AI Data Quality Tools

AI Data Quality Tools — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  YrWall

  YrWall is a Digital Graffiti Wall developed by event company Luma, where designs are created on a large wall using a modified spray paint can. The can contains no paint, instead it has an IR light which is tracked by a computer vision system and the image immediately back-projected onto the wall. The inbuilt YrWall software has much of the functionality of a typical computer paint program, with a pop-out interface which enables users to change colour, spray width, opacity, work with stencils and use animated items such as swirls, stars, drips and splats. Recent additions to YrWall include options to email a JPEG of the completed design and create personalised stickers and T-shirts. == Dragons' Den == The inventor of YrWall, Tom Hogan, and his business partner, Tim Williams, appeared on Episode 4 of Series 8 of the BBC show Dragons' Den. Seeking investment in YrWall, the entrepreneurs were successful in gaining £50,000 for 40% of the YrWall parent company Lumacoustics from Dragons Deborah Meaden and Peter Jones. == World's Largest Interactive Graffiti Wall == In September 2009 YrWall was used to create the 'World's Largest Interactive Graffiti Wall' at the Bristol Festival, UK. Artists used the standard 3.5 m2 YrWall to produce artwork which was in turn projected live onto a 26m x 10m space on the side of the iconic Lloyds amphitheatre building.

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  Factorization of polynomials over finite fields

  In mathematics and computer algebra the factorization of a polynomial consists of decomposing it into a product of irreducible factors. This decomposition is theoretically possible and is unique for polynomials with coefficients in any field, but rather strong restrictions on the field of the coefficients are needed to allow the computation of the factorization by means of an algorithm. In practice, algorithms have been designed only for polynomials with coefficients in a finite field, in the field of rationals or in a finitely generated field extension of one of them. All factorization algorithms, including the case of multivariate polynomials over the rational numbers, reduce the problem to this case; see polynomial factorization. It is also used for various applications of finite fields, such as coding theory (cyclic redundancy codes and BCH codes), cryptography (public key cryptography by the means of elliptic curves), and computational number theory. As the reduction of the factorization of multivariate polynomials to that of univariate polynomials does not have any specificity in the case of coefficients in a finite field, only polynomials with one variable are considered in this article. == Background == === Finite field === The theory of finite fields, whose origins can be traced back to the works of Gauss and Galois, has played a part in various branches of mathematics. Due to the applicability of the concept in other topics of mathematics and sciences like computer science there has been a resurgence of interest in finite fields and this is partly due to important applications in coding theory and cryptography. Applications of finite fields introduce some of these developments in cryptography, computer algebra and coding theory. A finite field or Galois field is a field with a finite order (number of elements). The order of a finite field is always a prime or a power of prime. For each prime power q = pr, there exists exactly one finite field with q elements, up to isomorphism. This field is denoted GF(q) or Fq. If p is prime, GF(p) is the prime field of order p; it is the field of residue classes modulo p, and its p elements are denoted 0, 1, ..., p−1. Thus a = b in GF(p) means the same as a ≡ b (mod p). === Irreducible polynomials === Let F be a finite field. As for general fields, a non-constant polynomial f in F[x] is said to be irreducible over F if it is not the product of two polynomials of positive degree. A polynomial of positive degree that is not irreducible over F is called reducible over F. Irreducible polynomials allow us to construct the finite fields of non-prime order. In fact, for a prime power q, let Fq be the finite field with q elements, unique up to isomorphism. A polynomial f of degree n greater than one, which is irreducible over Fq, defines a field extension of degree n which is isomorphic to the field with qn elements: the elements of this extension are the polynomials of degree lower than n; addition, subtraction and multiplication by an element of Fq are those of the polynomials; the product of two elements is the remainder of the division by f of their product as polynomials; the inverse of an element may be computed by the extended GCD algorithm (see Arithmetic of algebraic extensions). It follows that, to compute in a finite field of non prime order, one needs to generate an irreducible polynomial. For this, the common method is to take a polynomial at random and test it for irreducibility. For sake of efficiency of the multiplication in the field, it is usual to search for polynomials of the shape xn + ax + b. Irreducible polynomials over finite fields are also useful for pseudorandom number generators using feedback shift registers and discrete logarithm over F2n. The number of irreducible monic polynomials of degree n over Fq is the number of aperiodic necklaces, given by Moreau's necklace-counting function Mq(n). The closely related necklace function Nq(n) counts monic polynomials of degree n which are primary (a power of an irreducible); or alternatively irreducible polynomials of all degrees d which divide n. === Example === The polynomial P = x4 + 1 is irreducible over Q but not over any finite field. On any field extension of F2, P = (x + 1)4. On every other finite field, at least one of −1, 2 and −2 is a square, because the product of two non-squares is a square and so we have If − 1 = a 2 , {\displaystyle -1=a^{2},} then P = ( x 2 + a ) ( x 2 − a ) . {\displaystyle P=(x^{2}+a)(x^{2}-a).} If 2 = b 2 , {\displaystyle 2=b^{2},} then P = ( x 2 + b x + 1 ) ( x 2 − b x + 1 ) . {\displaystyle P=(x^{2}+bx+1)(x^{2}-bx+1).} If − 2 = c 2 , {\displaystyle -2=c^{2},} then P = ( x 2 + c x − 1 ) ( x 2 − c x − 1 ) . {\displaystyle P=(x^{2}+cx-1)(x^{2}-cx-1).} === Complexity === Polynomial factoring algorithms use basic polynomial operations such as products, divisions, gcd, powers of one polynomial modulo another, etc. A multiplication of two polynomials of degree at most n can be done in O(n2) operations in Fq using "classical" arithmetic, or in O(nlog(n) log(log(n)) ) operations in Fq using "fast" arithmetic. A Euclidean division (division with remainder) can be performed within the same time bounds. The cost of a polynomial greatest common divisor between two polynomials of degree at most n can be taken as O(n2) operations in Fq using classical methods, or as O(nlog2(n) log(log(n)) ) operations in Fq using fast methods. For polynomials h, g of degree at most n, the exponentiation hq mod g can be done with O(log(q)) polynomial products, using exponentiation by squaring method, that is O(n2log(q)) operations in Fq using classical methods, or O(nlog(q)log(n) log(log(n))) operations in Fq using fast methods. In the algorithms that follow, the complexities are expressed in terms of number of arithmetic operations in Fq, using classical algorithms for the arithmetic of polynomials. == Factoring algorithms == Many algorithms for factoring polynomials over finite fields include the following three stages: Square-free factorization Distinct-degree factorization Equal-degree factorization An important exception is Berlekamp's algorithm, which combines stages 2 and 3. === Berlekamp's algorithm === Berlekamp's algorithm is historically important as being the first factorization algorithm which works well in practice. However, it contains a loop on the elements of the ground field, which implies that it is practicable only over small finite fields. For a fixed ground field, its time complexity is polynomial, but, for general ground fields, the complexity is exponential in the size of the ground field. === Square-free factorization === The algorithm determines a square-free factorization for polynomials whose coefficients come from the finite field Fq of order q = pm with p a prime. This algorithm firstly determines the derivative and then computes the gcd of the polynomial and its derivative. If it is not one then the gcd is again divided into the original polynomial, provided that the derivative is not zero (a case that exists for non-constant polynomials defined over finite fields). This algorithm uses the fact that, if the derivative of a polynomial is zero, then it is a polynomial in xp, which is, if the coefficients belong to Fp, the pth power of the polynomial obtained by substituting x by x1/p. If the coefficients do not belong to Fp, the pth root of a polynomial with zero derivative is obtained by the same substitution on x, completed by applying the inverse of the Frobenius automorphism to the coefficients. This algorithm works also over a field of characteristic zero, with the only difference that it never enters in the blocks of instructions where pth roots are computed. However, in this case, Yun's algorithm is much more efficient because it computes the greatest common divisors of polynomials of lower degrees. A consequence is that, when factoring a polynomial over the integers, the algorithm which follows is not used: one first computes the square-free factorization over the integers, and to factor the resulting polynomials, one chooses a p such that they remain square-free modulo p. Algorithm: SFF (Square-Free Factorization) Input: A monic polynomial f in Fq[x] where q = pm Output: Square-free factorization of f R ← 1 # Make w be the product (without multiplicity) of all factors of f that have # multiplicity not divisible by p c ← gcd(f, f′) w ← f/c # Step 1: Identify all factors in w i ← 1 while w ≠ 1 do y ← gcd(w, c) fac ← w / y R ← R · faci w ← y; c ← c / y; i ← i + 1 end while # c is now the product (with multiplicity) of the remaining factors of f # Step 2: Identify all remaining factors using recursion # Note that these are the factors of f that have multiplicity divisible by p if c ≠ 1 then c ← c1/p R ← R·SFF(c)p end if Output(R) The idea is to identify the product of all irreducible factors of f with the same multiplicity. This is done in two steps. The first step uses the formal d

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  Data transformation (computing)

  In computing, data transformation is the process of converting data from one format or structure into another format or structure. It is a fundamental aspect of most data integration and data management tasks such as data wrangling, data warehousing, data integration and application integration. Data transformation can be simple or complex based on the required changes to the data between the source (initial) data and the target (final) data. Data transformation is typically performed via a mixture of manual and automated steps. Tools and technologies used for data transformation can vary widely based on the format, structure, complexity, and volume of the data being transformed. A master data recast is another form of data transformation where the entire database of data values is transformed or recast without extracting the data from the database. All data in a well-designed database is directly or indirectly related to a limited set of master database tables by a network of foreign key constraints. Each foreign key constraint is dependent upon a unique database index from the parent database table. Therefore, when the proper master database table is recast with a different unique index, the directly and indirectly related data are also recast or restated. The directly and indirectly related data may also still be viewed in the original form since the original unique index still exists with the master data. Also, the database recast must be done in such a way as to not impact the applications architecture software. When the data mapping is indirect via a mediating data model, the process is also called data mediation. == Data transformation process == Data transformation can be divided into the following steps, each applicable as needed based on the complexity of the transformation required. Data discovery Data mapping Code generation Code execution Data review These steps are often the focus of developers or technical data analysts who may use multiple specialized tools to perform their tasks. The steps can be described as follows: Data discovery is the first step in the data transformation process. Typically the data is profiled using profiling tools or sometimes using manually written profiling scripts to better understand the structure and characteristics of the data and decide how it needs to be transformed. Data mapping is the process of defining how individual fields are mapped, modified, joined, filtered, aggregated etc. to produce the final desired output. Developers or technical data analysts traditionally perform data mapping since they work in the specific technologies to define the transformation rules (e.g. visual ETL tools, transformation languages). Code generation is the process of generating executable code (e.g. SQL, Python, R, or other executable instructions) that will transform the data based on the desired and defined data mapping rules. Typically, the data transformation technologies generate this code based on the definitions or metadata defined by the developers. Code execution is the step whereby the generated code is executed against the data to create the desired output. The executed code may be tightly integrated into the transformation tool, or it may require separate steps by the developer to manually execute the generated code. Data review is the final step in the process, which focuses on ensuring the output data meets the transformation requirements. It is typically the business user or final end-user of the data that performs this step. Any anomalies or errors in the data that are found and communicated back to the developer or data analyst as new requirements to be implemented in the transformation process. == Types of data transformation == === Batch data transformation === Traditionally, data transformation has been a bulk or batch process, whereby developers write code or implement transformation rules in a data integration tool, and then execute that code or those rules on large volumes of data. This process can follow the linear set of steps as described in the data transformation process above. Batch data transformation is the cornerstone of virtually all data integration technologies such as data warehousing, data migration and application integration. When data must be transformed and delivered with low latency, the term "microbatch" is often used. This refers to small batches of data (e.g. a small number of rows or a small set of data objects) that can be processed very quickly and delivered to the target system when needed. === Benefits of batch data transformation === Traditional data transformation processes have served companies well for decades. The various tools and technologies (data profiling, data visualization, data cleansing, data integration etc.) have matured and most (if not all) enterprises transform enormous volumes of data that feed internal and external applications, data warehouses and other data stores. === Limitations of traditional data transformation === This traditional process also has limitations that hamper its overall efficiency and effectiveness. The people who need to use the data (e.g. business users) do not play a direct role in the data transformation process. Typically, users hand over the data transformation task to developers who have the necessary coding or technical skills to define the transformations and execute them on the data. This process leaves the bulk of the work of defining the required transformations to the developer, which often in turn do not have the same domain knowledge as the business user. The developer interprets the business user requirements and implements the related code/logic. This has the potential of introducing errors into the process (through misinterpreted requirements), and also increases the time to arrive at a solution. This problem has given rise to the need for agility and self-service in data integration (i.e. empowering the user of the data and enabling them to transform the data themselves interactively). There are companies that provide self-service data transformation tools. They are aiming to efficiently analyze, map and transform large volumes of data without the technical knowledge and process complexity that currently exists. While these companies use traditional batch transformation, their tools enable more interactivity for users through visual platforms and easily repeated scripts. Still, there might be some compatibility issues (e.g. new data sources like IoT may not work correctly with older tools) and compliance limitations due to the difference in data governance, preparation and audit practices. === Interactive data transformation === Interactive data transformation (IDT) is an emerging capability that allows business analysts and business users the ability to directly interact with large datasets through a visual interface, understand the characteristics of the data (via automated data profiling or visualization), and change or correct the data through simple interactions such as clicking or selecting certain elements of the data. Although interactive data transformation follows the same data integration process steps as batch data integration, the key difference is that the steps are not necessarily followed in a linear fashion and typically don't require significant technical skills for completion. There are a number of companies that provide interactive data transformation tools, including Trifacta, Alteryx and Paxata. They are aiming to efficiently analyze, map and transform large volumes of data while at the same time abstracting away some of the technical complexity and processes which take place under the hood. Interactive data transformation solutions provide an integrated visual interface that combines the previously disparate steps of data analysis, data mapping and code generation/execution and data inspection. That is, if changes are made at one step (like for example renaming), the software automatically updates the preceding or following steps accordingly. Interfaces for interactive data transformation incorporate visualizations to show the user patterns and anomalies in the data so they can identify erroneous or outlying values. Once they've finished transforming the data, the system can generate executable code/logic, which can be executed or applied to subsequent similar data sets. By removing the developer from the process, interactive data transformation systems shorten the time needed to prepare and transform the data, eliminate costly errors in the interpretation of user requirements and empower business users and analysts to control their data and interact with it as needed. == Transformational languages == There are numerous languages available for performing data transformation. Many transformation languages require a grammar to be provided. In many cases, the grammar is structured using something closely resembling Backus–Naur form (BNF). There are numerous languages

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  Content engineering

  Content engineering is a term applied to an engineering specialty dealing with the complexities around the use of content in computer-facilitated environments. Content authoring and production, content management, content modeling, content conversion, and content use and repurposing are all areas involving this practice. It is not a specialty with wide industry recognition and is often performed on an ad hoc basis by members of software development or content production or marketing staff, but is beginning to be recognized as a necessary function in any complex content-centric project involving both content production as well as software system development mainly involving content management systems (CMS) or digital experience platforms (DXP). Content engineering tends to bridge the gap between groups involved in the production of content (publishing and editorial staff, marketing, sales, human resources) and more technologically oriented departments such as software development, or IT that put this content to use in web or other software-based environments, and requires an understanding of the issues and processes of both sides. Typically, content engineering involves extensive use of embedded XML technologies, XML being the most widespread language for representing structured content. Content management systems are a key technology often used in the practice of content engineering. == Definition == Content engineering is the practice of organizing the shape and structure of content by deploying content and metadata models, in authoring and publishing processes in a manner that meets the requirements of an organization's Content Strategy, and its implementation through the use of technology such as CMS, XML, schema markup, artificial intelligence, APIs and others. == Purpose and goal == In very general terms, content engineering practices aim to maximize the ROI of content through content reuse and improving efficiency of content marketing, content operations, content strategy. Content engineering can help address content challenges that fairly typical organizations face: Siloed content supply chains Duplicate content in a myriad of formats Inefficient content authoring workflows Chunky, unstructured content Outdated technology Technology in place does not match needs Inability to reuse content across channels (multi-channel content) Metadata and schema are not used Lack of standards for metadata Lack of findability of content for internal and external use Poor SEO performance Inability to implement personalization == Key skills == Content engineering draws on a combination of technical, strategic, and editorial competencies. Practitioners typically require proficiency across several domains: === Content modeling and information architecture === Content engineers design structured content models that define how content is created, stored, and distributed. This includes building taxonomies, ontologies, and metadata schemas that enable content reuse across channels and platforms. === Structured content and markup languages === Proficiency in XML, JSON, HTML, and schema.org markup is fundamental. Content engineers use these languages to structure content for machine readability, search engine optimization, and interoperability between systems. === Content management systems and platforms === Content engineers require working knowledge of content management systems (CMS), digital experience platforms (DXP), and headless CMS architectures. This includes configuring content types, workflows, and publishing pipelines within these systems. === Workflow design and automation === Designing and implementing content workflows - from authoring through review, approval, and distribution - is a core function. Increasingly, this involves configuring AI-assisted and agentic workflows that automate research, drafting, repurposing, and distribution tasks at scale. === Content strategy and editorial understanding === Unlike purely technical roles, content engineering requires a working understanding of content strategy, brand management, editorial standards, and audience analysis. Content engineers must translate strategic objectives into technical content structures and system configurations. === API integration and data interoperability === Content engineers work with APIs to connect content systems, analytics platforms, distribution channels, and third-party services. Understanding how content flows between systems is essential for enabling multi-channel publishing and content personalization. === Analytics and performance measurement === Measuring content effectiveness through web analytics, SEO performance data, and engagement metrics informs how content engineers refine structures, metadata, and distribution workflows. == The role of a content engineer == Content engineers bridge the divide between content strategists and producers and the developers and content managers who publish and distribute content. But rather than simply wedging themselves between these players, content engineers help define and facilitate the content structure during the entire content strategy, production and distribution cycle from beginning to end. As the role has evolved, content engineers are increasingly expected to build and manage AI-powered content systems, moving beyond traditional CMS configuration into agentic workflows that automate content research, production, and distribution. By integrating skills in business and technology, content engineers do not see content as static or finished. Rather, they look at the value of the content and how it can best be adapted and personalized to serve customers and emerging content platforms, technologies, and opportunities. === Create customer experience === Content marketing suffers from two fundamental limitations that constrain the true power and potential that a great content marketing plan can bring to a business' bottom line: Content relevance: how to make content more relevant and personalized to their audiences. The marketer and content strategist direct the customer experience itself, and the content engineer makes it happen with content structure, schema, metadata, microdata, taxonomy, and CMS topology. Content agility: Marketers who are burdened with one-size-fits-all content remain stuck managing their content rather than their customers' experience. Content engineers give marketers the "super powers" to move content-powered experiences across interfaces and personalization variants. === Break down barriers === Empower content strategists: Content engineers work with content strategists by helping them connect content not as a fixed message, but as a modular construct which can be channeled and manipulated. Enable content producers: A content engineer will work with a content producer by helping to find new sources of content and ways the content can be combined and presented. Guide and free developers: The content engineer helps translate marketing strategy into clear technical needs and functions developers can build into content management systems Enhance content management: Develop content structures that make it easier for content writers and content managers to author to a single, very usable, interface for even complex content types that might contain dozens of elements. Engineer content for success: Content engineers help all members of a marketing team work more smoothly, with the support and structures needed to get the most out of the content they produce. === Salary benchmarks === Content engineering roles command significantly higher salaries than traditional content marketing positions. In the United States, IC-level content engineers earn between $120,000 and $165,000 annually, while senior roles reach $160,000 to $220,000. Head of content engineering positions range from $200,000 to $280,000, and VP-level roles can exceed $375,000. The emergence of dedicated content engineer job postings from companies such as Exit Five reflects the growing recognition of the role as a distinct function within marketing organizations.

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  Color quantization

  In computer graphics, color quantization or color image quantization is quantization applied to color spaces; it is a process that reduces the number of distinct colors used in an image, usually with the intention that the new image should be as visually similar as possible to the original image. Computer algorithms to perform color quantization on bitmaps have been studied since the 1970s. Color quantization is critical for displaying images with many colors on devices that can only display a limited number of colors, usually due to memory limitations, and enables efficient compression of certain types of images. The name "color quantization" is primarily used in computer graphics research literature; in applications, terms such as optimized palette generation, optimal palette generation, or decreasing color depth are used. Some of these are misleading, as the palettes generated by standard algorithms are not necessarily the best possible. == Algorithms == Most standard techniques treat color quantization as a problem of clustering points in three-dimensional space, where the points represent colors found in the original image and the three axes represent the three color channels. Almost any three-dimensional clustering algorithm can be applied to color quantization, and vice versa. After the clusters are located, typically the points in each cluster are averaged to obtain the representative color that all colors in that cluster are mapped to. The three color channels are usually red, green, and blue, but another popular choice is the Lab color space, in which Euclidean distance is more consistent with perceptual difference. The most popular algorithm by far for color quantization, invented by Paul Heckbert in 1979, is the median cut algorithm. Many variations on this scheme are in use. Before this time, most color quantization was done using the population algorithm or population method, which essentially constructs a histogram of equal-sized ranges and assigns colors to the ranges containing the most points. A more modern popular method is clustering using octrees, first conceived by Gervautz and Purgathofer and improved by Xerox PARC researcher Dan Bloomberg. If the palette is fixed, as is often the case in real-time color quantization systems such as those used in operating systems, color quantization is usually done using the "straight-line distance" or "nearest color" algorithm, which simply takes each color in the original image and finds the closest palette entry, where distance is determined by the distance between the two corresponding points in three-dimensional space. In other words, if the colors are ( r 1 , g 1 , b 1 ) {\displaystyle (r_{1},g_{1},b_{1})} and ( r 2 , g 2 , b 2 ) {\displaystyle (r_{2},g_{2},b_{2})} , we want to minimize the Euclidean distance: ( r 1 − r 2 ) 2 + ( g 1 − g 2 ) 2 + ( b 1 − b 2 ) 2 . {\displaystyle {\sqrt {(r_{1}-r_{2})^{2}+(g_{1}-g_{2})^{2}+(b_{1}-b_{2})^{2}}}.} This effectively decomposes the color cube into a Voronoi diagram, where the palette entries are the points and a cell contains all colors mapping to a single palette entry. There are efficient algorithms from computational geometry for computing Voronoi diagrams and determining which region a given point falls in; in practice, indexed palettes are so small that these are usually overkill. Color quantization is frequently combined with dithering, which can eliminate unpleasant artifacts such as banding that appear when quantizing smooth gradients and give the appearance of a larger number of colors. Some modern schemes for color quantization attempt to combine palette selection with dithering in one stage, rather than perform them independently. A number of other much less frequently used methods have been invented that use entirely different approaches. The Local K-means algorithm, conceived by Oleg Verevka in 1995, is designed for use in windowing systems where a core set of "reserved colors" is fixed for use by the system and many images with different color schemes might be displayed simultaneously. It is a post-clustering scheme that makes an initial guess at the palette and then iteratively refines it. In the early days of color quantization, the k-means clustering algorithm was deemed unsuitable because of its high computational requirements and sensitivity to initialization. In 2011, M. Emre Celebi reinvestigated the performance of k-means as a color quantizer. He demonstrated that an efficient implementation of k-means outperforms a large number of color quantization methods. The high-quality but slow NeuQuant algorithm reduces images to 256 colors by training a Kohonen neural network "which self-organises through learning to match the distribution of colours in an input image. Taking the position in RGB-space of each neuron gives a high-quality colour map in which adjacent colours are similar." It is particularly advantageous for images with gradients. Finally, one of the newer methods is spatial color quantization, conceived by Puzicha, Held, Ketterer, Buhmann, and Fellner of the University of Bonn, which combines dithering with palette generation and a simplified model of human perception to produce visually impressive results even for very small numbers of colors. It does not treat palette selection strictly as a clustering problem, in that the colors of nearby pixels in the original image also affect the color of a pixel. See sample images. == History and applications == In the early days of PCs, it was common for video adapters to support only 2, 4, 16, or (eventually) 256 colors due to video memory limitations; they preferred to dedicate the video memory to having more pixels (higher resolution) rather than more colors. Color quantization helped to justify this tradeoff by making it possible to display many high color images in 16- and 256-color modes with limited visual degradation. Many operating systems automatically perform quantization and dithering when viewing high color images in a 256 color video mode, which was important when video devices limited to 256 color modes were dominant. Modern computers can now display millions of colors at once, far more than can be distinguished by the human eye, limiting this application primarily to mobile devices and legacy hardware. Nowadays, color quantization is mainly used in GIF and PNG images. GIF, for a long time the most popular lossless and animated bitmap format on the World Wide Web, only supports up to 256 colors, necessitating quantization for many images. Some early web browsers constrained images to use a specific palette known as the web colors, leading to severe degradation in quality compared to optimized palettes. PNG images support 24-bit color, but can often be made much smaller in filesize without much visual degradation by application of color quantization, since PNG files use fewer bits per pixel for palettized images. The infinite number of colors available through the lens of a camera is impossible to display on a computer screen; thus converting any photograph to a digital representation necessarily involves some quantization. Practically speaking, 24-bit color is sufficiently rich to represent almost all colors perceivable by humans with sufficiently small error as to be visually identical (if presented faithfully), within the available color space. However, the digitization of color, either in a camera detector or on a screen, necessarily limits the available color space. Consequently there are many colors that may be impossible to reproduce, regardless of how many bits are used to represent the color. For example, it is impossible in typical RGB color spaces (common on computer monitors) to reproduce the full range of green colors that the human eye is capable of perceiving. With the few colors available on early computers, different quantization algorithms produced very different-looking output images. As a result, a lot of time was spent on writing sophisticated algorithms to be more lifelike. === Quantization for image compression === Many image file formats support indexed color. A whole-image palette typically selects 256 "representative" colors for the entire image, where each pixel references any one of the colors in the palette, as in the GIF and PNG file formats. A block palette typically selects 2 or 4 colors for each block of 4x4 pixels, used in BTC, CCC, S2TC, and S3TC. === Editor support === Many bitmap graphics editors contain built-in support for color quantization, and will automatically perform it when converting an image with many colors to an image format with fewer colors. Most of these implementations allow the user to set exactly the number of desired colors. Examples of such support include: Photoshop's Mode→Indexed Color function supplies a number of quantization algorithms ranging from the fixed Windows system and Web palettes to the proprietary Local and Global algorithms for generating palettes suited to a particu

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  Key Transparency

  Key Transparency allows communicating parties to verify public keys used in end-to-end encryption. In many end-to-end encryption services, to initiate communication a user will reach out to a central server and request the public keys of the user with which they wish to communicate. If the central server is malicious or becomes compromised, a man-in-the-middle attack can be launched through the issuance of incorrect public keys. The communications can then be intercepted and manipulated. Additionally, legal pressure could be applied by surveillance agencies to manipulate public keys and read messages. With Key Transparency, public keys are posted to a public log that can be universally audited. Communicating parties can verify public keys used are accurate.

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  Azuqua

  Azuqua is an American cloud-based integration and automation company headquartered in Seattle, Washington. As such, they integrate SaaS applications and create automations that are designed to eliminate manual work. Azuqua's platform has the ability to set up workflows between multiple applications so disparate teams can stay in the loop. Azuqua's customers include companies such as Charles Schwab, General Electric, General Motors, HubSpot, and Airbnb. == History == Nikhil Hasija and Craig Unger founded Azuqua in 2011. In 2013, the team participated in Techstars Microsoft's Windows Azure Accelerator, a Seattle-based incubator that helps entrepreneurs gain traction through deep mentor engagement and rapid iteration cycles. Azuqua announced in 2014 that they have received their Series A funding from Ignition Partners which amounted to $5 million. 2017 included a 65% growth in new customers, a doubling of new SaaS connectors, and a 50% growth in overall employee headcount. Azuqua also received their Series B funding which totaled to $10.8 million. This funding was led by Insight Ventures Partners, with DFJ and Ignition Partners also joining the round In March 2018, Azuqua hired Todd Owens as CEO. Owens was previously CEO of Appuri, a customer data platform. Hasija has transitioned to the role of Chief Product Officer. Azuqua also hired on Dan Kogan who has taken on the role of Chief Marketing Officer. Kogan previously worked at Tableau, a BI and analytics company, as a Senior Director of Product Marketing. Okta acquired Azuqua in 2019. == Product Description/Features == Logic Library: Logic functions that can be used for data processing, branching logic, and business rules Drag and Drop Visual Designer: No-code visual designer Use of API's for each cloud service a business is using to allow the various apps to communicate and share data API Publishing: Integrations and automations can be made available as secure endpoints, webhooks, or open services Connector Builder: Build a connector to an application Connector Library: Pre-built connectors to SaaS applications Error Handling: Automations that execute when an error is detected

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  Polygraphic substitution

  Polygraphic substitution is a substitution cipher in which a uniform substitution is performed on blocks of letters. When the length of the block is specifically known, more precise terms are used: for instance, a cipher in which pairs of letters are substituted is bigraphic. As a concept, polygraphic substitution contrasts with monoalphabetic (or simple) substitutions in which individual letters are uniformly substituted, or polyalphabetic substitutions in which individual letters are substituted in different ways depending on their position in the text. In theory, there is some overlap in these definitions; one could conceivably consider a Vigenère cipher with an eight-letter key to be an octographic substitution. In practice, this is not a useful observation since it is far more fruitful to consider it to be a polyalphabetic substitution cipher. == Specific ciphers == In 1563, Giambattista della Porta devised the first bigraphic substitution. However, it was nothing more than a matrix of symbols. In practice, it would have been all but impossible to memorize, and carrying around the table would lead to risks of falling into enemy hands. In 1854, Charles Wheatstone came up with the Playfair cipher, a keyword-based system that could be performed on paper in the field. This was followed up over the next fifty years with the closely related four-square and two-square ciphers, which are slightly more cumbersome but offer slightly better security. In 1929, Lester S. Hill developed the Hill cipher, which uses matrix algebra to encrypt blocks of any desired length. However, encryption is very difficult to perform by hand for any sufficiently large block size, although it has been implemented by machine or computer. This is therefore on the frontier between classical and modern cryptography. == Cryptanalysis of general polygraphic substitutions == Polygraphic systems do provide a significant improvement in security over monoalphabetic substitutions. Given an individual letter 'E' in a message, it could be encrypted using any of 52 instructions depending on its location and neighbors, which can be used to great advantage to mask the frequency of individual letters. However, the security boost is limited; while it generally requires a larger sample of text to crack, it can still be done by hand. One can identify a polygraphically-encrypted text by performing a frequency chart of polygrams and not merely of individual letters. These can be compared to the frequency of plaintext English. The distribution of digrams is even more stark than individual letters. For example, the six most common letters in English (23%) represent approximately half of English plaintext, but it takes only the most frequent 8% of the 676 digrams to achieve the same potency. In addition, even in a plaintext many thousands of characters long, one would expect that nearly half of the digrams would not occur, or only barely. In addition, looking over the text one would expect to see a fairly regular scattering of repeated text in multiples of the block length and relatively few that are not multiples. Cracking a code identified as polygraphic is similar to cracking a general monoalphabetic substitution except with a larger 'alphabet'. One identifies the most frequent polygrams, experiments with replacing them with common plaintext polygrams, and attempts to build up common words, phrases, and finally meaning. Naturally, if the investigation led the cryptanalyst to suspect that a code was of a specific type, like a Playfair or order-2 Hill cipher, then they could use a more specific attack.

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  Lessac Technologies

  Lessac Technologies, Inc. (LTI) is an American firm which develops voice synthesis software, licenses technology and sells synthesized novels as MP3 files. The firm currently has seven patents granted and three more pending for its automated methods of converting digital text into human-sounding speech, more accurately recognizing human speech and outputting the text representing the words and phrases of said speech, along with recognizing the speaker's emotional state. The LTI technology is partly based on the work of the late Arthur Lessac, a Professor of Theater at the State University of New York and the creator of Lessac Kinesensic Training, and LTI has licensed exclusive rights to exploit Arthur Lessac's copyrighted works in the fields of speech synthesis and speech recognition. Based on the view that music is speech and speech is music, Lessac's work and books focused on body and speech energies and how they go together. Arthur Lessac's textual annotation system, which was originally developed to assist actors, singers, and orators in marking up scripts to prepare for performance, is adapted in LTI's speech synthesis system as the basic representation of the speech to be synthesized (Lessemes), in contrast to many other systems which use a phonetic representation. LTI's software has two major components: (1) a linguistic front-end that converts plain text to a sequence of prosodic and phonosensory graphic symbols (Lessemes) based on Arthur Lessac's annotation system, which specify the speech units to be synthesized; (2) a signal-processing back-end that takes the Lessemes as acoustic data and produces human-sounding synthesized speech as output, using unit selection and concatenation. LTI's text-to-speech system came in second in the world-wide Blizzard Challenge 2011 and 2012. The first-place team in 2011 also employed LTI's "front-end" technology, but with its own back-end. The Blizzard Challenge, conducted by the Language Technologies Institute of Carnegie Mellon University, was devised as a way to evaluate speech synthesis techniques by having different research groups build voices from the same voice-actor recordings, and comparing the results through listening tests. LTI was founded in 2000 by H. Donald Wilson (chairman), a lawyer, LexisNexis entrepreneur and business associate of Arthur Lessac; and Gary A. Marple (chief inventor), after Marple suggested that Arthur Lessac's kinesensic voice training might be applicable to computational linguistics. After Wilson's death in 2006, his nephew John Reichenbach became the firm's CEO.

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  Knapsack cryptosystems

  Knapsack cryptosystems are cryptosystems whose security is based on the hardness of solving the knapsack problem. They remain quite unpopular because simple versions of these algorithms have been broken for several decades. However, that type of cryptosystem is a good candidate for post-quantum cryptography. The most famous knapsack cryptosystem is the Merkle-Hellman Public Key Cryptosystem, one of the first public key cryptosystems, published the same year as the RSA cryptosystem. However, this system has been broken by several attacks: one from Shamir, one by Adleman, and the low density attack. However, there exist modern knapsack cryptosystems that are considered secure so far: among them is Nasako-Murakami 2006. Knapsack cryptosystems, when not subject to classical cryptoanalysis, are believed to be difficult even for quantum computers. That is not the case for systems that rely on factoring large integers, like RSA, or computing discrete logarithms, like ECDSA, problems solved in polynomial time with Shor's algorithm.

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  Time-lock puzzle

  A time-lock puzzle, or time-released cryptography, encrypts a message that cannot be decrypted until a specified amount of time has passed. The concept was first described by Timothy C. May, and a solution first introduced by Ron Rivest, Adi Shamir, and David A. Wagner in 1996. Time-lock puzzle are useful in cases where confidentiality of information is determined by time, such as a diarist who does not want their views released until 50 years after their death, an auction where bids are sealed until the bidding period is closed, electronic voting, and contract signing. They can additionally be used in creating further cryptographic primitives, such as verifiable delay functions and zero knowledge proofs. Time-released cryptography can be achieved through several different mechanisms. Use mathematical problems requiring sequential calculations to solve, and cannot be solved with parallelization. Thus, adding more computers to a problem will not help solve the problem faster. Use of a trusted agent, or multiple agents who each hold a part of the message and cryptographic keys, who release the message after a specified time period has passed. Distribute public encryption keys to users, and place private cryptographic keys with a trusted agent in an offline location, to be released at a later date.

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  Vans challenge

  The Vans challenge is a viral internet challenge that began in March 2019 where people show their Vans shoes landing right-side up after tossing them in the air. The viral sensation reportedly started after a Twitter user shared a video of the occurrence, which was captioned: “Did you know it doesn’t matter how you throw your Vans they will land facing up.” Since then, multiple people on social media posted similar videos of them throwing their Vans in the air and landing right-side up, along with Crocs, UGG boots, and other popular shoes. This theory proved false, as these shoes have not always landed facing up after tossing them.

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  WhatsApp

  WhatsApp Messenger, commonly known simply as WhatsApp, is an American social media, instant messaging (IM), and Voice over IP (VoIP) service accessible via desktop and mobile app. Owned by Meta Platforms, the service allows users to send text messages, voice messages, and video messages, make voice and video calls, and share images, documents, user locations, and other content. The service requires a cellular mobile telephone number to register. WhatsApp was launched in May 2009. In January 2018, WhatsApp released a standalone business app called WhatsApp Business which can communicate with the standard WhatsApp client. As of May 2025, the service had 3 billion monthly active users, making it the most used messenger app. The name of the app is meant to sound like "what's up". The service was created by WhatsApp Inc. of Mountain View, California, which was acquired by Facebook in February 2014 for approximately US$19.3 billion. It became the world's most popular messaging application in 2015, with 900 million users, and had more than 2 billion active users worldwide in February 2020. WhatsApp Business had approximately 200 million monthly users in 2023. By 2016, it had become the primary means of Internet communication in regions including the Americas, the Indian subcontinent, and large parts of Europe and Africa. == History == === 2009–2014 === WhatsApp was founded by Brian Acton and Jan Koum, former employees of Yahoo. Koum incorporated WhatsApp Inc. in California on February 24, 2009. A month earlier, Koum had purchased an iPhone, and he and Acton decided to create an app for the App Store. The idea started off as an app that would display statuses in a phone's Contacts menu, showing if a person was at work or on a call. Their discussions often took place at the home of Koum's Russian friend Alex Fishman in West San Jose. They realized that to take the idea further, they would need an iPhone developer. Fishman visited RentACoder.com, found Russian developer Igor Solomennikov, and introduced him to Koum. Koum named the app WhatsApp to sound like "what's up" and it was published on the Apple App Store and BlackBerry App World in May and June 2009 respectively. However, when early versions of WhatsApp kept crashing, Koum considered giving up and looking for a new job. Acton encouraged him to wait for a "few more months". In June 2009, when the app had been downloaded by only a handful of Fishman's Russian-speaking friends, Apple launched push technology, allowing users to be pinged even when not using the app. Koum updated WhatsApp so that everyone in the user's network would be notified when a user's status changed. This new facility, to Koum's surprise, was used by users to ping "each other with jokey custom statuses like, 'I woke up late' or 'I'm on my way.'" Fishman said, "At some point it sort of became instant messaging". WhatsApp 2.0, released for iPhone in August 2009, featured a purpose-designed messaging component; the number of active users suddenly increased to 250,000. Although Acton was working on another startup idea, he decided to join the company. In October 2009, Acton persuaded five former friends at Yahoo! to invest $250,000 in seed funding, and Acton became a co-founder and was given a stake. He officially joined WhatsApp on November 1. Koum then hired a friend in Los Angeles, Chris Peiffer, to develop a BlackBerry version, which arrived two months later. Subsequently, WhatsApp for Symbian OS was added in May 2010, and for Android OS in August 2010. In 2010 Google made multiple acquisition offers for WhatsApp, which were all declined. To cover the cost of sending verification texts to users, WhatsApp was changed from a free service to a paid one. In December 2009, the ability to send photos was added to the iOS version. By early 2011, WhatsApp was one of the top 20 apps in the U.S. Apple App Store. In April 2011, Sequoia Capital invested about $8 million for more than 15% of the company, after months of negotiation by Sequoia partner Jim Goetz. By February 2013, WhatsApp had about 200 million active users and 50 staff members. Sequoia invested another $50 million at a $1.5 billion valuation. Some time in 2013 WhatsApp acquired Santa Clara–based startup SkyMobius, the developers of Vtok, a video and voice calling app. As of December 2013, the service had 400 million monthly active users. That year, the company had $148 million in expenses and a net loss of $138 million. === 2014–2015 === On February 19, 2014, one year after the venture capital financing round at a $1.5 billion valuation, Facebook, Inc. (now Meta Platforms) agreed to acquire the company for US$19 billion, its largest acquisition to date. At the time, it was the largest acquisition of a venture-capital-backed company in history. Sequoia Capital received an approximate 5,000% return on its initial investment. Facebook paid $4 billion in cash, $12 billion in Facebook shares, and an additional $3 billion in restricted stock units granted to WhatsApp's founders Koum and Acton. Employee stock was scheduled to vest over four years subsequent to closing. Days after the announcement, WhatsApp users experienced a loss of service, leading to anger across social media. The acquisition was influenced by the data provided by Onavo, Facebook's research app for monitoring competitors and trending usage of social activities on mobile phones, as well as startups that were performing "unusually well". The acquisition caused many users to try, or move to, other message services. Telegram claimed that it acquired 8 million new users, and Line, 2 million. At a keynote presentation at the Mobile World Congress in Barcelona in February 2014, Facebook CEO Mark Zuckerberg said that Facebook's acquisition of WhatsApp was closely related to the Internet.org vision. A TechCrunch article said about Zuckerberg's vision:The idea, he said, is to develop a group of basic internet services that would be free of charge to use – "a 911 for the internet". These could be a social networking service like Facebook, a messaging service, maybe search and other things like weather. Providing a bundle of these free of charge to users will work like a gateway drug of sorts – users who may be able to afford data services and phones these days just don't see the point of why they would pay for those data services. This would give them some context for why they are important, and that will lead them to pay for more services like this – or so the hope goes. Three days after announcing the Facebook purchase, Koum said they were working to introduce voice calls. He also said that new mobile phones would be sold in Germany with the WhatsApp brand, and that their ultimate goal was to be on all smartphones. In August 2014, WhatsApp was the most popular messaging app in the world, with more than 600 million users. By early January 2015, WhatsApp had 700 million monthly users and over 30 billion messages every day. In April 2015, Forbes predicted that between 2012 and 2018, the telecommunications industry would lose $386 billion because of "over-the-top" services like WhatsApp and Skype. That month, WhatsApp had over 800 million users. By September 2015, it had grown to 900 million; and by February 2016, one billion. On November 30, 2015, the Android WhatsApp client made links to Telegram unclickable and not copyable. Multiple sources confirmed that it was intentional, not a bug, and that it had been implemented when the Android source code that recognized Telegram URLs had been identified. (The word "telegram" appeared in WhatsApp's code.) Some considered it an anti-competitive measure; WhatsApp offered no explanation. === 2016–2019 === On January 18, 2016, WhatsApp's co-founder Jan Koum announced that it would no longer charge users a $1 annual subscription fee, in an effort to remove a barrier faced by users without payment cards. He also said that the app would not display any third-party ads, and that it would have new features such as the ability to communicate with businesses. On May 18, 2017, the European Commission announced that it was fining Facebook €110 million for "providing misleading information about WhatsApp takeover" in 2014. The Commission said that in 2014 when Facebook acquired the messaging app, it "falsely claimed it was technically impossible to automatically combine user information from Facebook and WhatsApp." However, in the summer of 2016, WhatsApp had begun sharing user information with its parent company, allowing information such as phone numbers to be used for targeted Facebook advertisements. Facebook acknowledged the breach, but said the errors in their 2014 filings were "not intentional". In September 2017, WhatsApp's co-founder Brian Acton left the company to start a nonprofit group, later revealed as the Signal Foundation, which developed the WhatsApp competitor Signal. He explained his reasons for leaving in an interview with Forbes a year later. WhatsApp also

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  AS1 (networking)

  AS1 (Applicability Statement 1) is a specification about how to transport structured business-to-business data securely and reliably over the Internet. Security is achieved by using digital certificates and encryption. == AS1 technical overview == The AS1 protocol is based on SMTP and S/MIME. It was the first AS protocol developed and uses signing, encryption and MDN conventions. In other words: Files are sent as "attachments" in a specially coded SMIME email message Messages can be signed, but do not have to be Messages can be encrypted, but do not have to be Messages may request an MDN back if all went well, but do not have to request such a message If the original AS1 message requested an MDN... Upon the receipt of the message and its successful decryption or signature validation (as necessary) a "success" MDN will be sent back to the original sender. This MDN is typically signed but not encrypted. Upon the receipt and successful verification of the signature on the MDN, the original sender will "know" that the recipient got their message (this provides the "Non-repudiation" element of AS1) If there are any problems receiving or interpreting the original AS1 message, a "failed" MDN may be sent back. Like any other AS file transfer, AS1 file transfers typically require both sides of the exchange to trade X.509 certificates and specific "trading partner" names before any transfers can take place.

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  Campus network

  A campus network, campus area network, corporate area network or CAN is a computer network made up of an interconnection of local area networks (LANs) within a limited geographical area. The networking equipments (switches, routers) and transmission media (optical fiber, copper plant, Cat5 cabling etc.) are almost entirely owned by the campus tenant / owner: an enterprise, university, government etc. A campus area network is larger than a local area network but smaller than a metropolitan area network (MAN) or wide area network (WAN). == University campuses == College or university campus area networks often interconnect a variety of buildings, including administrative buildings, academic buildings, laboratories, university libraries, or student centers, residence halls, gymnasiums, and other outlying structures, like conference centers, technology centers, and training institutes. Early examples include the Stanford University Network at Stanford University, Project Athena at MIT, and the Andrew Project at Carnegie Mellon University. == Corporate campuses == Much like a university campus network, a corporate campus network serves to connect buildings. Examples of such are the networks at Googleplex and Microsoft's campus. Campus networks are normally interconnected with high speed Ethernet links operating over optical fiber such as gigabit Ethernet and 10 Gigabit Ethernet. == Area range == The range of CAN is 1 to 5 km (1 to 3 mi). If two buildings have the same domain and they are connected with a network, then it will be considered as CAN only. Though the CAN is mainly used for corporate campuses so the link will be high speed.

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