AI Assistant Job Description

AI Assistant Job Description — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  AI Security Institute

  The AI Security Institute (AISI) is a research organisation under the Department for Science, Innovation and Technology, UK, that aims "to equip governments with a scientific understanding of the risks posed by advanced AI". It conducts research and develop and test mitigations. Previously, it was known as the AI Safety Institute. Its creation followed world's first major AI Safety Summit that was held in Bletchley Park in 2023. The institute's professed goal is "building the world's leading understanding of advanced AI risks and solutions, to inform governments so they can keep the public safe". It is designed like a startup in the government "combining the authority of government with the expertise and agility of the private sector". AISI has made access agreements with Anthropic, Google and OpenAI to test their models before release. It has an open source platform called Inspect that permits companies, governments and academics to run standardised safety tests for AI usage. Among the works AISI has done is the reported detection of multiple serious vulnerabilities that could enable development of biological weapons; the vulnerabilities were fixed before the model was launched. It conducts research on diverse fields of AI application. One study by AISI found that LLMs post-trained for political persuasiveness became systematically less accurate and up to 51% more persuasive on political issues. AISI has also worked on the usage of AI for emotional needs. It found that nearly 10 percent of UK citizens used systems like chatbots for emotional purposes on a weekly basis. It found that "systems are now outperforming PhD-level researchers on scientific knowledge tests and helping non-experts succeed at lab work that would previously have been out of reach" in a report published in December 2025. Former chief AI officer of GCHQ Adam Beaumont is the institution's interim director. UK prime minister's AI advisor Jade Leung is the chief technology officer.

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  DUAL table

  The DUAL table is a special one-row, one-column table present by default in Oracle and other database installations. In Oracle, the table has a single VARCHAR2(1) column called DUMMY that has a value of 'X'. It is suitable for use in selecting a pseudo column such as SYSDATE or USER. == Example use == Oracle's SQL syntax requires the FROM clause but some queries don't require any tables - DUAL can be used in these cases. == History == Charles Weiss explains why he created DUAL: I created the DUAL table as an underlying object in the Oracle Data Dictionary. It was never meant to be seen itself, but instead used inside a view that was expected to be queried. The idea was that you could do a JOIN to the DUAL table and create two rows in the result for every one row in your table. Then, by using GROUP BY, the resulting join could be summarized to show the amount of storage for the DATA extent and for the INDEX extent(s). The name, DUAL, seemed apt for the process of creating a pair of rows from just one. == Optimization == Beginning with 10g Release 1, Oracle no longer performs physical or logical I/O on the DUAL table, though the table still exists. DUAL is readily available for all authorized users in a SQL database. == In other database systems == Several other databases (including Microsoft SQL Server, MySQL, PostgreSQL, SQLite, and Teradata) enable one to omit the FROM clause entirely if no table is needed. This avoids the need for any dummy table. ClickHouse has a one-row system table system.one with a single column named "dummy" of type UInt8 and value 0. This table is implicitly used when no table is specified in the SELECT query. Firebird has a one-row system table RDB$DATABASE that is used in the same way as Oracle's DUAL, although it also has a meaning of its own. IBM Db2 has a view that resolves DUAL when using Oracle Compatibility. It also has a table called sysibm.sysdummy1 that has similar properties to the Oracle DUAL one. Informix: Informix version 11.50 and later has a table named sysmaster:"informix".sysdual with the same functionality but a more verbose name. You can use CREATE PUBLIC SYNONYM dual FOR sysmaster:"informix".sysdual to create a name dual in the current database with the same functionality. Microsoft Access: A table named DUAL may be created and the single-row constraint enforced via ADO (Table-less UNION query in MS Access) Microsoft SQL Server: SQL Server does not require a dummy table. Queries like 'select 1 + 1' can be run without a "from" clause/table name. MySQL allows DUAL to be specified as a table in queries that do not need data from any tables. It is suitable for use in selecting a result function such as SYSDATE() or USER(), although it is not essential. PostgreSQL: A DUAL-view can be added to ease porting from Oracle. Snowflake: DUAL is supported, but not explicitly documented. It appears in sample SQL for other operations in the documentation. SQLite: A VIEW named "dual" that works the same as the Oracle "dual" table can be created as follows: CREATE VIEW dual AS SELECT 'x' AS dummy; SAP HANA has a table called DUMMY that works the same as the Oracle "dual" table. Teradata database does not require a dummy table. Queries like 'select 1 + 1' can be run without a "from" clause/table name. Vertica has support for a DUAL table in their official documentation.

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  Reflection lines

  Engineers use reflection lines to judge a surface's quality. Reflection lines reveal surface flaws, particularly discontinuities in normals indicating that the surface is not C 2 {\displaystyle C^{2}} . Reflection lines may be created and examined on physical surfaces or virtual surfaces with the help of computer graphics. For example, the shiny surface of an automobile body is illuminated with reflection lines by surrounding the car with parallel light sources. Virtually, a surface can be rendered with reflection lines by modulating the surfaces point-wise color according to a simple calculation involving the surface normal, viewing direction and a square wave environment map. == Mathematical definition == Consider a point p {\displaystyle p} on a surface M {\displaystyle M} with (normalized) normal n {\displaystyle n} . If an observer views this point from infinity at view direction v {\displaystyle v} then the reflected view direction r {\displaystyle r} is: r = v − 2 ( n ⋅ v ) n . {\displaystyle r=v-2(n\cdot v)n.} (The vector v {\displaystyle v} is decomposed into its normal part v n = ( n ⋅ v ) v {\displaystyle v_{n}=(n\cdot v)v} and tangential part v t = v − v n {\displaystyle v_{t}=v-v_{n}} . Upon reflection, the tangential part is kept and the normal part is negated.) For reflection lines we consider the surface M {\displaystyle M} surrounded by parallel lines with direction a {\displaystyle a} , representing infinite, non-dispersive light sources. For each point p {\displaystyle p} on M {\displaystyle M} we determine which line is seen from direction v {\displaystyle v} . The position on each line is of no interest. Define the vector r p {\displaystyle r_{p}} to be the reflection direction r {\displaystyle r} projected onto a plane P {\displaystyle P} that is orthogonal to a {\displaystyle a} : r p = r − ( r ⋅ a ) a {\displaystyle r_{p}=r-(r\cdot a)a} and similarly let v p {\displaystyle v_{p}} be the viewing direction projected onto P {\displaystyle P} : v p = v − ( v ⋅ a ) a {\displaystyle v_{p}=v-(v\cdot a)a} Finally, define v o {\displaystyle v_{o}} to be the direction lying in P {\displaystyle P} perpendicular to a {\displaystyle a} and v p {\displaystyle v_{p}} : v o = a × v p {\displaystyle v_{o}=a\times v_{p}} Using these vectors, the reflection line function θ ( p ) : M → ( − π , π ] {\displaystyle \theta (p):M\rightarrow (-\pi ,\pi ]} is a scalar function mapping points p {\displaystyle p} on the surface to angles between v p {\displaystyle v_{p}} and r p {\displaystyle r_{p}} : θ = arctan ⁡ ( r p ⋅ v o , r p ⋅ v p ) {\displaystyle \theta =\arctan {(r_{p}\cdot v_{o},r_{p}\cdot v_{p})}} where a r c t a n ( y , x ) {\displaystyle arctan(y,x)} is the atan2 function producing a number in the range ( − π , π ] {\displaystyle (-\pi ,\pi ]} . ( v p {\displaystyle v_{p}} and v o {\displaystyle v_{o}} can be viewed as a local coordinate system in P {\displaystyle P} with x {\displaystyle x} -axis in direction v p {\displaystyle v_{p}} and y {\displaystyle y} -axis in direction v o {\displaystyle v_{o}} .) Finally, to render the reflection lines positive values θ > 0 {\displaystyle \theta >0} are mapped to a light color and non-positive values to a dark color. == Highlight lines == Highlight lines are a view-independent alternative to reflection lines. Here the projected normal is directly compared against some arbitrary vector x {\displaystyle x} perpendicular to the light source: θ = arctan ⁡ ( n a ⋅ a ⊥ , n a ⋅ x ) {\displaystyle \theta =\arctan {(n_{a}\cdot a^{\perp },n_{a}\cdot x)}} where n a {\displaystyle n_{a}} is the surface normal projected on the light source plane P {\displaystyle P} : n a ^ / | n a ^ | , n a ^ = n − ( n ⋅ a ) a {\displaystyle {\hat {n_{a}}}/|{\hat {n_{a}}}|,{\hat {n_{a}}}=n-(n\cdot a)a} The relationship between reflection lines and highlight lines is likened to that between specular and diffuse shading.

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  Universal IR Evaluation

  In computer science, Universal IR Evaluation (information retrieval evaluation) aims to develop measures of database retrieval performance that shall be comparable across all information retrieval tasks. == Measures of "relevance" == IR (information retrieval) evaluation begins whenever a user submits a query (search term) to a database. If the user is able to determine the relevance of each document in the database (relevant or not relevant), then for each query, the complete set of documents is naturally divided into four distinct (mutually exclusive) subsets: relevant documents that are retrieved, not relevant documents that are retrieved, relevant documents that are not retrieved, and not relevant documents that are not retrieved. These four subsets (of documents) are denoted by the letters a, b, c, d respectively and are called Swets variables, named after their inventor. In addition to the Swets definitions, four relevance metrics have also been defined: Recall refers to the fraction of relevant documents that are retrieved (a/(a+b)), and Precision refers to the fraction of retrieved documents that are relevant (a/(a+c)). These are the most commonly used and well-known relevance metrics found in the IR evaluation literature. Two less commonly used metrics include the Fallout, i.e., the fraction of not relevant documents that are retrieved (b/(b+d)), and the Miss, which refers to the fraction of relevant documents that are not retrieved (c/(c+d)) during any given search. == Universal IR evaluation techniques == Universal IR evaluation addresses the mathematical possibilities and relationships among the four relevance metrics Precision, Recall, Fallout and Miss, denoted by P, R, F and M, respectively. One aspect of the problem involves finding a mathematical derivation of a complete set of universal IR evaluation points. The complete set of 16 points, each one a quadruple of the form (P, R, F, M), describes all the possible universal IR outcomes. For example, many of us have had the experience of querying a database and not retrieving any documents at all. In this case, the Precision would take on the undetermined form 0/0, the Recall and Fallout would both be zero, and the Miss would be any value greater than zero and less than one (assuming a mix of relevant and not relevant documents were in the database, none of which were retrieved). This universal IR evaluation point would thus be denoted by (0/0, 0, 0, M), which represents only one of the 16 possible universal IR outcomes. The mathematics of universal IR evaluation is a fairly new subject since the relevance metrics P, R, F, M were not analyzed collectively until recently (within the past decade). A lot of the theoretical groundwork has already been formulated, but new insights in this area await discovery.

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  Audio inpainting

  Audio inpainting (also known as audio interpolation) is an audio restoration task which deals with the reconstruction of missing or corrupted portions of a digital audio signal. Inpainting techniques are employed when parts of the audio have been lost due to various factors such as transmission errors, data corruption or errors during recording. The goal of audio inpainting is to fill in the gaps (i.e., the missing portions) in the audio signal seamlessly, making the reconstructed portions indistinguishable from the original content and avoiding the introduction of audible distortions or alterations. Many techniques have been proposed to solve the audio inpainting problem and this is usually achieved by analyzing the temporal and spectral information surrounding each missing portion of the considered audio signal. Classic methods employ statistical models or digital signal processing algorithms to predict and synthesize the missing or damaged sections. Recent solutions, instead, take advantage of deep learning models, thanks to the growing trend of exploiting data-driven methods in the context of audio restoration. Depending on the extent of the lost information, the inpainting task can be divided in three categories. Short inpainting refers to the reconstruction of few milliseconds (approximately less than 10) of missing signal, that occurs in the case of short distortions such as clicks or clipping. In this case, the goal of the reconstruction is to recover the lost information exactly. In long inpainting instead, with gaps in the order of hundreds of milliseconds or even seconds, this goal becomes unrealistic, since restoration techniques cannot rely on local information. Therefore, besides providing a coherent reconstruction, the algorithms need to generate new information that has to be semantically compatible with the surrounding context (i.e., the audio signal surrounding the gaps). The case of medium duration gaps lays between short and long inpainting. It refers to the reconstruction of tens of millisecond of missing data, a scale where the non-stationary characteristic of audio already becomes important. == Definition == Consider a digital audio signal x {\displaystyle \mathbf {x} } . A corrupted version of x {\displaystyle \mathbf {x} } , which is the audio signal presenting missing gaps to be reconstructed, can be defined as x ~ = m ∘ x {\displaystyle \mathbf {\tilde {x}} =\mathbf {m} \circ \mathbf {x} } , where m {\displaystyle \mathbf {m} } is a binary mask encoding the reliable or missing samples of x {\displaystyle \mathbf {x} } , and ∘ {\displaystyle \circ } represents the element-wise product. Audio inpainting aims at finding x ^ {\displaystyle \mathbf {\hat {x}} } (i.e., the reconstruction), which is an estimation of x {\displaystyle \mathbf {x} } . This is an ill-posed inverse problem, which is characterized by a non-unique set of solutions. For this reason, similarly to the formulation used for the inpainting problem in other domains, the reconstructed audio signal can be found through an optimization problem that is formally expressed as x ^ ∗ = argmin X ^ L ( m ∘ x ^ , x ~ ) + R ( x ^ ) {\displaystyle \mathbf {\hat {x}} ^{}={\underset {\hat {\mathbf {X} }}{\text{argmin}}}~L(\mathbf {m} \circ \mathbf {\hat {x}} ,\mathbf {\tilde {x}} )+R(\mathbf {\hat {x}} )} . In particular, x ^ ∗ {\displaystyle \mathbf {\hat {x}} ^{}} is the optimal reconstructed audio signal and L {\displaystyle L} is a distance measure term that computes the reconstruction accuracy between the corrupted audio signal and the estimated one. For example, this term can be expressed with a mean squared error or similar metrics. Since L {\displaystyle L} is computed only on the reliable frames, there are many solutions that can minimize L ( m ∘ x ^ , x ~ ) {\displaystyle L(\mathbf {m} \circ \mathbf {\hat {x}} ,\mathbf {\tilde {x}} )} . It is thus necessary to add a constraint to the minimization, in order to restrict the results only to the valid solutions. This is expressed through the regularization term R {\displaystyle R} that is computed on the reconstructed audio signal x ^ {\displaystyle \mathbf {\hat {x}} } . This term encodes some kind of a-priori information on the audio data. For example, R {\displaystyle R} can express assumptions on the stationarity of the signal, on the sparsity of its representation or can be learned from data. == Techniques == There exist various techniques to perform audio inpainting. These can vary significantly, influenced by factors such as the specific application requirements, the length of the gaps and the available data. In the literature, these techniques are broadly divided in model-based techniques (sometimes also referred as signal processing techniques) and data-driven techniques. === Model-based techniques === Model-based techniques involve the exploitation of mathematical models or assumptions about the underlying structure of the audio signal. These models can be based on prior knowledge of the audio content or statistical properties observed in the data. By leveraging these models, missing or corrupted portions of the audio signal can be inferred or estimated. An example of a model-based techniques are autoregressive models. These methods interpolate or extrapolate the missing samples based on the neighboring values, by using mathematical functions to approximate the missing data. In particular, in autoregressive models the missing samples are completed through linear prediction. The autoregressive coefficients necessary for this prediction are learned from the surrounding audio data, specifically from the data adjacent to each gap. Some more recent techniques approach audio inpainting by representing audio signals as sparse linear combinations of a limited number of basis functions (as for example in the Short Time Fourier Transform). In this context, the aim is to find the sparse representation of the missing section of the signal that most accurately matches the surrounding, unaffected signal. The aforementioned methods exhibit optimal performance when applied to filling in relatively short gaps, lasting only a few tens of milliseconds, and thus they can be included in the context of short inpainting. However, these signal-processing techniques tend to struggle when dealing with longer gaps. The reason behind this limitation lies in the violation of the stationarity condition, as the signal often undergoes significant changes after the gap, making it substantially different from the signal preceding the gap. As a way to overcome these limitations, some approaches add strong assumptions also about the fundamental structure of the gap itself, exploiting sinusoidal modeling or similarity graphs to perform inpainting of longer missing portions of audio signals. === Data-driven techniques === Data-driven techniques rely on the analysis and exploitation of the available audio data. These techniques often employ deep learning algorithms that learn patterns and relationships directly from the provided data. They involve training models on large datasets of audio examples, allowing them to capture the statistical regularities present in the audio signals. Once trained, these models can be used to generate missing portions of the audio signal based on the learned representations, without being restricted by stationarity assumptions. Data-driven techniques also offer the advantage of adaptability and flexibility, as they can learn from diverse audio datasets and potentially handle complex inpainting scenarios. As of today, such techniques constitute the state-of-the-art of audio inpainting, being able to reconstruct gaps of hundreds of milliseconds or even seconds. These performances are made possible by the use of generative models that have the capability to generate novel content to fill in the missing portions. For example, generative adversarial networks, which are the state-of-the-art of generative models in many areas, rely on two competing neural networks trained simultaneously in a two-player minmax game: the generator produces new data from samples of a random variable, the discriminator attempts to distinguish between generated and real data. During the training, the generator's objective is to fool the discriminator, while the discriminator attempts to learn to better classify real and fake data. In GAN-based inpainting methods the generator acts as a context encoder and produces a plausible completion for the gap only given the available information surrounding it. The discriminator is used to train the generator and tests the consistency of the produced inpainted audio. Recently, also diffusion models have established themselves as the state-of-the-art of generative models in many fields, often beating even GAN-based solutions. For this reason they have also been used to solve the audio inpainting problem, obtaining valid results. These models generate new data instances by inverting the

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  Joint constraints

  Joint constraints are rotational constraints on the joints of an artificial system. They are used in an inverse kinematics chain, in fields including 3D animation or robotics. Joint constraints can be implemented in a number of ways, but the most common method is to limit rotation about the X, Y and Z axis independently. An elbow, for instance, could be represented by limiting rotation on X and Z axis to 0 degrees, and constraining the Y-axis rotation to 130 degrees. To simulate joint constraints more accurately, dot-products can be used with an independent axis to repulse the child bones orientation from the unreachable axis. Limiting the orientation of the child bone to a border of vectors tangent to the surface of the joint, repulsing the child bone away from the border, can also be useful in the precise restriction of shoulder movement.

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  Webull

  Webull Corporation, often stylized as simply Webull, is a U.S.-based financial services holding company headquartered in St. Petersburg, Florida. It owns and operates the Webull electronic trading platform for self-directed retail investors. Depending on jurisdiction, the Webull platform offers trading in stocks, exchange-traded funds (ETFs), options, margin, bonds, cryptocurrency and futures, as well as market-data tools. Webull began operations in 2016 under Hunan Fumi Information Technology, a China-based financial technology company founded by Wang Anquan. It launched U.S. brokerage services through Webull Financial LLC in 2018 and expanded during the retail-trading boom of 2020 and 2021. In April 2025, Webull became a publicly traded company on the Nasdaq through a merger with special-purpose acquisition company SK Growth Opportunities Corporation. The company's U.S. brokerage revenue relies substantially on payment for order flow, with options trading accounting for the larger share of its order-flow rebates in 2025. Webull has faced regulatory actions related to options customer approvals, complaint handling, suspicious activity reporting, social-media marketing and customer disclosures. It has also faced scrutiny from U.S. lawmakers and state officials over its historical and operational ties to China and the handling of U.S. customer data. == History == === Founding === Webull was founded in 2016 under Hunan Fumi Information Technology, a China-based financial technology company, by Wang Anquan, a former employee of Alibaba Group and Xiaomi. Hunan Fumi Information Technology received backing from Xiaomi, Shunwei Capital, and other investors in China. Fumi Technology was a Hunan-based fintech start-up incubated by Xiaomi and raised about CNY200 million (approximately US$30 million) in a Series B financing round in 2018. On May 24, 2017, Webull Financial LLC was established as a Delaware limited liability company. It began offering brokerage services in the United States in May 2018. Wang hired Anthony Denier as CEO of the U.S. brokerage that year and the two mapped out their strategy on napkins at a Mexican restaurant in New York City. Webull Corporation was incorporated in the Cayman Islands in September 2019 as the group's holding company. === Retail trading boom === In May 2020, the company received SEC approval to launch a robo-advisor on its platform. By August 2020, the platform had over 11 million registered users, and in October 2020, it had 750,000 daily active users. Webull introduced options trading in 2020 and later added cryptocurrency trading through a separate digital-asset business. In November 2020, Webull began supporting cryptocurrency transactions. In December 2020, Webull launched trading services in Hong Kong. During the GameStop short squeeze in January 2021, Webull gained attention as some retail traders looked for alternatives to Robinhood. On January 27, 2021, Webull recorded its highest-ever number of active daily users, at 952,000, and the Webull app was downloaded across the Apple App and Google Play stores an estimated 100,000 times. That week, approximately 1.2 million people downloaded the Webull mobile app, which the company reported as a 1,548% week-over-week increase. On January 28, 2021, Webull was directed by its clearing house to temporarily halt buy orders for stocks affected by the GameStop short squeeze. In June 2021, Webull was reported to be considering a U.S. initial public offering that could raise up to $400 million. === Restructuring and expansion === Webull restructured its China-related corporate arrangements in 2022 and later stated that Hunan Fumi was no longer affiliated with the group. In 2022 and 2023, Webull expanded in several non-U.S. markets, including Singapore, Australia, South Africa, Japan, the United Kingdom and Indonesia. In June 2023, Webull moved cryptocurrency trading to a separate app called Webull Pay. By the end of 2023, Webull had 4.3 million funded accounts and US$8.2 billion in customer assets. In January 2024, Anthony Denier was promoted to group president of Webull Corporation. In November 2024, Webull launched overnight, or extended-hours, trading, expanding the trading window of U.S. stocks for users inside and outside the United States. === SPAC merger and Nasdaq listing === On February 28, 2024, Webull agreed to go public through a business combination with SK Growth Opportunities Corporation (NASDAQ: SKGR), a special-purpose acquisition company, in a deal that valued the company at approximately US$7.3 billion. The proposed valuation drew scrutiny because of Webull's limited financial disclosure at announcement, reliance on payment for order flow and small expected public float. SK Growth shareholders approved the business combination on March 30, 2025, and the transaction closed on April 10, 2025. Webull's Class A ordinary shares and warrants began trading on the Nasdaq on April 11, 2025 under the ticker symbols BULL and BULLW (incentive warrants traded under BULLZ until their redemption in June 2025). The merger brought Webull to the public market but generated little cash for the company: after shareholder redemptions, Webull disclosed net proceeds of US$430,066 from the transaction. After the listing, Webull's shares experienced extreme volatility, rising as much as 500% to US$79.56 on April 14, 2025, after closing at US$13.25 on the prior trading day. The initial post-listing surge increased the value of Webull holdings owned by earlier investors, including RIT Capital Partners, which had first invested in Webull in 2021. In April 2026, after Webull's shares had fallen about 70% over the previous year, the company authorized a US$100 million share repurchase program. == Business model and financials == Webull provides a self-directed electronic trading platform available through mobile, desktop and web applications. Depending on jurisdiction, the platform offers trading in stocks, exchange-traded funds, options, margin, futures, fixed income products, cryptocurrency, cash management features and market data tools. In the United States, Webull Financial LLC is a registered broker-dealer and member of FINRA and the Securities Investor Protection Corporation, while Webull operates in other markets through locally licensed brokerage subsidiaries. Webull operates a commission-free or low-cost brokerage model for self-directed retail investors. In the United States, a substantial part of its trading-related revenue comes from payment for order flow, while in some non-U.S. markets the company more commonly charges commissions directly to customers. The platform is aimed at more active retail investors, including users seeking options tools, extended-hours trading and real-time market data. For 2025, Webull reported total revenue of US$571.0 million, up from US$390.2 million in 2024. Equity and option order-flow rebates accounted for US$304.1 million, or 53.3% of revenue, making order-flow rebates the company's largest reported revenue category. Interest-related income accounted for US$154.3 million, handling charge income for US$87.3 million and other revenue for US$25.3 million. Options were the larger component of the company's order-flow rebates in 2025, generating US$210.0 million compared with US$94.2 million from equities. Webull also generates revenue from interest-related activities, including margin financing, customer bank deposits, stock lending and corporate bank deposits. The company has stated that its interest-related income is affected by interest rates, customer cash balances, margin balances and demand for stock lending. The company had approximately 20 million registered users worldwide as of February 2024. As of December 31, 2025, it reported 26.8 million registered users, 5.0 million funded accounts and US$24.6 billion in customer assets. As of March 2025, Webull operated in Hong Kong, Singapore, Australia, South Africa, Japan, the United Kingdom, the United States, Indonesia, Canada, Brazil, Thailand, Malaysia and Mexico. == Marketing and sponsorships == Webull has used paid digital advertising, referral incentives, free-stock promotions, affiliate marketing and sports sponsorships to acquire customers and promote its brand. In its 2025 annual filing, the company reported marketing and branding expenses of US$152.3 million in 2023, US$138.7 million in 2024 and US$135.9 million in 2025. Webull said most of its advertising and promotion costs were related to paid search and paid social advertising, and that it had reduced free-stock promotions while shifting toward deposit- and asset-transfer-based incentives. In September 2021, BSE Global, the parent company of the Brooklyn Nets and New York Liberty, entered into a global multi-year agreement with Webull. Under the agreement, Webull became an official sponsor and online brokerage partner of the teams, with branding that included a jersey patch on Brooklyn Nets uniforms. Spo

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  Digital on-screen graphics by country

  Digital on-screen graphics by country are the varying logos and differences of digital on-screen graphics in different countries and regions. == Overview == Digital on-screen graphics (DOGs; also called a digitally originated graphic, bug, network bug, on-screen bug, or screenbug) are almost always placed in one of four corners: the top left, the top right, the bottom left, or the bottom right. There are few exceptions to this rule: most notably, Saturday! in Russia, which places their DOG in the top center. Many news broadcasters, as well as a few television networks, also place a clock alongside their bug. In the United States, Canada, Australia, and New Zealand, DOGs may also include the show's parental guideline rating. In Australia, this is known as a Program Return Graphic (PRG). It has become common to place text above the station's logo advertising other programs on the network. In many countries, some TV networks insert the word "live" near the DOG to advise viewers that the program is live, rather than pre-recorded. During televised sports events, a DOG may also display game-related statistics such as the current score. This has led people in Canada and the United States to refer to such a DOG as a score bug. In many countries, DOGs are removed in non-program sections such as commercials and program trailers, but TV channels in some other countries have retained in full color or instead replaced them in either of these sections or in both sections (like Turkey, Indonesia, Italy, the entirety of South Asia, Vietnam, Taiwan, and Russia). == MENA == === Arab world === Arabic TV logos are placed in the top-right and top-left except for Al-Jazeera, whose logo appears on the bottom-right of the screen. Some Arabian TV stations hide their logos during commercial breaks and promos/trailers, such as Dubai TV, Dubai One, Funoon, the Egyptian CBC and Nile TV networks, ART Hekayat, ART Hekayat 2, Iqraa, and Al-Jazeera. Abu Dhabi TV and MBC1 initially had their logos at the bottom-right corner from their launch until the mid-2000s, when they were moved to the top-right corner. === Iran === Iranian broadcaster IRIB introduced DOGs in early 2000s. Unlike other Middle Eastern nations that introduced DOGs on their TV networks in 1990s, Iran was very late in this practice. Almost all Iranian TV channels display DOGs at top-left corner of the screen. The few exception is IRIB-owned channels remove DOGs during news broadcasts. === Israel === In Israel, Television DOGs were first introduced in 1991. Israeli channel watermarks most often appear on the top left or the top right corner since Israeli cable and satellite-based services often have the channel description and programming (OSD) on the bottom of the screen. Most channels have an opaque, full-color watermark, though exceptions exist, for example Channel 9, which displays a blue-tinted semi-transparent logo. In ad breaks, it is required to replace the channel watermark with another symbol – sometimes on the other edge of the screen – indicating there are ads at the moment. The Israel Broadcasting Authority, whose channels placed their logos in the top left corner, ceased broadcasting in May 2017. The new public broadcaster, the Israeli Public Broadcasting Corporation, displays its logos at the top right instead. The erstwhile Channel 2 as well as its successors, Keshet 12 and Reshet 13, also use the top right corner. However, Channel 10 used the top left corner before rebranding to Eser (Literally "Ten") in 2017 and simultaneously moving its logo to the top right (Not long after, in January 2019, it ceased broadcasting as it merged with Reshet 13). Channel 14 as well as its predecessor Channel 20 use the top right corner as well. The Knesset Channel, however, uses the top left corner. === Morocco === The SNRT and 2M And Al-Aoula Uses permanent on-screen DOGs for their TV channels. In contrast, other channels such as Medi 1 TV hide their DOGs during commercial breaks. == Asia == === Brunei === Radio Television Brunei introduced DOGs in 1994. Like TV channels from neighbouring Malaysia, all DOGs are removed during advertisement breaks. === Cambodia === Cambodian TV channels introduced DOGs in 1995. Like Thailand, all logos are full-color and displayed on the top-right corner of the screen. Some channels such as TV5 hide their logos during commercial breaks. Hang Meas HDTV Logo on the top-left corner of the screen, CTN (Cambodian Television Network), MyTV, Bayon TV, PNN, Logo on the top-right corner of the screen. === China === TV stations in mainland China always place their logo (usually semi-transparent and sometimes animated) in the top-left corner of the screen in full-color or grey-scale. Regardless of the content being broadcast (program or advertisements), some channels like Phoenix Television hide their logos during commercial breaks; although in some rare cases, the DOG may be placed elsewhere to avoid covering the score bug during the broadcast of a sporting event. China introduced logos in 1983 on the bottom-left corner of the screen, but they were used only during commercial breaks and clock idents. Later China Central Television (CCTV) introduced permanent DOGs for all programs in 1992, on the top-left corner of the screen. China also displays a clock on top-right corner of the screen for 1 minute between 59:30–00:30 & 29:30–30:30 time in transition between programs. === Hong Kong === Hong Kong TV introduced DOGs in 1994. Hong Kong DOGs can be either of full color or semi-transparent and (except for RTHK 31) always be hidden during commercial breaks. Television Broadcasts Limited (TVB) placed their logos at the top-right corner of the screen while now-defunct Asia Television and other channels placed their logos at the top-left corner of the screen. Sometimes, weather information, date, and time clocks had been used alongside DOGs in news programs, continuity & live broadcasts. === India === The first on-screen logo in India was introduced in 1984 by DD2 Metro (now DD News). It was white and slightly transparent. All Indian TV channels have on-screen logos. They are always full-colors, never transparent, and they are almost never removed during commercial breaks (though the channels of the South Indian Sun TV Network did so until 2015). The great majority of Indian TV channels place their logos in the top right corner of the screen, though there are exceptions. The corner used may be broadcaster-dependent. Among the big national broadcasters: Channels from the Sony network always use the top right corner, without exception. Star channels also use the top right, with the exception of National Geographic and Nat Geo Wild, which use the top left corner in line with their international counterparts. Past exceptions include The History Channel, whose logo was placed in the top left until it rebranded to Fox History & Entertainment in 2008; the now-defunct Channel V, which used the top left between 2013 and 2016; and Nat Geo People, Nat Geo Music and BabyTV, were withdrawn from India in June 2019. TV18 and Viacom18 channels use the top right corner as well, with the exceptions of regional-language movie channels (e.g., Colors Kannada Cinema and Colors Gujarati Cinema) as well as Colors Super, which have shown their logos at the top left corner since 2018; and VH1, which has always used the bottom right corner. Also, CNBC-TV18, CNBC Awaaz and CNBC Bajar use the bottom right. Moreover, MTV showed its logo in the top left corner until 23 April 2018, when it was moved to the top right (its HD version, launched in 2017, has always used the top right). Unlike most other major networks, the Zee Network's non-news channels containing 'Zee' in their name display their logos at the top left corner and not the top right. This has been the case since 15 October 2017, when almost all the Zee-branded TV channels of the Zee network rebranded with a new logo and, in many cases, a new graphics package and look. Before then, the logos were shown at the top right, as with other broadcasters. (News channels' logos—i.e., logos of channels owned by Zee Media Corporation—stayed put at the top right corner, with the exception of WION, which uses the bottom left.) All the major Zee-branded channels—such as Zee TV, Zee Cinema, Zee Café and the regional-language channels like Zee Tamil, Zee Telugu, Zee Marathi and Zee Bangla—show their logos at the top left; moreover, the Odia-language channel Sarthak TV rebranded to Zee Sarthak and moved its logo to the top left. Among the Zee channels not containing the word 'Zee' that moved their logos to the top left during the big rebrand in 2017 was English movie channel Zee Studio; when it was renamed to &flix on 3 June 2018, the logo remained at the top left. Moreover, Hindi movie channel &pictures has always shown its logo at the top left since its launch in 2013. However, &privé HD, Zee's other English movie channel, and Hindi entertainment channel &TV place the

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  Gemini Enterprise Agent Platform

  Gemini Enterprise Agent Platform (formerly known as Vertex AI) is a managed machine learning (ML) and artificial intelligence (AI) platform developed by Google Cloud. It provides a unified environment for building, training, deploying, and scaling ML models and generative AI applications. The platform integrates tools for the full ML lifecycle, including data preparation, model training, evaluation, deployment, and monitoring, under a single API and user interface. Vertex AI was announced at Google I/O and released as a generally available product on May 18, 2021. At launch, Google described Vertex AI as unifying its AutoML offerings with its prior Cloud AI Platform capabilities, and as adding operational features intended to help teams move models from experimentation into production use. On April 22, 2026, Google announced Gemini Enterprise Agent Platform as the replacement evolution of Vertex AI. == History == Google Cloud announced the general availability of Vertex AI on May 18, 2021, at the Google I/O developer conference. The platform was designed to consolidate Google Cloud's previously separate ML offerings, including AutoML and the legacy AI Platform, into a single system. At launch, Google claimed that Vertex AI required roughly 80% fewer lines of code to train a model compared to competing platforms. In June 2023, Google made generative AI support in Vertex AI generally available, giving developers access to foundation models including PaLM 2, Imagen, and Codey through the platform's Model Garden and the newly launched Generative AI Studio. At the time of this launch, Model Garden included over 60 models from Google and its partners. In August 2023, at the Google Cloud Next conference, Google announced further updates to Vertex AI, including the addition of third-party models such as Claude 2 from Anthropic and Llama 2 from Meta to the Model Garden, as well as new tools called Vertex AI Extensions for connecting models to APIs for real-time data retrieval. At the same event, Vertex AI Search and Conversation were made generally available, providing enterprise search and chatbot capabilities powered by foundation models. In April 2024, at Google Cloud Next, the company introduced Vertex AI Agent Builder, a no-code tool for creating AI-powered conversational agents built on top of Gemini large language models. This brought together the existing Vertex AI Search and Conversation products with new developer tools for building generative AI experiences. == Features == === Model training === Vertex AI supports both AutoML, which enables code-free model training on tabular, image, text, or video data, and custom training, which gives users full control over the ML framework, training code, and hyperparameter tuning. The platform provides serverless training as well as dedicated training clusters with GPU and TPU accelerators. Vertex AI Vizier handles automatic hyperparameter tuning, and Vertex AI Experiments allows comparison and tracking of training runs. === Model Garden === The Vertex AI Model Garden is a curated catalog of over 200 enterprise-ready models, including Google's own foundation models (such as Gemini, Imagen, and Veo), third-party models (such as Anthropic's Claude and Mistral AI models), and popular open-source models (such as Llama and Gemma). Models are accessible as fully managed model-as-a-service APIs. === Pipelines (workflow orchestration) === Vertex AI Pipelines provides managed orchestration of ML workflows and supports pipelines built with the Kubeflow Pipelines SDK, among other options described in Google Cloud documentation. === Vertex AI Studio === Vertex AI Studio provides tools for prompt design, testing, and model management, allowing developers to prototype and build generative AI applications using natural language, code, images, or video. === Agent Builder and Agent Engine === Vertex AI Agent Builder is a suite of products for building, deploying, and governing AI agents in production environments. It supports development with the open-source Agent Development Kit (ADK) and other frameworks. Vertex AI Agent Engine provides the underlying infrastructure for deploying and scaling agents, with support for enterprise security features including HIPAA compliance, customer-managed encryption keys (CMEK), and VPC Service Controls. === Generative AI tooling and model access === Google markets Vertex AI as providing access to Google foundation models (including the Gemini family) and developer tools such as Vertex AI Studio, along with a model catalog that includes Google and selected open source models (marketed as "Model Garden"). Google has also offered products within Vertex AI aimed at building generative search and conversational applications, including offerings named "Vertex AI Search" and "Vertex AI Conversation" as reported in 2023 coverage of platform updates. === MLOps tools === The platform includes a range of MLOps capabilities: Vertex AI Pipelines for orchestrating and automating ML workflows as reusable pipelines. Vertex AI Feature Store for serving, sharing, and reusing ML features across projects. Vertex AI Model Registry for storing, versioning, and managing trained models. Vertex AI Model Monitoring for detecting training-serving skew and inference drift in deployed models. Vertex Explainable AI for interpreting model predictions. Vertex AI Workbench for managed JupyterLab notebook environments integrated with Google Cloud Storage and BigQuery. == Industry recognition == Google was named a Leader for the fifth consecutive year in the 2024 Gartner Magic Quadrant for Cloud AI Developer Services, a recognition that encompasses Vertex AI and its related offerings. Google was also recognized as a Leader in the 2024 Gartner Magic Quadrant for Data Science and Machine Learning Platforms and was named a Leader in the Forrester Wave for AI/ML Platforms, Q3 2024. In October 2025, Google was also named a Leader in the 2025 IDC (International Data Corporation) MarketScape for Worldwide GenAI Life-Cycle Foundation Model Software. == Pricing == Vertex AI uses a pay-as-you-go pricing model, with costs determined by the specific services consumed, including model training, prediction serving, and data storage. For generative AI tasks, pricing is based on a per-token model, with rates varying depending on the specific model used and whether tokens are input or output. Google offers a free tier for new users, which includes limited custom training hours and online prediction usage, along with an introductory US$300 in Google Cloud credits valid for 90 days. == Adoption == In the year following its 2021 launch, Google reported that usage of Vertex AI and BigQuery had driven 2.5 times more machine learning predictions compared to the prior year, and that active customers of Vertex AI Workbench had grown 25-fold over a six-month period. Early enterprise adopters included Ford, Wayfair, and Seagate, among others. Wayfair reported that it was able to run large model training jobs 5 to 10 times faster using the platform.

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  Fragment (computer graphics)

  In computer graphics, a fragment is the data necessary to generate a single pixel's worth of a drawing primitive in the frame buffer. These data may include, but are not limited to: raster position depth interpolated attributes (color, texture coordinates, etc.) stencil alpha window ID As a scene is drawn, drawing primitives (the basic elements of graphics output, such as points, lines, circles, text etc.) are rasterized into fragments which are textured and combined with the existing frame buffer. How a fragment is combined with the data already in the frame buffer depends on various settings. In a typical case, a fragment may be discarded if it is further away than the pixel which is already at that location (according to the depth buffer). If it is nearer than the existing pixel, it may replace what is already there, or, if alpha blending is in use, the pixel's color may be replaced with a mixture of the fragment's color and the pixel's existing color, as in the case of drawing a translucent object. In general, a fragment can be thought of as the data needed to shade the pixel, plus the data needed to test whether the fragment survives to become a pixel (depth, alpha, stencil, scissor, window ID, etc.). Shading a fragment is done through a fragment shader (or pixel shaders in Direct3D). In computer graphics, a fragment is not necessarily opaque, and could contain an alpha value specifying its degree of transparency. The alpha is typically normalized to the range of [0, 1], with 0 denotes totally transparent and 1 denotes totally opaque. If the fragment is not totally opaque, then part of its background object could show through, which is known as alpha blending.

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  Jordan Antiquities Database and Information System

  The Jordan Antiquities Database and Information System (JADIS) was a computer database of antiquities in Jordan, the first of its kind in the Arab world. It was established by the Department of Antiquities in 1990, in cooperation with the American Center for Oriental Research in Amman and sponsored by the United States Agency for International Development. JADIS was in use until 2002, when it was superseded by a new system, MEGA-J. Over 10,841 antiquities were registered in the database. An introduction and printed summary of the database was published by the Department of Antiquities in 1994, edited by Gaetano Palumbo.

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  Altibase

  Altibase is a hybrid database, relational database management system manufactured by the Altibase Corporation. The software's hybrid architecture allows it to access both memory-resident and disk-resident tables using single interface. It supports both synchronous and asynchronous replication and offers real-time ACID compliance. Support is also offered for a variety of SQL standards and programming languages. Other important capabilities include data import and export, data encryption for security, multiple data access command sets, materialized view and temporary tables, and others. == History == From 1991 through 1997 the Mr. RT project was an in-memory database research project, conducted by the Electronics and Telecommunications Research Institute a government-funded research organization in South Korea. Altibase was incorporated in 1999. Altibase acquired an in-memory database engine from the Electronics and Telecommunications Research Institute in February 2000, and commercialized the database in October of the same year. In 2001, Altibase changed the name of the in-memory database product from "Spiner" to "Altibase" in 2001. In 2004, Altibase integrated the in-memory database with a disk-resident database to create a hybrid DBMS, released version 4.0 and renamed it as ALTIBASE HDB. Altibase released version 5.5.1 and 6.1.1 in 2012, version 6.3.1 in November 2013, and 6.5.1 in May 2015. Altibase claims that this is the world's first hybrid DBMS. Altibase released its open source edition version 7.1, however, closed the source in 2023. In August 2023, Altibase released its cloud-optimized version 7.3. === Awards === In 2006, Received the Presidential Award at the Korea Software Awards In 2007, Selected as World-Class Product by the Ministry of Commerce, Industry and Energy In 2009, Awarded the Outstanding Product Award in China's Telecommunications Industry In 2009, Received Outstanding Product Award at the China Billing China 2009 Telecommunication Industry Awards In 2010, Commendation from the Minister of Knowledge Economy for Technological Practicalization In 2011, Received the Grand Prize at the 10th Software Enterprise Competitiveness Award In 2011, Selected as Top 10 Emerging Technologies and received Special Award at the Korea Technology Grand Prize In 2012, Awarded for Contributions to Military Manpower Administration In 2014~2016, Included in Gartner Magic Quadrant for Operational DBMS In 2015, Selected as Outstanding BSS by China Fujian Mobile. In 2023, Awarded as the Excellent Research and Development Institution by the Korean Ministry Science and ICT In 2023, Won the Global Premium Commercial Software Presidential Award at the 9th Global Commercial Software Grand Exhibition in Korea === Release === The first version, called Spiner, was released in 2000 for commercial use. It took half of the in-memory DBMS market share in South Korea. In 2002 the second version was released renamed to Altibase v2.0. By 2003, Altibase v3.0 was released and it entered the Chinese market. Released version 4.0 with hybrid architecture, combining RAM and disk databases, was released in 2004. In 2005 Altibase began working with Chinese telecommunications providers for billing systems, and some financial companies in Taiwan, China, for home trading systems. The software was certified by the Telecommunications Technology Association. The Ministry of Government Administration and Home Affairs gave it an award in 2006. Offices in China and United States opened in 2009. In 2011, version 5.5.1 was renamed it to HDB (for "hybrid database"). The Altibase Data Stream product for complex event processing was renamed DSM. The product received a Korean technology award. Altibase introduced certification services. In 2012, HDB Zeta and Extreme were announced, and DSM renamed to CEP. In 2013, yet another variant called XDB was announced, and the company received ISO/IEC 20000 certification. In 2018, Altibase went open source. Altibase went open source in February, 2018. Altibase Corp has made the decision to discontinue the Altibase 7.1 open source edition, effective March 17, 2023. As a result, the open-source edition of Altibase 7.1 will no longer be available for download or use. Altibase released version 7.3 in September, 2023, its notable feature is the world’s first hybrid partition, allowing data to be stored in both memory and on disk at the partition level. Version 7.3 also added parallel processing capabilities for high-speed performance in both partitioned and non-partitioned scenarios. Improving potential bottlenecks associated with Commit and logging that impact transaction performance, version 7.3 has achieved an approximately 490% enhancement in performance compared to previous versions. === Release history === == Clients == According to marketing research, Altibase have over 700 customers and more than 8,000 of installations and deployments, including 22 Fortune Global 500 Companies. Altibase's clients in the telecommunications, financial services, manufacturing, and utilities sectors include Bloomberg, AT&T, LG, Intel, LGU+, ETRADE, HP, UAT Inc., POSCO, SK Telecom, KT Corporation, Samsung Electronics, Shinhan Bank, Woori Bank, Canon(Toshiba), Hanhwa, The South Korean Ministry of Defense, G-Market, CJ, and Chung-Ang University. === Global clients === Japan FX Prime, a foreign exchange services company Retela Crea Securities United States AT&T Implemented Altibase for its PS-LTE Safety network, where the Presence service plays a vital role. This service handles the reception and storage of user information, conducting real-time checks for online presence and location as needed. Canada Telus One of the major telecommunication companies. Utilizes Altibase for its operations involving real-time user management, processing high volumes of dedicated terminal data, and managing real-time location information (GIS) for terminals. Altibase contributes to the company's in-house solution for maintaining uninterrupted services during national disasters or similar situations, ensuring efficiency and reliability. China China Mobile, China Unicom, China Telecom The three major telecommunications companies. Utilize ALTIBASE HDB in 29 of 31 Chinese provinces. Turkish Ziraat Bank, Halk Bank, Deniz Bank, Garanti BBVA, TEB, Oyak Bank, QNB, Burgan Bank, and others. In 2018, Altibase entered the market through a partnership with ATP-Tradesoft, a subsidiary of Ata Holdings. Collaborating with ATP-Tradesoft. Altibase integrated into the Online Trading System XFront. This integration was well-received by major financial institutions and securities firms in Turkey. Altibase is currently implemented in the XFront Online Trading System, used by 13 significant financial institutions and banks in the Turkey. Thailand Bualuang Securities Altibase has been supplied its DBMS to support the construction of the online stock trading platform. Mongolia MobiCom The Mongolian telecommunication giant, has adopted Altibase’s 7.0 version for its mobile platform for storing the infrequently used data. Azerbaijan M1 highway Altibase has been supplied as the Database Management System (DBMS) for the electronic toll collection system. One of the most crucial transportation networks in the country. India State-owned Karur Vysya Bank In 2013, Altibase provided its hybrid database solution and was deployed for the online banking system === Industries === Telecommunications LGU+ SK Telecom KT Corporation AT&T Telus Financial services Shinhan Bank Woori Bank KakaoPay Securities Implemented Altibase in its stock trading system Leveraging Altibase's replication feature, along with offline replication through shared disk and adapter functionality, the system ensures a high level of availability and consistency, with a reliability rate of 99.999% even in the event of system failures. COREDAX Cryptocurrency market Altibase has entered into a strategic partnership by signing a database management system (DBMS) supply contract with the cryptocurrency exchange Bloomberg ETRADE Manufacturing Samsung Electronics LG POSCO Hanhwa Canon(Toshiba) Intel HP Utilities South Korean Ministry of Defense G-Market CJ UAT Inc. Chung-Ang University == Features == Altibase is a so-called "hybrid DBMS", meaning that it simultaneously supports access to both memory-resident and disk-resident tables via a single interface. It is compatible with Solaris, HP-UX, AIX, Linux, and Windows. It supports the complete SQL standard, features Multiversion concurrency control (MVCC), implements Fuzzy and Ping-Pong Checkpointing for periodically backing up memory-resident data, and ships with Replication and Database Link functionality. High performance, large -capacity service Fast real-time data processing and large amounts of data stable Provide parallel processing architecture for large data management Developed and provided Hybrid Partitioned Table function for efficiency according to data personality High stability

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  Algorithm selection

  Algorithm selection (sometimes also called per-instance algorithm selection or offline algorithm selection) is a meta-algorithmic technique to choose an algorithm from a portfolio on an instance-by-instance basis. It is motivated by the observation that on many practical problems, different algorithms have different performance characteristics. That is, while one algorithm performs well in some scenarios, it performs poorly in others and vice versa for another algorithm. If we can identify when to use which algorithm, we can optimize for each scenario and improve overall performance. This is what algorithm selection aims to do. The only prerequisite for applying algorithm selection techniques is that there exists (or that there can be constructed) a set of complementary algorithms. == Definition == Given a portfolio P {\displaystyle {\mathcal {P}}} of algorithms A ∈ P {\displaystyle {\mathcal {A}}\in {\mathcal {P}}} , a set of instances i ∈ I {\displaystyle i\in {\mathcal {I}}} and a cost metric m : P × I → R {\displaystyle m:{\mathcal {P}}\times {\mathcal {I}}\to \mathbb {R} } , the algorithm selection problem consists of finding a mapping s : I → P {\displaystyle s:{\mathcal {I}}\to {\mathcal {P}}} from instances I {\displaystyle {\mathcal {I}}} to algorithms P {\displaystyle {\mathcal {P}}} such that the cost ∑ i ∈ I m ( s ( i ) , i ) {\displaystyle \sum _{i\in {\mathcal {I}}}m(s(i),i)} across all instances is optimized. == Examples == === Boolean satisfiability problem (and other hard combinatorial problems) === A well-known application of algorithm selection is the Boolean satisfiability problem. Here, the portfolio of algorithms is a set of (complementary) SAT solvers, the instances are Boolean formulas, the cost metric is for example average runtime or number of unsolved instances. So, the goal is to select a well-performing SAT solver for each individual instance. In the same way, algorithm selection can be applied to many other N P {\displaystyle {\mathcal {NP}}} -hard problems (such as mixed integer programming, CSP, AI planning, TSP, MAXSAT, QBF and answer set programming). Competition-winning systems in SAT are SATzilla, 3S and CSHC === Machine learning === In machine learning, algorithm selection is better known as meta-learning. The portfolio of algorithms consists of machine learning algorithms (e.g., Random Forest, SVM, DNN), the instances are data sets and the cost metric is for example the error rate. So, the goal is to predict which machine learning algorithm will have a small error on each data set. == Instance features == The algorithm selection problem is mainly solved with machine learning techniques. By representing the problem instances by numerical features f {\displaystyle f} , algorithm selection can be seen as a multi-class classification problem by learning a mapping f i ↦ A {\displaystyle f_{i}\mapsto {\mathcal {A}}} for a given instance i {\displaystyle i} . Instance features are numerical representations of instances. For example, we can count the number of variables, clauses, average clause length for Boolean formulas, or number of samples, features, class balance for ML data sets to get an impression about their characteristics. === Static vs. probing features === We distinguish between two kinds of features: Static features are in most cases some counts and statistics (e.g., clauses-to-variables ratio in SAT). These features ranges from very cheap features (e.g. number of variables) to very complex features (e.g., statistics about variable-clause graphs). Probing features (sometimes also called landmarking features) are computed by running some analysis of algorithm behavior on an instance (e.g., accuracy of a cheap decision tree algorithm on an ML data set, or running for a short time a stochastic local search solver on a Boolean formula). These feature often cost more than simple static features. === Feature costs === Depending on the used performance metric m {\displaystyle m} , feature computation can be associated with costs. For example, if we use running time as performance metric, we include the time to compute our instance features into the performance of an algorithm selection system. SAT solving is a concrete example, where such feature costs cannot be neglected, since instance features for CNF formulas can be either very cheap (e.g., to get the number of variables can be done in constant time for CNFs in the DIMACs format) or very expensive (e.g., graph features which can cost tens or hundreds of seconds). It is important to take the overhead of feature computation into account in practice in such scenarios; otherwise a misleading impression of the performance of the algorithm selection approach is created. For example, if the decision which algorithm to choose can be made with perfect accuracy, but the features are the running time of the portfolio algorithms, there is no benefit to the portfolio approach. This would not be obvious if feature costs were omitted. == Approaches == === Regression approach === One of the first successful algorithm selection approaches predicted the performance of each algorithm m ^ A : I → R {\displaystyle {\hat {m}}_{\mathcal {A}}:{\mathcal {I}}\to \mathbb {R} } and selected the algorithm with the best predicted performance a r g min A ∈ P m ^ A ( i ) {\displaystyle arg\min _{{\mathcal {A}}\in {\mathcal {P}}}{\hat {m}}_{\mathcal {A}}(i)} for an instance i {\displaystyle i} . === Clustering approach === A common assumption is that the given set of instances I {\displaystyle {\mathcal {I}}} can be clustered into homogeneous subsets and for each of these subsets, there is one well-performing algorithm for all instances in there. So, the training consists of identifying the homogeneous clusters via an unsupervised clustering approach and associating an algorithm with each cluster. A new instance is assigned to a cluster and the associated algorithm selected. A more modern approach is cost-sensitive hierarchical clustering using supervised learning to identify the homogeneous instance subsets. === Pairwise cost-sensitive classification approach === A common approach for multi-class classification is to learn pairwise models between every pair of classes (here algorithms) and choose the class that was predicted most often by the pairwise models. We can weight the instances of the pairwise prediction problem by the performance difference between the two algorithms. This is motivated by the fact that we care most about getting predictions with large differences correct, but the penalty for an incorrect prediction is small if there is almost no performance difference. Therefore, each instance i {\displaystyle i} for training a classification model A 1 {\displaystyle {\mathcal {A}}_{1}} vs A 2 {\displaystyle {\mathcal {A}}_{2}} is associated with a cost | m ( A 1 , i ) − m ( A 2 , i ) | {\displaystyle |m({\mathcal {A}}_{1},i)-m({\mathcal {A}}_{2},i)|} . == Requirements == The algorithm selection problem can be effectively applied under the following assumptions: The portfolio P {\displaystyle {\mathcal {P}}} of algorithms is complementary with respect to the instance set I {\displaystyle {\mathcal {I}}} , i.e., there is no single algorithm A ∈ P {\displaystyle {\mathcal {A}}\in {\mathcal {P}}} that dominates the performance of all other algorithms over I {\displaystyle {\mathcal {I}}} (see figures to the right for examples on complementary analysis). In some application, the computation of instance features is associated with a cost. For example, if the cost metric is running time, we have also to consider the time to compute the instance features. In such cases, the cost to compute features should not be larger than the performance gain through algorithm selection. == Application domains == Algorithm selection is not limited to single domains but can be applied to any kind of algorithm if the above requirements are satisfied. Application domains include: hard combinatorial problems: SAT, Mixed Integer Programming, CSP, AI Planning, TSP, MAXSAT, QBF and Answer Set Programming combinatorial auctions in machine learning, the problem is known as meta-learning software design black-box optimization multi-agent systems numerical optimization linear algebra, differential equations evolutionary algorithms vehicle routing problem power systems For an extensive list of literature about algorithm selection, we refer to a literature overview. == Variants of algorithm selection == === Online selection === Online algorithm selection refers to switching between different algorithms during the solving process. This is useful as a hyper-heuristic. In contrast, offline algorithm selection selects an algorithm for a given instance only once and before the solving process. === Computation of schedules === An extension of algorithm selection is the per-instance algorithm scheduling problem, in which we do not select only one solver, but we select a time budget for each algorithm

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  Vulnerability Discovery Model

  A Vulnerability Discovery Model (VDM) uses discovery event data with software reliability models for predicting the same. A thorough presentation of VDM techniques is available in. Numerous model implementations are available in the MCMCBayes open source repository. Several VDM examples include: Alhazmi-Malaiya: Time based model (Alhazmi-Malaiya Logistic (AML) model) Alhazmi-Malaiya: Effort based model Rescorla: Quadratic Model and Exponential Model Anderson: Thermodynamic Model Kim: Weibull Model Linear Model Hump-Shaped Model Independent and Dependent Model Vulnerability Discovery Modeling using Bayesian model averaging Multivariate Vulnerability Discovery Models

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  Kernel Assisted Superuser

  Kernel Assisted Superuser (short: KernelSU) is an alternative method for obtaining root privileges on Android devices. KernelSU implementations are developed as free and open-source software under the terms of the GPLv3 license. == Technical differences == KernelSU differs from other methods in that root access is implemented directly in the kernel. Compared to other root methods that run in userspace, such as Magisk, this has the advantage that commands with su can be executed like normal commands, but still have root privileges. This is not prevented by SELinux or detected by the PlayIntegrity API check, so applications that use it will continue to function. Unlike Magisk, /system/bin/su is a virtual file implemented by hooking system calls with kprobes, and overlayfs is used for systemless modifications to the system partition instead of magic mount. == History == The planning of KernelSU was started in 2018 by developer Jason Donenfeld, also known as XDA user zx2c4. The lack of a root manager app and the difficulty of creating boot images meant that KernelSU was not suitable for productive use, and for a long time this method remained theoretical and could only be used by developers. In 2021, Google launched Generic Kernel Images (GKI for short), which facilitates the creation of a set of device-independent rooted boot images. In response, the developer known on XDA as weishu, who had also worked on projects such as VirtualXposed, adapted KernelSU for GKI-compatible kernels. The adaptation, which was released in January 2023, ensures that any device booting with Linux kernel version 5.10 or higher should be compatible. In addition, the developer also offers a special manager app that, in addition to managing root privileges, also offers overlay-based modding similar to Magisk modules. As of November 2025, 310 developers have contributed to the development of the KernelSU implementation. == Distribution == KernelSU can be installed on all devices that use GKI, as well as on individually supported devices without GKI. Some custom ROMs already have it integrated by default, including ROMs such as CrDroid, Bliss OS, and Evolution X.

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