In mathematics, the intrinsic dimension of a subset can be thought of as the minimal number of variables needed to represent the subset. The concept has widespread applications in geometry, dynamical systems, signal processing, statistics, and other fields. Due to its widespread applications and vague conceptualization, there are many different ways to define it rigorously. Consequently, the same set might have different intrinsic dimensions according to different definitions. The intrinsic dimension can be used as a lower bound of what dimension it is possible to compress a data set into through dimension reduction, but it can also be used as a measure of the complexity of the data set or signal. For a data set or signal of N variables, its intrinsic dimension M satisfies 0 ≤ M ≤ N, although estimators may yield higher values. == Exact dimension == === Differential === In differential geometry, given a differentiable manifold N and a submanifold M, the intrinsic dimension of M is its dimension. Suppose N has n dimensions and M has m dimensions, then that means around any point in M, there exists a local coordinate system ( x 1 , … , x m , x m + 1 , … , x n ) {\displaystyle (x_{1},\dots ,x_{m},x_{m+1},\dots ,x_{n})} of N, such that the manifold M is simply the subset of N defined by x m + 1 = 0 , … , x n = 0 {\displaystyle x_{m+1}=0,\dots ,x_{n}=0} . === Metric === Given a mere metric space, we can still define its intrinsic dimension. The most general case is the Hausdorff dimension, though for metric spaces occurring in practice, the box-counting dimension and the packing dimension often are identical to the Hausdorff dimension. Let X , d {\textstyle X,d} be a metric space and A ⊂ X {\textstyle A\subset X} be totally bounded. Define the covering number N ( A , ε ) = min { k : A ⊂ ⋃ i = 1 k B ( x i , ε ) } . {\displaystyle N(A,\varepsilon )=\min \left\{k:A\subset \bigcup _{i=1}^{k}B\left(x_{i},\varepsilon \right)\right\}.} The metric entropy is H ( A , ε ) = log N ( A , ε ) {\textstyle H(A,\varepsilon )=\log N(A,\varepsilon )} (any log base). The upper and lower metric entropy dimensions are dim ¯ E A = lim sup ε ↓ 0 H ( A , ε ) log ( 1 / ε ) , dim _ E A = lim inf ε ↓ 0 H ( A , ε ) log ( 1 / ε ) . {\displaystyle {\overline {\dim }}_{E}A=\limsup _{\varepsilon \downarrow 0}{\frac {H(A,\varepsilon )}{\log(1/\varepsilon )}},\quad {\underline {\dim }}_{E}A=\liminf _{\varepsilon \downarrow 0}{\frac {H(A,\varepsilon )}{\log(1/\varepsilon )}}.} If they are equal, then dim E A {\textstyle \operatorname {dim} _{E}A} is that common value, called the metric entropy dimension. The entropy dimensions are usually used in information theory, and especially coding theory, since entropy is involved in its definition. === Topological === If X {\displaystyle X} is merely a topological space, then we can still define its intrinsic dimension, using the topological dimension or Lebesgue covering dimension. An open cover of a topological space X is a family of open sets Uα such that their union is the whole space, ∪ α {\displaystyle \cup _{\alpha }} Uα = X. The order or ply of an open cover A {\displaystyle {\mathfrak {A}}} = {Uα} is the smallest number m (if it exists) for which each point of the space belongs to at most m open sets in the cover: in other words Uα1 ∩ ⋅⋅⋅ ∩ Uαm+1 = ∅ {\displaystyle \emptyset } for α1, ..., αm+1 distinct. A refinement of an open cover A {\displaystyle {\mathfrak {A}}} = {Uα} is another open cover B {\displaystyle {\mathfrak {B}}} = {Vβ}, such that each Vβ is contained in some Uα. The covering dimension of a topological space X is defined to be the minimum value of n such that every finite open cover A {\displaystyle {\mathfrak {A}}} of X has an open refinement B {\displaystyle {\mathfrak {B}}} with order n + 1. The refinement B {\displaystyle {\mathfrak {B}}} can always be chosen to be finite. Thus, if n is finite, Vβ1 ∩ ⋅⋅⋅ ∩ Vβn+2 = ∅ {\displaystyle \emptyset } for β1, ..., βn+2 distinct. If no such minimal n exists, the space is said to have infinite covering dimension. == Introductory example == Let f ( x 1 , x 2 ) {\textstyle f(x_{1},x_{2})} be a two-variable function (or signal) which is of the form f ( x 1 , x 2 ) = g ( x 1 ) {\textstyle f(x_{1},x_{2})=g(x_{1})} for some one-variable function g which is not constant. This means that f varies, in accordance to g, with the first variable or along the first coordinate. On the other hand, f is constant with respect to the second variable or along the second coordinate. It is only necessary to know the value of one, namely the first, variable in order to determine the value of f. Hence, it is a two-variable function but its intrinsic dimension is one. A slightly more complicated example is f ( x 1 , x 2 ) = g ( x 1 + x 2 ) {\textstyle f(x_{1},x_{2})=g(x_{1}+x_{2})} . f is still intrinsic one-dimensional, which can be seen by making a variable transformation y 1 = x 1 + x 2 {\textstyle y_{1}=x_{1}+x_{2}} and y 2 = x 1 − x 2 {\textstyle y_{2}=x_{1}-x_{2}} which gives f ( y 1 + y 2 2 , y 1 − y 2 2 ) = g ( y 1 ) {\textstyle f\left({\frac {y_{1}+y_{2}}{2}},{\frac {y_{1}-y_{2}}{2}}\right)=g\left(y_{1}\right)} . Since the variation in f can be described by the single variable y1 its intrinsic dimension is one. For the case that f is constant, its intrinsic dimension is zero since no variable is needed to describe variation. For the general case, when the intrinsic dimension of the two-variable function f is neither zero or one, it is two. In the literature, functions which are of intrinsic dimension zero, one, or two are sometimes referred to as i0D, i1D or i2D, respectively. == Signal processing == In signal processing of multidimensional signals, the intrinsic dimension of the signal describes how many variables are needed to generate a good approximation of the signal. For an N-variable function f, the set of variables can be represented as an N-dimensional vector x: f = f ( x ) where x = ( x 1 , … , x N ) {\textstyle f=f\left(\mathbf {x} \right){\text{ where }}\mathbf {x} =\left(x_{1},\dots ,x_{N}\right)} . If for some M-variable function g and M × N matrix A it is the case that for all x; f ( x ) = g ( A x ) , {\textstyle f(\mathbf {x} )=g(\mathbf {Ax} ),} M is the smallest number for which the above relation between f and g can be found, then the intrinsic dimension of f is M. The intrinsic dimension is a characterization of f, it is not an unambiguous characterization of g nor of A. That is, if the above relation is satisfied for some f, g, and A, it must also be satisfied for the same f and g′ and A′ given by g ′ ( y ) = g ( B y ) {\textstyle g'\left(\mathbf {y} \right)=g\left(\mathbf {By} \right)} and A ′ = B − 1 A {\textstyle \mathbf {A'} =\mathbf {B} ^{-1}\mathbf {A} } where B is a non-singular M × M matrix, since f ( x ) = g ′ ( A ′ x ) = g ( B A ′ x ) = g ( A x ) {\textstyle f\left(\mathbf {x} \right)=g'\left(\mathbf {A'x} \right)=g\left(\mathbf {BA'x} \right)=g\left(\mathbf {Ax} \right)} . == The Fourier transform of signals of low intrinsic dimension == An N variable function which has intrinsic dimension M < N has a characteristic Fourier transform. Intuitively, since this type of function is constant along one or several dimensions its Fourier transform must appear like an impulse (the Fourier transform of a constant) along the same dimension in the frequency domain. === A simple example === Let f be a two-variable function which is i1D. This means that there exists a normalized vector n ∈ R 2 {\textstyle \mathbf {n} \in \mathbb {R} ^{2}} and a one-variable function g such that f ( x ) = g ( n T x ) {\textstyle f(\mathbf {x} )=g(\mathbf {n} ^{\operatorname {T} }\mathbf {x} )} for all x ∈ R 2 {\textstyle \mathbf {x} \in \mathbb {R} ^{2}} . If F is the Fourier transform of f (both are two-variable functions) it must be the case that F ( u ) = G ( n T u ) ⋅ δ ( m T u ) {\textstyle F\left(\mathbf {u} \right)=G\left(\mathbf {n} ^{\mathrm {T} }\mathbf {u} \right)\cdot \delta \left(\mathbf {m} ^{\mathrm {T} }\mathbf {u} \right)} . Here G is the Fourier transform of g (both are one-variable functions), δ is the Dirac impulse function and m is a normalized vector in R 2 {\textstyle \mathbb {R} ^{2}} perpendicular to n. This means that F vanishes everywhere except on a line which passes through the origin of the frequency domain and is parallel to m. Along this line F varies according to G. === The general case === Let f be an N-variable function which has intrinsic dimension M, that is, there exists an M-variable function g and M × N matrix A such that f ( x ) = g ( A x ) ∀ x {\textstyle f(\mathbf {x} )=g(\mathbf {Ax} )\quad \forall \mathbf {x} } . Its Fourier transform F can then be described as follows: F vanishes everywhere except for a subspace of dimension M The subspace M is spanned by the rows of the matrix A In the subspace, F varies according to G the Fourier transform of g == Generalizations == The type of intrinsic dimension described above assume
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
Audio mining
Audio mining is a technique by which the content of an audio signal can be automatically analyzed and searched. It is most commonly used in the field of automatic speech recognition, where the analysis tries to identify any speech within the audio. The term audio mining is sometimes used interchangeably with audio indexing, phonetic searching, phonetic indexing, speech indexing, audio analytics, speech analytics, word spotting, and information retrieval. Audio indexing, however, is mostly used to describe the pre-process of audio mining, in which the audio file is broken down into a searchable index of words. == History == Academic research on audio mining began in the late 1970s in schools like Carnegie Mellon University, Columbia University, the Georgia Institute of Technology, and the University of Texas. Audio data indexing and retrieval began to receive attention and demand in the early 1990s, when multimedia content started to develop and the volume of audio content significantly increased. Before audio mining became the mainstream method, written transcripts of audio content were created and manually analyzed. == Process == Audio mining is typically split into four components: audio indexing, speech processing and recognition systems, feature extraction and audio classification. The audio will typically be processed by a speech recognition system in order to identify word or phoneme units that are likely to occur in the spoken content. This information may either be used immediately in pre-defined searches for keywords or phrases (a real-time "word spotting" system), or the output of the speech recognizer may be stored in an index file. One or more audio mining index files can then be loaded at a later date in order to run searches for keywords or phrases. The results of a search will normally be in terms of hits, which are regions within files that are good matches for the chosen keywords. The user may then be able to listen to the audio corresponding to these hits in order to verify if a correct match was found. === Audio Indexing === In audio, there is the main problem of information retrieval - there is a need to locate the text documents that contain the search key. Unlike humans, a computer is not able to distinguish between the different types of audios such as speed, mood, noise, music or human speech - an effective searching method is needed. Hence, audio indexing allows efficient search for information by analyzing an entire file using speech recognition. An index of content is then produced, bearing words and their locations done through content-based audio retrieval, focusing on extracted audio features. It is done through mainly two methods: Large Vocabulary Continuous Speech Recognition (LVCSR) and Phonetic-based Indexing. ==== Large Vocabulary Continuous Speech Recognizers (LVCSR) ==== In text-based indexing or large vocabulary continuous speech recognition (LVCSR), the audio file is first broken down into recognizable phonemes. It is then run through a dictionary that can contain several hundred thousand entries and matched with words and phrases to produce a full text transcript. A user can then simply search a desired word term and the relevant portion of the audio content will be returned. If the text or word could not be found in the dictionary, the system will choose the next most similar entry it can find. The system uses a language understanding model to create a confidence level for its matches. If the confidence level be below 100 percent, the system will provide options of all the found matches. ===== Advantages and disadvantages ===== The main draw of LVCSR is its high accuracy and high searching speed. In LVCSR, statistical methods are used to predict the likelihood of different word sequences, hence the accuracy is much higher than the single word lookup of a phonetic search. If the word can be found, the probability of the word spoken is very high. Meanwhile, while initial processing of audio takes a fair bit of time, searching is quick as just a simple test to text matching is needed. On the other hand, LVCSR is susceptible to common issues of speech recognition. The inherent random nature of audio and problems of external noise all affect the accuracies of text-based indexing. Another problem with LVCSR is its over reliance on its dictionary database. LVCSR only recognizes words that are found in their dictionary databases, and these dictionaries and databases are unable to keep up with the constant evolving of new terminology, names and words. Should the dictionary not contain a word, there is no way for the system to identify or predict it. This reduces the accuracy and reliability of the system. This is named the Out-of-vocabulary (OOV) problem. Audio mining systems try to cope with OOV by continuously updating the dictionary and language model used, but the problem still remains significant and has probed a search for alternatives. Additionally, due to the need to constantly update and maintain task-based knowledge and large training databases to cope with the OOV problem, high computational costs are incurred. This makes LVCSR an expensive approach to audio mining. ==== Phonetic-based Indexing ==== Phonetic-based indexing also breaks the audio file into recognizable phonemes, but instead of converting them to a text index, they are kept as they are and analyzed to create a phonetic-based index. The process of phonetic-based indexing can be split into two phases. The first phase is indexing. It begins by converting the input media into a standard audio representation format (PCM). Then, an acoustic model is applied to the speech. This acoustic model represents characteristics of both an acoustic channel (an environment in which the speech was uttered and a transducer through which it was recorded) and a natural language (in which human beings expressed the input speech). This produces a corresponding phonetic search track, or phonetic audio track (PAT), a highly compressed representation of the phonetic content of the input media. The second phase is searching. The user's search query term is parsed into a possible phoneme string using a phonetic dictionary. Then, multiple PAT files can be scanned at high speed during a single search for likely phonetic sequences that closely match corresponding strings of phonemes in the query term. ===== Advantages and disadvantages ===== Phonetic indexing is most attractive as it is largely unaffected by linguistic issues such as unrecognized words and spelling errors. Phonetic preprocessing maintains an open vocabulary that does not require updating. That makes it particularly useful for searching specialized terminology or words in foreign languages that do not commonly appear in dictionaries. It is also more effective for searching audio files with disruptive background noise and/or unclear utterances as it can compile results based on the sounds it can discern, and should the user wish to, they can search through the options until they find the desired item. Furthermore, in contrast to LVCSR, it can process audio files very quickly as there are very few unique phonemes between languages. However, phonemes cannot be effectively indexed like an entire word, thus searching on a phonetic-based system is slow. An issue with phonetic indexing is its low accuracy. Phoneme-based searches result in more false matches than text-based indexing. This is especially prevalent for short search terms, which have a stronger likelihood of sounding similar to other words or being part of bigger words. It could also return irrelevant results from other languages. Unless the system recognizes exactly the entire word, or understands phonetic sequences of languages, it is difficult for phonetic-based indexing to return accurate findings. === Speech processing and recognition system === Deemed as the most critical and complex component of audio mining, speech recognition requires the knowledge of human speech production system and its modeling. To correspond the Human speech production system, the electrical speech production system is developed to consist of: Speech generation Speech perception Voiced & unvoiced speech Model of human speech The electrical speech production system converts acoustic signal into corresponding representation of the spoken through the acoustic models in their software where all phonemes are represented. A statistical language model aids in the process by identifying how likely words are to follow each other in certain languages. Put together with a complex probability analysis, the speech recognition system is capable of taking an unknown speech signal and transcribing it into words based on the program's dictionary. ASR (automatic speech recognition) system includes: Acoustic analysis: input sound waveform is transformed into a feature Acoustic model: establishes relationship between speech signal and phonemes, pronunciation model and lang
Affinity (software)
Affinity is a graphics editor developed by Serif, a subsidiary of Canva. It is simultaneously a vector graphics editor, a raster graphics editor and a desktop publishing application. It was first released in 2025 as a successor to Serif's Affinity Designer, Affinity Photo and Affinity Publisher, uniting the three editors into one application. While the previous versions competed individually against Adobe's Illustrator, Photoshop, and InDesign, Affinity 3.0 integrates their functionality into a single application. It uses a freemium model monetized by AI features exclusive to Canva Pro subscribers. == Functionality == Affinity is divided into a number of workspaces ("studios"), which are equivalent to the previous suite of Affinity applications: "vector" for vector graphics (Designer), "pixel" for raster editing (Photo), and "layout" for desktop publishing (Publisher). Additionally, it introduces the ability to create custom workspaces. The application supports real-time previews and non-destructive editing, which are based on GPU acceleration. Supported file formats include Adobe Photoshop, InDesign and Illustrator files, PDF, SVG, and TIFF, as well as a custom .af file format. === Vector editing === === Raster editing === Affinity includes photo editing tools including adjustments, masks, blend modes, batch processing, and retouching facilities. Additionally, the application can develop RAW files, similar to Adobe Lightroom. === Desktop publishing === Publishing features include master pages, text styles, and advanced typography. === AI features === The application supports Canva's existing AI features, such as background removal and generative fill. This requires a Canva subscription. == Development == === Background and acquisition (2014–2024) === Serif launched the original Affinity suite starting with Affinity Designer in 2014, followed by Photo (2015) and Publisher (2019). The software gained popularity for its one-time purchase model, contrasting with Adobe's subscription-based Creative Cloud. In November 2022, Serif released Version 2 of the suite, introducing a "Universal License" that covered all three apps across all platforms. In March 2024, Canva acquired Serif for approximately A$580 million (£300 million). Following user backlash regarding a potential shift to subscriptions, Canva and Serif issued a joint "Pledge" committing to four key principles: fair pricing, no mandatory subscriptions, perpetual licenses for existing products, and continued development of Affinity as a standalone suite. === Unified release (2025) === In September 2025, Serif pulled all existing versions of Affinity Designer, Affinity Photo and Affinity Publisher from sale ahead an upcoming announcement on 30 October; also ahead of the announcement, the iPadOS versions of the Affinity suite became free on App Store. During a "Creative Freedom" keynote on 30 October 2025, Canva released a new version now simply branded as "Affinity" (also known as "Affinity by Canva"), and referred to internally as version 3.0. Version 3 drops the separate applications and integrates their functionality into a singular application, and adds the ability to export directly to the Canva platform. It also adds a Canva AI studio, including background removal, "Expand & Edit", and generative fill. As of version 3, Affinity has switched to a freemium model; it is now available at no charge to users, although access to Canva AI features are locked behind the existing Canva Pro subscription service. Serif stated that the perpetually-licensed version 2 will remain available to existing owners, although it will no longer be actively maintained. The new version is currently available for macOS and Windows only, with an iPadOS version to be released soon. == Reception == The change in business model by Canva in 2025 was met with mixed reception, including concerns about its incorporation of AI features. Some users were concerned that their projects would be used for machine learning purposes, or that future versions would suffer from a lack of maintenance or become adware. Additionally, some felt it turned Affinity into fundamentally subscription-based software, given the prevalence of these features in professional contexts. Affinity publicly stated on social media that it would remain "free forever", users' projects would not be used to train AI models, and that "Canva has built a sustainable business model that allows this kind of generosity. And when more professionals use Affinity, Canva can sell more seats into businesses."
Alexis Spectral Data
Alexis Spectral Data is a software developed for colour matching processes that calculates from available spectral data the colour numbers used by computers to display colours on screen. It displays the colour for each spectral reflectance curve and records the calculated trichromatic values and colour numbers along with the spectral curves. This eliminates the need to scan the samples separately with a truecolour Scanner while creating the database. The spectral data can be introduced manually as a series of reflectance values at wavelengths measured in different standard illuminants with an arbitrary but fixed increment that must be kept for each spectral curve throughout the creation of the whole database. Therefore, older UV-VIS Spectrophotometers that can't be interfaced with computers can also be used for creating the database needed for colour matching. Alexis Spectral Data determines the whiteness degree in a less time-consuming method, which permits storage and easier handling of the obtained data. Alexis Spectral Data can export the trichromatic values, calculated from the spectral curves, to Alexis Analyser, software that handles only trichromatic data. The earliest information about the development of this software comes from a paper published by a student at the University Politehnica Bucharest in 1993. The software runs on Windows based computers but not on other operating systems.
JDoodle
JDoodle is a cloud-based online integrated development environment and compiler platform that supports execution of source code in 70+ programming languages including Java, Python, C/C++, PHP, Ruby, Perl, HTML, and more. It provides zero‑setup code for compilation, execution, and sharing via a web browser interface. == Features == Provides real‑time collaboration and code embedding via shareable URLs and APIs Offers an integrated terminal interface supporting database engines such as MySQL and MongoDB. JDroid — AI‑assistant to generate code snippets, optimize code, and assist debugging. == Languages and frameworks supported ==
Inpainting
Inpainting is a conservation process where damaged, deteriorated, or missing parts of an artwork are filled in to present a complete image. This process is commonly used in image restoration. It can be applied to both physical and digital art mediums such as oil or acrylic paintings, chemical photographic prints, sculptures, or digital images and video. With its roots in physical artwork, such as painting and sculpture, traditional inpainting is performed by a trained art conservator who has carefully studied the artwork to determine the mediums and techniques used in the piece, potential risks of treatments, and ethical appropriateness of treatment. == History == The modern use of inpainting can be traced back to Pietro Edwards (1744–1821), Director of the Restoration of the Public Pictures in Venice, Italy. Using a scientific approach, Edwards focused his restoration efforts on the intentions of the artist. It was during the 1930 International Conference for the Study of Scientific Methods for the Examination and Preservation of Works of Art, that the modern approach to inpainting was established. Helmut Ruhemann (1891–1973), a German restorer and conservator, led the discussions on the use of inpainting in conservation. Helmut Ruhemann was a leading figure in modernizing restoration and conservation. His greatest contribution to the field of conservation "was his insistence on following the methods of the original painter exactly, and on understanding the painter's artistic intention". After his career of over 40 years as a conservator, Ruhemann published his treatise The Cleaning of Paintings: Problems & Potentialities in 1968. In describing his method, Ruhemann states that "The surface [of the fill] should be slightly lower than that of the surrounding paint to allow for the thickness of the inpainting...Inpainting medium should look and behave like the original medium, but must not darken with age." Cesare Brandi (1906–1988) developed the teoria del restauro, the inpainting approach combining aesthetics and psychology. However, this approach was used primarily by Italian restorers and conservators, with the terminology becoming widespread in the 1990s. Technological advancements led to new applications of inpainting. Widespread use of digital techniques range from entirely automatic computerized inpainting to tools used to simulate the process manually. Since the mid-1990s, the process of inpainting has evolved to include digital media. More commonly known as image or video interpolation, a form of estimation, digital inpainting includes the use of computer software that relies on sophisticated algorithms to replace lost or corrupted parts of the image data. == Ethics == In order to preserve the integrity of an original artwork, any inpainting technique or treatment applied to physical or digital work should be reversible or distinguishable from the original content of the artwork. Prior to any treatments, conservators proceed according to the American Institute of Conservation of Historical and Artistic Works. There are several ethic considerations before Inpainting can be justified. Various deliberation decisions over the ethical appropriateness of the amount and type of inpainting done, resides on many factors. As most conservation treatments, inpainting's ethical questions rest mainly with authenticity, reversibility and documentation.Any intervention to compensate for loss should be documented in treatment records and reports and should be detectable by common examination methods. Such compensation should be reversible and should not falsely modify the known aesthetic, conceptual, and physical characteristics of the cultural property, especially by removing or obscuring original material.New technologies and the aesthetic demand for perfect images without imperfections challenge conservators' ethical practices to protect the integrity of originals. == Methods == Inpainting methods and techniques depend on the desired goal and type of image being treated. Treatments to fill in the gaps are different between physical and digital art. In inpainting, detailed records of the initial state of the images can help with the treatment and replicate the original closer. === Physical inpainting === Inpainting is rooted in the conservation and restoration of paintings. Inpainting can aim to make a visual improvement to the artwork as a whole by repairing missing or damaged parts using methods and materials equivalent to the original artist's work. ==== Application techniques ==== By studying the painting methods of various artists and the composition of paints used historically, conservators are able to restore works very closely to their original visual appearance. The picture as a whole determines how to fill in the gap. Helmut Ruhemann's inpainting techniques by Jessell have procedures to "preserve" the quality of oil and tempera paintings. === Digital inpainting === Many programs are able to reconstruct missing or damaged areas of digital photographs and videos. Most widely known for use with digital images is Adobe Photoshop. Given the various abilities of the digital camera and the digitization of old photos, inpainting has become an automatic process that can be performed on digital images. The inpainting techniques can be applied to object removal, text removal, and other automatic modifications of images and videos. In video special effects, inpainting is usually performed after video matting. They can also be observed in applications like image compression and super-resolution. In photography and cinema, it is used for film restoration to reverse, repair, or mitigate deterioration (e.g., physical damage such as cracks in photographs, scratches and dust spots in film, or chemical damage resulting in image loss; performed infrared cleaning). It can also be used for removing red-eye, the stamped date from photographs, and objects for creative effect. This technique can be used to replace any lost blocks in the coding and transmission of images, for example, in a streaming video. It can also be used to remove logos or watermarks in videos. Deep learning neural network-based inpainting can be used for decensoring images. Deep image prior-based techniques can be used for digital image inpainting, where a trained deep learning model is either unavailable or infeasible. Deep models for visual content generation, like text-to-image or text-to-video, learn complex priors over the distribution of visual content, and can be used to inpaint missing parts. For example, videos can be separated into layers, using a technique called omnimatte, which either pretrain an omnimatte model or without any training using an omnimatte-zero model. Three main groups of 2D image-inpainting algorithms can be found in the literature. The first one to be noted is structural (or geometric) inpainting, the second one is texture inpainting, the last one is a combination of these two techniques. They use the information of the known or non-destroyed image areas in order to fill the gap, similar to how physical images are restored. ==== Structural ==== Structural or geometric inpainting is used for smooth images that have strong, defined borders. There are many different approaches to geometric inpainting, but they all come from the idea that geometry can be recovered from similar areas or domains. Bertalmio proposed a method of structural inpainting that mimics how conservators address painting restoration. Bertalmio proposed that by progressively transferring similar information from the borders of an inpainting domain inwards, the gap can be filled. ==== Textural ==== While structural/geometric inpainting works to repair smooth images, textural inpainting works best with images that are heavily textured. Texture has a repetitive pattern which means that a missing portion cannot be restored by continuing the level lines into the gap; level lines provide a complete, stable representation of an image. To repair texture in an image, one can combine frequency and spatial domain information to fill in a selected area with a desired texture. This method, while the most simple and very effective, works well when selecting a texture to be in-painted. For a texture that covers a wider area or a larger frame one would have to go through the image segmenting the areas to be in-painted and selecting the corresponding textures from throughout the image; there are programs that can help find the corresponding areas that work in a similar way as 'find and replace' works in a word processor. ==== Combined structural and textural ==== Combined structural and textural inpainting approaches simultaneously try to perform texture- and structure-filling in regions of missing image information. Most parts of an image consist of texture and structure and the boundaries between image regions contain a large amount of structural information. This is the result when blending differ