the opening. The company subsequently encountered major setbacks as a result of heightened regulatory restrictions on Chinese internet firms, which contributed to its share price falling by nearly 80% from its post-IPO peak. By December 2021, Kuaishou announced a major reorganization, including the layoff of 30% of its staff, primarily targeting mid-level employees earning an annual salary of $157,000 or more. This restructuring aimed to cut costs and mitigate financial losses. In October 2022, state-owned Beijing Radio and Television Station took a minority ownership stake in Kuaishou. In April 2024, a Financial Times article citing current and former Kuaishou employees stated that the company has been running an ageist redundancy programme known internally as "Limestone", culling workers in their mid-30s. In June 2024, Kuaishou and the Sichuan international communication center launched a branch center in São Paulo, Brazil. In June 2024, Kuaishou released its diffusion transformer text-to-video model, Kling, which they claimed could generate two minutes of video at 30 frames per second and in 1080p resolution. The model has been compared to that of OpenAI's Sora text-to-video model. It is accessible to the public on Kuaishou's video editing app KwaiCut via signing up for a waitlist with a Chinese phone number. In December 2025, Kuaishou came under a cyberattack which led to a temporary influx of violent and pornographic content. == Popularity == As of 2019, it had a worldwide user base of over 200 million, leading the "Most Downloaded" lists of the Google Play and Apple App Store in eight countries, such as Brazil, where it was introduced in 2019. Its main short-video platform competitor was Douyin, which is known as TikTok outside China. Compared to Douyin, Kuaishou is more popular with older users living outside China's Tier 1 cities. Its initial popularity came from videos of Chinese rural life. The app is particularly well known for its "rustic" aesthetic and is popular among rural people. Kuaishou also relied more on e-commerce revenue than on advertising revenue compared to its main competitor. == Reception == Kwai (as the app is called outside of China) was banned in India in 2020 along with other short video apps like TikTok. Kuaishou then released the clone SnackVideo, which was subsequently also banned. The app is one of the most popular social media platforms in Brazil, where Kuaishou partnered with creators to make telenovela style content, and appeals to football fans by working with football teams CR Flamengo and Santos FC and sponsoring the tournament Copa América. Kwai was notable in Brazil for spreading information (and misinformation) about the COVID-19 vaccine and political misinformation. === Manjiao Wenhua === "Manjiao wenhua" (慢脚文化) is a sarcasm term on Chinese internet on the unethical or illegal contents on Kuaishou. State broadcaster China Central Television (CCTV) reported that many contents are about child pregnancy. "Dating, pregnancy, bearing a child...these are strictly prohibited in the real time by a minor, but these contents can easily shown to audiences here." In addition, many students from primary or secondary schools make a pose of smoking. Wang Zhenhui (王贞会) from CUPSL stated that these kinds of bad values will give negative effects to the minors.

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  • Depth peeling

    Depth peeling

    In computer graphics, depth peeling is an exact multipass method of order-independent transparency that extracts transparent fragments into depth layers and composites those layers in depth order. Depth peeling has the advantage of being able to generate correct results even for complex images containing intersecting transparent objects. == Method == Depth peeling works by rendering the image multiple times. Depth peeling uses two Z buffers, one that works conventionally, and one that is not modified, and sets the minimum distance at which a fragment can be drawn without being discarded. For each pass, the previous pass' conventional Z-buffer is used as the minimal Z-buffer, so each pass removes already-captured nearer fragments and draws the next depth layer behind them. The resulting images can then be composited in depth order to form a single image. A major drawback of classical depth peeling is performance: it requires one geometry pass per peeled layer, so scenes with high depth complexity require many passes that each re-rasterize the transparent geometry. Later variants reduce the number of passes by peeling multiple layers or both front and back layers in a pass. Dual depth peeling reduces the geometry-pass count from N to N/2+1 by peeling one layer from the front and one from the back in each pass, while multi-layer depth peeling peels several layers per pass and reported up to an 8x speed-up in RGBA8 settings.

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  • Data event

    Data event

    A data event is a relevant state transition defined in an event schema. Typically, event schemata are described by pre- and post condition for a single or a set of data items. In contrast to ECA (Event condition action), which considers an event to be a signal, the data event not only refers to the change (signal), but describes specific state transitions, which are referred to in ECA as conditions. Considering data events as relevant data item state transitions allows defining complex event-reaction schemata for a database. Defining data event schemata for relational databases is limited to attribute and instance events. Object-oriented databases also support collection properties, which allows defining changes in collections as data events, too.

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  • Likewise, Inc.

    Likewise, Inc.

    Likewise, Inc., is an American technology startup company which provides a social networking service for finding and saving content recommendations for movies, TV shows, books, and podcasts. A team of ex-Microsoft employees founded Likewise in October 2017 with financial investment from Microsoft co-founder Bill Gates. The company is led by CEO Ian Morris and as of 2020 had a team of about 35 employees. Its headquarters operates in Bellevue, Washington. As of July 2020, 1 million users had joined the platform. == History == === Ideation (October 2017) === In 2017, former Microsoft Communications Chief Larry Cohen came up with the idea for Likewise in Bill Gates’ private office, Gates Ventures. Cohen currently serves as Gates Ventures’ CEO and managing partner. Cohen collaborated with colleagues Michael Dix and Ian Morris to co-found what would become Likewise, with Morris as its CEO. Gates funded the company's early development. The company developed its platform in stealth mode before launching publicly in October 2018. === Release (October 2018) === Likewise officially released its platform in the US and Canada on October 3, 2018. === Growth (2020 COVID-19 pandemic) === Likewise experienced accelerated growth alongside the COVID-19 pandemic. From March 2020 to July 2020, the platform's monthly active users tripled in numbers. The company reached one million users in July 2020. == Applications == === Mobile === Likewise is available as a mobile app for the Android and iOS mobile operating systems. Users receive recommendations from the Likewise algorithm, people they follow, and the Likewise editorial team. === Likewise TV === In October 2019, the company launched its Apple TV app called Likewise TV. The television app organizes shows across streaming services under one watchlist. On July 20, 2020, Likewise TV expanded to Android TV and Amazon Fire TV users.

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  • Hint (app)

    Hint (app)

    Hint (hint.app) is an American software platform that provides astrological content, personality assessments, and relationship compatibility tools. The application was launched in 2018 and is based in Claymont, Delaware. The platform has been described in media coverage as part of a broader trend of astrology-based and self-reflection applications, particularly among younger users. As of 2026, the company reports that it has reached more than 25 million users worldwide. == History == Hint was founded in 2018 and is headquartered in Claymont, Delaware. The platform was developed to address a growing demand among Millennials and Gen Z for structured self-reflection tools that deviate from traditional religious or clinical psychological frameworks. The app has become a prominent figure in the "emotional technology" sector, reaching over 25 million global users by 2026. The platform is frequently cited by sociologists and media outlets as a primary driver of the Open-source intelligence trend, where individuals use digital tools to vet and analyze personal relationships in the dating economy. Media coverage has described the platform as part of a broader trend in which digital tools incorporate astrology and symbolic frameworks into wellness and relationship advice. == Reception == Coverage of Hint has appeared alongside reporting on changing attitudes toward dating and relationships, particularly among younger adults. Surveys reported by media outlets have described shifts in dating behavior, including reduced interest in casual relationships and increased reliance on digital tools for emotional reflection and compatibility assessment. Additional reporting has linked the use of astrology apps to broader trends in emotional fatigue and changing relationship expectations. Lifestyle and culture publications have described Hint, as an example of applications that integrate astrology into digital self-reflection and relationship analysis.

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  • Comparison of operating systems

    Comparison of operating systems

    These tables provide a comparison of operating systems, of computer devices, as listing general and technical information for a number of widely used and currently available PC or handheld (including smartphone and tablet computer) operating systems. The article "Usage share of operating systems" provides a broader, and more general, comparison of operating systems that includes servers, mainframes and supercomputers. Because of the large number and variety of available Linux distributions, they are all grouped under a single entry; see comparison of Linux distributions for a detailed comparison. There is also a variety of BSD and DOS operating systems, covered in comparison of BSD operating systems and comparison of DOS operating systems. == Nomenclature == The nomenclature for operating systems varies among providers and sometimes within providers. For purposes of this article the terms used are; kernel In some operating systems, the OS is split into a low level region called the kernel and higher level code that relies on the kernel. Typically the kernel implements processes but its code does not run as part of a process. hybrid kernel monolithic kernel Nucleus In some operating systems there is OS code permanently present in a contiguous region of memory addressable by unprivileged code; in IBM systems this is typically referred to as the nucleus. The nucleus typically contains both code that requires special privileges and code that can run in an unprivileged state. Typically some code in the nucleus runs in the context of a dispatching unit, e.g., address space, process, task, thread, while other code runs independent of any dispatching unit. In contemporary operating systems unprivileged applications cannot alter the nucleus. License and pricing policies vary widely among different systems. Among others, the tables below use the following terms: BSD BSD licenses are a family of permissive free software licenses, imposing minimal restrictions on the use and distribution of covered software. bundled The fee is included in the price of the hardware == General information == == Technical information == == Security == == Commands == For POSIX compliant (or partly compliant) systems like FreeBSD, Linux, macOS or Solaris, the basic commands are the same because they are standardized. NOTE: Linux systems may vary by distribution which specific program, or even 'command' is called, via the POSIX alias function. For example, if you wanted to use the DOS dir to give you a directory listing with one detailed file listing per line you could use alias dir='ls -lahF' (e.g. in a session configuration file).

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  • Color clock

    Color clock

    The color clock, or color timer, is a part of the video circuitry of computer graphics hardware that works with analog color television systems. The clock is timed to match the timing of the color standard it works with, typically NTSC or PAL, ensuring that the data being read from the computer memory to create the image on-screen is in sync with the display. Depending on the speed of the color clock, the product of the resolution and number of colors is defined. Slow color clocks of many early games consoles and home computers resulted in limited color palettes at the highest resolutions.

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  • Tensor operator

    Tensor operator

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

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  • Screen space ambient occlusion

    Screen space ambient occlusion

    Screen space ambient occlusion (SSAO) is a computer graphics technique for efficiently approximating the ambient occlusion effect in real time. It was developed by Vladimir Kajalin while working at Crytek and was used for the first time in 2007 by the video game Crysis, also developed by Crytek. == Implementation == The algorithm is implemented as a pixel shader, analyzing the scene depth buffer which is stored in a texture. For every pixel on the screen, the pixel shader samples the depth values around the current pixel and tries to compute the amount of occlusion from each of the sampled points. In its simplest implementation, the occlusion factor depends only on the depth difference between sampled point and current point. Without additional smart solutions, such a brute force method would require about 200 texture reads per pixel for good visual quality. This is not acceptable for real-time rendering on current graphics hardware. In order to get high quality results with far fewer reads, sampling is performed using a randomly rotated kernel. The kernel orientation is repeated every N screen pixels in order to have only high-frequency noise in the final picture. In the end this high frequency noise is greatly removed by a NxN post-process blurring step taking into account depth discontinuities (using methods such as comparing adjacent normals and depths). Such a solution allows a reduction in the number of depth samples per pixel to about 16 or fewer while maintaining a high quality result, and allows the use of SSAO in soft real-time applications like computer games. Compared to other ambient occlusion solutions, SSAO has the following advantages: Independent from scene complexity. No data pre-processing needed, no loading time and no memory allocations in system memory. Works with dynamic scenes. Works in the same consistent way for every pixel on the screen. No CPU usage – it can be executed completely on the GPU. May be easily integrated into any modern graphics pipeline. SSAO also has the following disadvantages: Rather local and in many cases view-dependent, as it is dependent on adjacent texel depths which may be generated by any geometry whatsoever. Hard to correctly smooth/blur out the noise without interfering with depth discontinuities, such as object edges (the occlusion should not "bleed" onto objects). Because SSAO operates only on the current depth buffer, it can miss occluding geometry that is not rasterized into the z-buffer and may produce undersampling-related artifacts.

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  • Spotify Live

    Spotify Live

    Spotify Live, formerly Spotify Greenroom, was a social audio app by Spotify, that allowed users to host or participate in live-audio virtual environments called "room" for conversations. Each room had a maximum capacity of 1000 people. The app was available on Android and iOS, competing with Twitter Spaces and Clubhouse in the social media segment. It was shut down on April 30, 2023. == History == In October 2020, Betty Labs released Locker Room exclusively on the iOS App Store. The app featured virtual audio chat rooms for sports enthusiasts. In late March 2021, Spotify acquired Betty Labs for $50 million and announced plans to rebrand the app with a broader focus on sports, music, and pop culture. On June 16, 2021, Spotify launched the app as Spotify Greenroom on Android (early access) and iOS, expanding its scope beyond just sports. At launch, Spotify introduced the Greenroom Creator Fund to support creators and shows, serving as a rival to Clubhouse's Creator First Accelerator Program. The fund aimed to provide a monetization path for podcasters integrating Greenroom into their verified Spotify accounts. By July 2021, the app had accumulated over 140,000 iOS installs and 100,000 Android installs. In August 2021, Spotify collaborated with the WWE to produce professional wrestling-related podcasts, many of which would be recorded by The Ringer, Spotify's in-house podcasting team, using Greenroom. In March 2022, Spotify Greenroom announced its rebranding as Spotify Live and its migration to the main Spotify app. After a year, Spotify announced it would shut down the Spotify Live app at the end of April 2023. == Features == Greenroom allowed users to create or join a room, which, in the context of the application, was a virtual space for real-time voice chats. Users could only create a room within a pre-defined group, representing either a brand or a generic category. If a user chose to create a room, they became the host, with the ability to invite people, control who could talk, and enable features like recording and the Discussions tab during room creation. Enabling recording displayed a disclaimer informing users that the conversation was being recorded, and the audio, recorded in mp4 format, would be sent to the host via email after the room concluded. If the Discussions tab was enabled, users could send text messages in the public chat section. The host also had the authority to ban users if necessary. When joining a room, a user could opt to be a listener or request to become a speaker. Users had the freedom to follow or block others and join groups at their discretion. Notifications about new rooms in joined groups would be sent to users. Additionally, users could discover new individuals and groups using the search tab. == Partnered creators == By October 2021, Spotify had a variety of partnered creators aimed at boosting traffic and validating its vertically integrated podcast model. These creators primarily focused on Generation Z. In-house Spotify talent, such as The Ringer, produced sports-related content. Simultaneously, the company recruited creators from various social channels to grow Greenroom's audience while also promoting its integration with Spotify and Anchor. Each verified Spotify partner had their Greenroom shows featured in both the Greenroom app and their profiles on the Spotify app. This was part of the company's strategy leading into the 2022 ramp-up to compete with Clubhouse. == Platforms == The app was accessible on both Android and iOS platforms, and users could download the app from their respective app stores. Android users needed Android 8 or above to launch the app, while iOS consumers required iOS 13 or later to run it.

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  • Visible (mobile app)

    Visible (mobile app)

    Visible is a health tracking mobile app for people with long COVID and myalgic encephalomyelitis/chronic fatigue syndrome (ME/CFS). The company was founded by a Harry Leeming, an engineer from London living with long Covid since 2020, and Luke Martin-Fuller. In November 2022, Visible released an open beta of an app that aims to help people pace their activities to avoid post-exertional malaise. The app gathers data on exertion levels, symptom severity, and heart-rate variability. HRV is approximated using a smartphone's camera via a technique called photoplethysmography, and according to the app's developers, can indicate how much someone needs rest. The app is currently free, but is expected to be freemium in the future. Users can also opt to allow their data be used for research purposes. In July 2023, Visible and Imperial College London announced the start of the first two studies. One is on the effects of the menstrual cycle on long COVID symptoms, and the other is on the condition's epidemiology and economic impact. Visible has announced plans to couple the app with activity trackers for continuous monitoring of heart-rate and actimetry data, which the developers claim will be more effective. As of 2022, no clinical trials on Visible's effectiveness have been conducted.

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  • GoodRx

    GoodRx

    GoodRx Holdings, Inc. is an American healthcare company that operates a telemedicine platform and free-to-use website and mobile app that track prescription drug prices in the United States and provide drug coupons for discounts on medications. GoodRx compares prescription drug prices at more than 75,000 pharmacies in the United States. The platform allows users to consult a doctor online and obtain a prescription for certain types of medications. == History == === Financial performance === GoodRx was founded in Santa Monica, California in 2011. GoodRx experienced substantial growth in net income in 2017 ($9 million), 2018 ($44 million), and 2019 ($66 million), but recorded a loss of $293.6 million in 2020 due to IPO-related expenses. In September 2020, GoodRx went public on the Nasdaq under the ticker symbol GDRX. The company priced its initial public offering at $33 per share, above the expected range of $24 to $28, raising more than $1.1 billion at an initial valuation of approximately $12.7 billion. In the first half of 2020, the company reported revenues of $257 million and net income of $55 million. GoodRx generated $745.4 million in revenue for the full year 2021, a 35.36% increase over 2020. During the first half of 2021, the company’s share price declined by 10.7%. The decline was attributed to increased competition in online pharmacy services and slower user growth. GoodRx reported full-year revenue of $766.6 million, with adjusted EBITDA reaching $213.5 million, exceeding guidance in the fourth quarter. GoodRx reported that 41% of prescriptions filled using its coupons were newly adherent, meaning they would not have been filled without the service. GoodRx reported a full-year 2023 revenue of $750.3 million, a decrease of 2.1% from 2022. However, its fourth-quarter revenue increased by 7% year-over-year. GoodRx achieved an Adjusted EBITDA of $217.4 million for the year and an Adjusted EBITDA Margin of 28.6%. In 2024, GoodRx achieved 6% revenue growth with $792.3 million for the full year and turned a net loss into a positive net income of $16.4 million. The company also demonstrated strong operational efficiency, with a 32.8% increase in full-year Adjusted EBITDA. In Q2 2025, GoodRx reported revenue of $203.1 million, a 1.2% increase from the previous year, and a net income of $12.8 million, a significant 92% jump, which resulted in a 6.3% net income margin. However, prescription transaction revenue declined by 3% due to a decrease in monthly active consumers, but this was offset by strong 32% growth in its Pharma Manufacturer Solutions business. GoodRx also saw a 7% decrease in subscription revenue. === Mergers and acquisitions === In 2019, GoodRx acquired HeyDoctor, a telemedicine company, to integrate virtual healthcare services into the platform. In 2021, a health video content producer, HealthiNation was acquired by GoodRx, which helped provide consumers with health information and offered pharmaceutical manufacturers new ways to reach relevant audiences. In April 2022, GoodRx acquired VitaCare Prescription Services from TherapeuticsMD to strengthen its pharma manufacturer solutions business. === Partnerships === In 2017, the company announced partnerships with major pharmaceutical companies to negotiate lower prescription drug costs. GoodRx has deep relationships with major pharmacy chains, including Walgreens, Walmart, CVS Caremark, and Publix, to allow customers to use GoodRx discounts and Gold benefits. GoodRx began its partnership with CVS Caremark in July 2023 to automatically apply coupons to insured CVS customers purchasing generic prescriptions at certain locations. In April 2024, GoodRx added Publix into its network, allowing GoodRx Gold members to use their cards at Publix Pharmacies. GoodRx partners with Pharmacy Benefit Management like Caremark, Express Scripts, and MedImpact to apply their savings directly to eligible insurance plans and members. GoodRx partners with companies like Affirm, Benefitfocus, and DoorDash to integrate their services that offer members discounts and financial flexibility for prescriptions. GoodRx also partners with organizations like the American Academy of Family Physicians Foundation to support broader access to care. In October 2022, GoodRx launched Provider Mode, which allows healthcare providers to use the app to compare costs of drugs for patients based on different payment methods and drug alternatives. In 2025, GoodRx partnered with Novo Nordisk to offer discounted cash-pay access to semaglutide products like Ozempic and Wegovy through its platform and participating pharmacies. == Products and services == GoodRx started its telemedicine service GoodRx Care in September 2019. It lets people talk to a licensed provider online for common issues and get prescriptions even if they don't have insurance. They also run condition-specific subscription plans that bundle online doctor visits, FDA-approved meds, and home delivery into one monthly payment. On the weight management side, GoodRx offers prescriptions for GLP-1 drugs like semaglutide through their telemedicine platform. This got a boost when the oral version of Wegovy became widely available in the US in early 2026. GoodRx works with drug makers like Novo Nordisk to make some medications (including semaglutide options) more affordable for people paying cash. The telemedicine part took off after GoodRx bought HeyDoctor in 2019 and brought their virtual care tools into the main platform. == Key people == The Santa Monica-based startup was founded in September 2011 by Trevor Bezdek and former Facebook executives Doug Hirsch and Scott Marlette. Marlette was one of the first 20 employees at Facebook and built Facebook's photo application. In 2005, Hirsch was the Vice President of Product at Facebook, working closely with Mark Zuckerberg. Bezdek and Hirsch served as co-chief executive officers until April 2023, when they stepped down from those roles and technology executive Scott Wagner was appointed interim chief executive officer. Bezdek became chair of the board, while Hirsch took on the role of chief mission officer. In December 2024, GoodRx announced that healthcare executive Wendy Barnes would become president and chief executive officer effective January 1, 2025. As of 2025, Barnes serves as the company’s CEO, while Trevor Bezdek and Scott Wagner serve as co-chairs of the board, and Doug Hirsch remains involved as a co-founder and senior executive. == Controversy == On February 25, 2020, Consumer Reports published an article stating that GoodRx shared user data—specifically, pseudonymized advertising ID numbers that companies use to track the behavior of web users across websites, the names of the drugs that users browsed, and the pharmacies where users sought to fill prescriptions—with Google, Facebook, and around twenty other Internet-based companies. A few days later, GoodRx released a statement saying that it had made changes to prevent user search data on medical conditions and pharmaceuticals from being shared with Facebook. In March 2020, GoodRx stopped sending data about user prescriptions to Facebook. On February 1, 2023, the Federal Trade Commission fined GoodRx US$1.5 million for violations of the Breach Notification Rule and the Federal Trade Commission Act for allegedly failing to obtain specific, informed, and unambiguous consent from users before disclosing health-related information to Facebook and Google. In November 2024, independent pharmacies filed at least three class action lawsuits against GoodRx and major pharmacy benefit managers. The cases, brought by independent pharmacies in California, Michigan, Pennsylvania, and Rhode Island, allege that GoodRx and the PBMs collaborated to suppress reimbursements for generic prescription drugs. They allege that agreements using GoodRx’s software suppressed reimbursements for generic drugs and violated the Sherman Antitrust Act. The suits claim the practices amount to price fixing which harms small pharmacies while benefiting PBMs and their affiliates. GoodRx settled both the 2023 FTC action and the 2025 class action lawsuit without admitting wrongdoing.

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  • Spotify Live

    Spotify Live

    Spotify Live, formerly Spotify Greenroom, was a social audio app by Spotify, that allowed users to host or participate in live-audio virtual environments called "room" for conversations. Each room had a maximum capacity of 1000 people. The app was available on Android and iOS, competing with Twitter Spaces and Clubhouse in the social media segment. It was shut down on April 30, 2023. == History == In October 2020, Betty Labs released Locker Room exclusively on the iOS App Store. The app featured virtual audio chat rooms for sports enthusiasts. In late March 2021, Spotify acquired Betty Labs for $50 million and announced plans to rebrand the app with a broader focus on sports, music, and pop culture. On June 16, 2021, Spotify launched the app as Spotify Greenroom on Android (early access) and iOS, expanding its scope beyond just sports. At launch, Spotify introduced the Greenroom Creator Fund to support creators and shows, serving as a rival to Clubhouse's Creator First Accelerator Program. The fund aimed to provide a monetization path for podcasters integrating Greenroom into their verified Spotify accounts. By July 2021, the app had accumulated over 140,000 iOS installs and 100,000 Android installs. In August 2021, Spotify collaborated with the WWE to produce professional wrestling-related podcasts, many of which would be recorded by The Ringer, Spotify's in-house podcasting team, using Greenroom. In March 2022, Spotify Greenroom announced its rebranding as Spotify Live and its migration to the main Spotify app. After a year, Spotify announced it would shut down the Spotify Live app at the end of April 2023. == Features == Greenroom allowed users to create or join a room, which, in the context of the application, was a virtual space for real-time voice chats. Users could only create a room within a pre-defined group, representing either a brand or a generic category. If a user chose to create a room, they became the host, with the ability to invite people, control who could talk, and enable features like recording and the Discussions tab during room creation. Enabling recording displayed a disclaimer informing users that the conversation was being recorded, and the audio, recorded in mp4 format, would be sent to the host via email after the room concluded. If the Discussions tab was enabled, users could send text messages in the public chat section. The host also had the authority to ban users if necessary. When joining a room, a user could opt to be a listener or request to become a speaker. Users had the freedom to follow or block others and join groups at their discretion. Notifications about new rooms in joined groups would be sent to users. Additionally, users could discover new individuals and groups using the search tab. == Partnered creators == By October 2021, Spotify had a variety of partnered creators aimed at boosting traffic and validating its vertically integrated podcast model. These creators primarily focused on Generation Z. In-house Spotify talent, such as The Ringer, produced sports-related content. Simultaneously, the company recruited creators from various social channels to grow Greenroom's audience while also promoting its integration with Spotify and Anchor. Each verified Spotify partner had their Greenroom shows featured in both the Greenroom app and their profiles on the Spotify app. This was part of the company's strategy leading into the 2022 ramp-up to compete with Clubhouse. == Platforms == The app was accessible on both Android and iOS platforms, and users could download the app from their respective app stores. Android users needed Android 8 or above to launch the app, while iOS consumers required iOS 13 or later to run it.

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  • EPUAP

    EPUAP

    ePUAP (Electronic Platform of Public Administration Services) is a Polish nationwide platform for communication of citizens with public administrations in a uniform and standardized way. Built as part of the ePUAP-WKP project (State Informatization Plan). Service providers are public administration units and public institutions (especially entities that perform tasks commissioned by the state). The platform provides service providers with technological infrastructure to provide services to citizens (recipients). Among the participants of ePUAP there are both central administration units and local governments, including municipal offices. Among the services offered by ePUAP is also Profil Zaufany (Trusted Profile), which enables electronic filing with legal effect without the need to use a qualified signature and SAML-based single sign-on mechanism, which enables the same ePUAP account to log on to websites of various service providers. The website www.epuap.gov.pl enables defining citizen and businesses service processes, creates channels of access to different systems of public administration and extends the package of public services provided electronically. Services available through the ePUAP platform may be accessed at the official website. Currently all administration services are available in Polish only. == Overview == It is described by the Polish government as "a coherent and systematic action program designed and developed to allow public institutions make their electronic services available to the public". The platform provides citizens, businesses and institutions with a number of services intended to ensure smooth and safe communication between: customer to administrations (C2A), business to administration (B2A), administration to administration (A2A). === Main goals === The main project objectives are to create a single, secure and electronic access channel to public services for citizens, businesses and public administration and also to reduce time and lower the costs of sharing information resources and functionalities of administration domain systems. Within the project, the following functionalities and services were delivered: Public services catalogue – a method of presenting and describing administration services, ePUAP platform – a web platform designed to provide public services on the Internet, Interoperability portal – a portal for experts working on recommendations for electronic documents and forms used within Polish administration systems to assure the uniformity of IT standards, Central Repository of Electronic Document Models – a database for valid document models and electronic forms. == History and background == The ePUAP project was carried out in the years 2005–2008. Currently, a continuation project ePUAP2 is being carried out with the following objectives: to increase the number of online services available to the public including the registry services, to widen the scale of usage of public electronic services, to integrate subsequent systems of public administration and business on ePUAP portal, to define new processes of customer and business services. === ePUAP2 === ePUAP2 is a public and administrative project that extends the set of functional services developed during the first edition of the project and is another step in the process of transforming Poland into a modern and citizen-friendly country. The implementation period for the project covers the years 2009–2013. Project financing The cost of the project “Construction of electronic Platform of Public Administration Services” – 32 million PLN was covered in 75% by the funds from the European Regional Development Fund (under the Sector Operational Programme "Supporting Competitiveness of Enterprises for the years 2004–2006"), while the remaining 25% of the cost was covered by a Polish national co-financing. Funds for the ePUAP2 project were gained from the 7th priority axis of the Innovative Economy Operational Programme and amounts to 140 million PLN (85% of eligible expenses were covered by the European Regional Development Fund, 15% were covered by a national co-financing). The trustee of ePUAP is the Polish Ministry of the Interior and Administration. == Legal regulations == According to the Polish law from 1 May 2008, public authorities are required to accept documents in electronic form (bringing applications and proposals and other activities in electronic form). ePUAP enables public institutions to meet this requirement by providing a service infrastructure to set up am electronic inbox. The ePUAP inbox meets legal requirements, in particular: issuing an official confirmation of receipt in accordance with the regulation of the Prime Minister of 29 September 2005 on the organizational and technical conditions for the delivery of electronic documents to public entities; cooperation with hardware security modules (HSM), meeting the technical requirements set out in the law; handling documents electronically in accordance with the minimum requirements set out in the Regulation of the Polish Council of Ministers of 11 October 2005 on minimum requirements for ICT systems. == Incidents == === Crashes === The ePUAP system very often happens smaller or larger failures. Because it is used to sign the application profiles trusted also in other electronic systems such as public administration. Electronic Services Platform created by ZUS, the system fault ePUAP it very difficult to settle official matters most electronically. === "Infoafera" === According to TVN and the release of TVP News from 10 April 2014, the creation of ePUAP is also associated with the so-called "Infoafera." On 10 April 2014, the Minister of Internal Affairs of Poland confirmed the information that the American technology company HP confessed to its participation in the Polish info-tour and corruption of Polish officials. By March 2014, the construction of ePUAP and its maintenance cost PLN 98.4 million. PLN 67.8 million has been used for this project. Challenged expenses only on the portal itself is approx. PLN 20 million.

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