AI Chatbot Options

AI Chatbot Options — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

  • Procreate (software)

    Procreate (software)

    Procreate is a raster graphics editor app for digital painting developed and published by the Australian company Savage Interactive for iOS and iPadOS. It was launched on the App Store in 2011. == Versions == === Procreate === Procreate for iPad was first released in 2011 by the Tasmanian software company Savage Interactive. In June 2013, Savage launched Procreate 2 in conjunction with iOS 7, adding new features such as higher resolution capabilities and more brush options. In 2016, Procreate became one of the top ten best-selling iPad apps on the App Store. In 2018, Procreate became the overall best selling iPad app. With iOS 26, Procreate adapted Liquid Glass into its software. As of March 2026, the most recent version of Procreate for the iPad is 5.4.9. === Procreate Pocket === Procreate Pocket was released to the App Store in December 2014. In 2018, Savage launched Procreate Pocket 2.0 to the App Store. In December 2018, Procreate Pocket received Apple's "App of the Year" award. As of September 2025, the most recent version of Procreate Pocket (for the iPhone) is 4.0.15. === Procreate Dreams === Procreate Dreams, their more recent app focused on 2D animation, was released on the App Store on November 22, 2023. While the application is commended for its intuitive interface and accessibility, some reviewers have noted that it may lack some key animations features, such as reference layers. In June 2024, Procreate Dreams received the 2024 Apple Design Award for Innovation. In December 2025, Savage Interactive released Procreate Dreams 2, a long awaited update and redesign to Procreate Dreams. == Features == The current versions of Procreate use Valkyrie, a proprietary graphics engine to allow customisable brush options and importing brushes from Adobe Photoshop. Procreate offers known features like layers, masks, and blending mode. Its biggest standout compared to other professional drawing software is its simple UI and comparatively easy learning curve. The app also allows for animation. Savage expanded upon Procreate's animation features with a companion app dedicated to 2D animation called Procreate Dreams, released in November 2023. On August 2024, Procreate announced that it would not be incorporating generative artificial intelligence into its software. Savage offers a free internet forum called Procreate Discussions in which users can ask for help, suggest ideas, and share user-generated content on the marketplace or the resources board. == Notable users == Concept artist Doug Chiang creates robot, vehicle, and creature designs for Star Wars in Procreate. Professional artists have also used Procreate to create the posters for Stranger Things, Logan, and Blade Runner 2049, as well as several covers for The New Yorker. It has also been professionally adopted at Marvel Comics, DC Comics, Disney Animation, and Pixar.

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  • Snake oil (cryptography)

    Snake oil (cryptography)

    In cryptography, snake oil is any cryptographic method or product considered to be bogus or fraudulent. The name derives from snake oil, one type of patent medicine widely available in the 19th century United States. Distinguishing secure cryptography from insecure cryptography can be difficult from the viewpoint of a user. Many cryptographers, such as Bruce Schneier and Phil Zimmermann, undertake to educate the public in how secure cryptography is done, as well as highlighting the misleading marketing of some cryptographic products. The Snake Oil FAQ describes itself as "a compilation of common habits of snake oil vendors. It cannot be the sole method of rating a security product, since there can be exceptions to most of these rules. [...] But if you're looking at something that exhibits several warning signs, you're probably dealing with snake oil." == Some examples of snake oil cryptography techniques == This is not an exhaustive list of snake oil signs. A more thorough list is given in the references. Secret system Some encryption systems will claim to rely on a secret algorithm, technique, or device; this is categorized as security through obscurity. Criticisms of this are twofold. First, a 19th-century rule known as Kerckhoffs's principle, later formulated as Shannon's maxim, teaches that "the enemy knows the system" and the secrecy of a cryptosystem algorithm does not provide any advantage. Second, secret methods are not open to public peer review and cryptanalysis, so potential mistakes and insecurities can go unnoticed. Technobabble Snake oil salespeople may use "technobabble" to sell their product since cryptography is a complicated subject. "Unbreakable" Claims of a system or cryptographic method being "unbreakable" are always false (or true under some limited set of conditions), and are generally considered a sure sign of snake oil. "Military grade" There is no accepted standard or criterion for "military grade" ciphers. One-time pads One-time pads are a popular cryptographic method to invoke in advertising, because it is well known that one-time pads, when implemented correctly, are genuinely unbreakable. The problem comes in implementing one-time pads, which is rarely done correctly. Cryptographic systems that claim to be based on one-time pads are considered suspect, particularly if they do not describe how the one-time pad is implemented, or they describe a flawed implementation. Unsubstantiated "bit" claims Cryptographic products are often accompanied with claims of using a high number of bits for encryption, apparently referring to the key length used. However key lengths are not directly comparable between symmetric and asymmetric systems. Furthermore, the details of implementation can render the system vulnerable. For example, in 2008 it was revealed that a number of hard drives sold with built-in "128-bit AES encryption" were actually using a simple and easily defeated "XOR" scheme. AES was only used to store the key, which was easy to recover without breaking AES.

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  • List of cryptography journals

    List of cryptography journals

    List of cryptography journals includes notable peer-reviewed academic journals that focus on cryptography, cryptanalysis, information security, and related areas in computer science and mathematics. == Notable journals == Cryptologia Designs, Codes and Cryptography IEEE Transactions on Information Theory International Journal of Information Security Journal of Cryptology Journal of Computer Security ACM Transactions on Privacy and Security Information Processing Letters Information and Computation

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  • Data exchange

    Data exchange

    Data exchange is the process of moving data from one information system to another. It often involves transforming data that is native to the source system into a form that is consumable by the target system or to a standardized form that is consumable by any compatible system. In particular, data exchange allows data to be shared between computer programs. Data exchange is similar to data integration except that data may be restructured with possible loss of content. There may be no way to transform a particular collection based on exchange constraints. Conversely, there may be multiple ways to transform the data, in which case one option must be identified in order to achieve compatibility between source and target. There are two main types of data exchange: broadcast and peer-to-peer (a.k.a. unicast). For broadcast, data is transmitted simultaneously to all consumers. Just as a conference call, all participants get the same information from the speaker at the same time. For peer-to-peer, data is sent to a single receiver, defined by a specific address. For example, a letter goes to just one mail box. == Single-domain == In some domains, a multiple source and target schema (proprietary data formats) may exist. An exchange or interchange format is often developed for a single domain, and then necessary routines (mappings) are written to (indirectly) transform/translate each and every source schema to each and every target schema by using the interchange format as an intermediate step. That requires less work than writing and debugging the many routines that would be required to directly translate each source schema directly to each target schema. Examples of these transformative interchange formats include: Standard Interchange Format for geospatial data; Data Interchange Format for spreadsheet data; Open Document Format for spreadsheets, charts, presentations and word processing documents; GPS eXchange Format or Keyhole Markup Language for describing GPS data; GDSII for integrated circuit layout. == Representation == A data exchange (a.k.a. interchange) language defines a domain-independent way to represent data. These languages have evolved from being markup and display-oriented to support the encoding of metadata that describes the structural attributes of the information. Practice has shown that certain types of formal languages are better suited for this task than others, since their specification is driven by a formal process instead of particular software implementation. For example, XML is a markup language that was designed to enable the creation of dialects (the definition of domain-specific sublanguages). However, it does not contain domain-specific dictionaries or fact types. Beneficial to a reliable data exchange is the availability of standard dictionaries-taxonomies and tools libraries such as parsers, schema validators, and transformation tools. === XML === The popularity of XML for data exchange on the World Wide Web has several reasons. First of all, it is closely related to the preexisting standards Standard Generalized Markup Language (SGML) and Hypertext Markup Language (HTML), and as such a parser written to support these two languages can be easily extended to support XML as well. For example, XHTML has been defined as a format that is formal XML, but understood correctly by most (if not all) HTML parsers. === YAML === YAML was designed to be human-readable and authored via a text editor with notion similar to reStructuredText and wiki syntax. YAML 1.2 also includes a shorthand notion that is compatible with JSON, and as such any JSON document is also valid YAML; this however does not hold the other way. === REBOL === REBOL was designed to be human-readable and authored via a text editor. It uses a simple free-form syntax with minimal punctuation and a rich set of data types (such as URL, email, date and time, tuple, string, tag) that respect common standards. It is designed to not need any additional meta-language, being designed in a metacircular fashion which is why the parse dialect used for definitions and transformations of REBOL dialects is also itself a dialect of REBOL. REBOL was used as a source of inspiration for JSON. === Gellish === Gellish English is a formalized subset of natural English (language), which includes a simple grammar and a large, extensible dictionary (taxonomy) that defines the general and domain specific terminology, whereas the concepts are arranged in a hierarchy, which supports inheritance of knowledge and requirements. The dictionary also includes standardized fact types. The terms and relation types together can be used to create and interpret expressions of facts, knowledge, requirements and other information. Gellish can be used in combination with SQL, RDF/XML, OWL and various other meta-languages. The Gellish standard is a combination of ISO 10303-221 (AP221) and ISO 15926. === List === The following describes and compares popular data exchange languages. Columns Schemas – Whether supports representing domain specific data structure definition Flexible – Whether supports extension of the semantic expression capabilities without modifying the schema Semantic verification – Whether supports semantic verification of the correctness of expressions in the language Dictionary – Whether includes a dictionary and a taxonomy (hierarchy) of concepts with inheritance Information model – Whether supports an information model Synonyms and homonyms – Whether supports the use of synonyms and homonyms in expressions Dialecting – Whether is available in multiple natural languages or dialects Web standard – Whether is standardized by a recognized body Transformations – Whether includes a translation to other standards Lightweight – Whether a lightweight version is available Human readable – Whether expressions are understandable without training Compatibility – Which other tools can be used or are required

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  • Skipper (computer software)

    Skipper (computer software)

    Skipper is a visualization tool and code/schema generator for PHP ORM frameworks like Doctrine2, Doctrine, Propel, and CakePHP, which are used to create database abstraction layer. Skipper is developed by Czech company Inventic, s.r.o. based in Brno, and was known as ORM Designer prior to rebranding in 2014. == Overview == Generates visual model from the schema definition files Repetitive import/export of schema definitions in supported formats (XML, YML, PHP annotations) Schema definition files are automatically generated from the visual model Visual representation uses ER diagram extended by concepts of inheritance and many-to-many Supports customization using .xml configuration files and JavaScript Does not support direct connections to the database Crude and simplistic visual representation and menus == Architecture == Skipper was built on the Qt framework. Import/export of the schema definitions uses XSL transformations powered by LibXslt library. Imported source files are first converted to XML format: no conversion for XML, simple conversion for YML, creating the Abstract Syntax Tree and its subsequent conversion to XML for PHP annotations. The import/export scripts are configured in JavaScript and can be freely customized. == Supported ORM frameworks == Frameworks supported for visual model and schema files generation: Doctrine2 Doctrine CakePHP == History == Skipper was created as an internal tool for the web applications developed by Inventic. It was first published as a commercial tool under the name ORM Designer in 2009. Application was reworked and optimized in January 2013, and released as ORM Designer 2. In May 2013 ORM Designer became part of the South Moravian Innovation Center Incubator program (support program for innovative technological startups). In June 2014, ORM Designer version 3 was released and rebranded under the name of Skipper

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  • Protecting Kids From Social Media Act

    Protecting Kids From Social Media Act

    Protecting Kids on Social Media Act or HB 1891 is an American law that was introduced by William Lamberth of Sumner County, Tennessee and was signed into law by Tennessee's governor on May 2, 2024. The bill requires social media websites such as X, YouTube, TikTok, Facebook and others to verify the age of users and if those users are under 18, they must have parental consent. == Progress == The law passed the Tennessee State Legislature with little opposition: the bill had only two no votes in the House from Aftyn Behn and Vincent B. Dixie, and it had zero no votes in the Senate. == Bill summary == Every social media company must verify the age of new users after the law takes effect, and if the user had created an account before the law took effect, they must verify the age of the person attempting to access the account within 14 days. If the new user or the user who originally owned an account is under 18 years of age, they must get parental consent and the third party or social media company must not retain the data from the age verification process or obtaining parental consent. Parents who are account holders of those under 18 can view the privacy settings, set daily time restrictions, and implement breaks during which the minor cannot access the account. The law is enforced by the Attorney General of Tennessee and went into effect on January 1, 2025. == Lawsuit == On October 3, 2024, the trade association NetChoice filed a lawsuit against Tennessee Attorney General Jonathan Skrmetti in the Middle District Court of Tennessee, claiming that the law violates the First Amendment. The Judge for the case is William L. Campbell Jr. An initial case management conference was originally scheduled for December 4, 2024, however it was delayed because of the Supreme Court case United States v. Skrmetti, recommending that the conference be delayed after January 20, 2025. On February 14, 2025, Judge Eli Richardson denied NetChoice's motion for a temporary restraining order because it would disrupt the status quo of the case.

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  • Simply Local

    Simply Local

    Simply Local is a decentralized community social networking and neighborhood broadcasting service developed by Simply Local, based in New Delhi. The app is used as a tool by residents to bridge the information gap and know what is happening in the locality. Simply Local creates private geo-fenced networks for people living in an area and provides social and community related services within that network. The user doesn’t post to a single person but broadcasts to a chosen community. One of its primary purposes is also to connect citizens to their elected representatives. Each community is independent of the other and information shared remains telescoped to that particular community. The app has been designed to maintain privacy and security of users and provides decentralized social networking in the sense that it forms an owner-independent, micro community, which is not connected with the world outside. Simply Local is available on Android Play and iOS App Store. It is available in two languages - English and Hindi. Simply Local’s founder and CEO is Nikhil Bapna. == History == 2020 May: Included as a Top 5 Useful App by Zee News. 2020: Used to connect candidates with local residents during the Delhi assembly elections. 2019: Renamed from Gadfly to its current name. 2018: Used for Karnataka State Elections to get detailed information on candidates. 2017: Launched under the name Gadfly as a tool to connect citizens with their elected representatives.

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  • Correlation immunity

    Correlation immunity

    In mathematics, the correlation immunity of a Boolean function is a measure of the degree to which its outputs are uncorrelated with some subset of its inputs. Specifically, a Boolean function is said to be correlation-immune of order m if every subset of m or fewer variables in x 1 , x 2 , … , x n {\displaystyle x_{1},x_{2},\ldots ,x_{n}} is statistically independent of the value of f ( x 1 , x 2 , … , x n ) {\displaystyle f(x_{1},x_{2},\ldots ,x_{n})} . == Definition == A function f : F 2 n → F 2 {\displaystyle f:\mathbb {F} _{2}^{n}\rightarrow \mathbb {F} _{2}} is k {\displaystyle k} -th order correlation immune if for any independent n {\displaystyle n} binary random variables X 0 … X n − 1 {\displaystyle X_{0}\ldots X_{n-1}} , the random variable Z = f ( X 0 , … , X n − 1 ) {\displaystyle Z=f(X_{0},\ldots ,X_{n-1})} is independent from any random vector ( X i 1 … X i k ) {\displaystyle (X_{i_{1}}\ldots X_{i_{k}})} with 0 ≤ i 1 < … < i k < n {\displaystyle 0\leq i_{1}<\ldots Read more →

  • Advanced automation functions

    Advanced automation functions

    In automation production technology the actions performed by an automated process are executed by a program of instructions which is run during a work cycle. To execute work cycle programs, an automated system should be available to execute these advanced functions. == Safety monitoring == If there is a need for workers in an automated system, a safety monitoring is required for the occupational safety and health of the workers. In a safety monitoring various steps can take place including a complete stop of the system, sounding an alarm or reducing the operating speed. Usually, limiting switches are sensors like temperature probes, heat and smoke detectors or pressure sensitive floor pads. == Maintenance and repair diagnostics == There are three modes of operations which are used in a cycle of maintenance and repair diagnostics: status monitoring, failure diagnostics and recommendation of the repair procedure. In the status monitoring mode, the current system status is displayed. The failure diagnostics mode takes place when a failure occurs. The system will then suggest an adequate repair procedure to a team of experts. == Error detection and recovery == The error detection mode is a step to determine if and when a failure occurs in automated system. The possible errors can be divided into three categories. random errors, systematic errors and aberrations. While in the error recovery mode, remedy actions take place for all detected errors.

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  • Cognos ReportNet

    Cognos ReportNet

    Cognos ReportNet (CRN) was a web-based software product for creating and managing ad hoc and custom-made reports. ReportNet was developed by the Ottawa-based company Cognos (formerly Cognos Incorporated), an IBM company. The web-based reporting tool was launched in September 2003. Since IBM's acquisition of Cognos, ReportNet has been renamed IBM Cognos ReportNet like all other Cognos products. ReportNet uses web services standards such as XML and Simple Object Access Protocol and also supports dynamic HTML and Java. ReportNet is compatible with multiple databases including Oracle, SAP, Teradata, Microsoft SQL server, DB2 and Sybase. The product provides interface in over 10 languages, has Web Services architecture to meet the needs of multi-national, diversified enterprises and helps reduce total cost of ownership. Multiple versions of Cognos ReportNet have since been released by the company. Cognos ReportNet was awarded the Software and Information Industry Association (SIIA) 2005 Codie awards for the "Best Business Intelligence or Knowledge Management Solution" category. CRN's capabilities have been further used in IBM Cognos 8 BI (2005), the latest reporting tool. CRN comes with its own software development kit (SDK). == Launch == Early adopters of Cognos ReportNet for their corporate reporting needs included Bear Stearns, BMW and Alfred Publishing. Around this same time of launch, Cognos competitor Business Objects released version 6.1 of its enterprise reporting tool. Cognos ReportNet has been successful since its launch, raising revenues in 2004 from licensing fees. == Controversy == Cognos rival Business Objects announced in 2005 that BusinessObjects XI significantly outperformed Cognos ReportNet in benchmark tests conducted by VeriTest, an independent software testing firm. The tests performed showed Cognos ReportNet performed poorly when processing styled reports, complex business reports and combination of both. The tests reported a massive 21 times higher report throughput for BusinessObjects XI than Cognos ReportNet at capacity loads. Cognos soon dismissed the claims by stating Business Objects dictated the environment and testing criteria and Cognos did not provide the software to participate in benchmark test. Cognos later performed their own test to demonstrate Cognos ReportNet capabilities. == Components == Cognos Report Studio – A Web-based product for creating complex professional looking reports. Cognos Query Studio - A Web-based product for creating ad-hoc reports. Cognos Framework Manager – A metadata modeling tool to create BI metadata for reporting and dashboard applications. Cognos Connection – Main portal used to access reports, schedule reports and perform administrator activities. == Versions == Cognos ReportNet 1.1 – Java EE-style professional web-based authoring tool. (base version) Cognos ReportNet IBM Special Edition – comes with an embedded version of IBM WebSphere as its application server and IBM DB2 as its data store. Cognos Linux – for Intel-based Linux platforms.

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  • Content management

    Content management

    Content management (CM) are a set of processes and technologies that support the collection, managing, and publishing of information in any form or medium. When stored and accessed via computers, this information may be more specifically referred to as digital content, or simply as content. Digital content may take the form of text (such as electronic documents), images, multimedia files (such as audio or video files), or any other file type that follows a content lifecycle requiring management. The process of content development and management is complex enough that various commercial software vendors (large and small), such as Interwoven and Microsoft, offer content management software to control and automate significant aspects of the content lifecycle. == Process == Content management practices and goals vary by mission and by organizational governance structure. News organizations, e-commerce websites, and educational institutions all use content management, but in different ways. This leads to differences in terminology and in the names and number of steps in the process. For example, some digital content is created by one or more authors. Over time that content may be edited. One or more individuals may provide some editorial oversight, approving the content for publication. Publishing may take many forms: it may be the act of "pushing" content out to others, or simply granting digital access rights to certain content to one or more individuals. Later that content may be superseded by another version of the content and thus retired or removed from use (as when this wiki page is modified). Content management is an inherently collaborative process. It often consists of the following basic roles and responsibilities: Creator – responsible for creating and editing content. Editor – responsible for tuning the content message and the style of delivery, including translation and localization. Publisher – responsible for releasing the content for use. Administrator – responsible for managing access permissions to folders, collections and files, usually accomplished by assigning access rights to user groups or roles. Admins may also assist and support users in various ways. Consumer, viewer or guest – the person who reads or otherwise consumes the content after it is published or shared. A critical aspect of content management is the ability to manage versions of content as it evolves (see also version control). Authors and editors often need to restore older versions of edited products due to a process failure or an undesirable series of edits. Time-sensitive content may also require updates as the subject matter evolves over time. Another equally important aspect of content management involves the creation, maintenance, and application of review standards. Each member of the content creation and review process has a unique role and set of responsibilities in the development or publication of the content. Each review team member requires clear and concise review standards. These must be maintained on an ongoing basis to ensure the long-term consistency and health of the knowledge base. A content management system is a set of automated processes that may support the following features: Import and creation of documents and multimedia material Identification of all key users and their roles The ability to assign roles and responsibilities to different instances of content categories or types Definition of workflow tasks often coupled with messaging so that content managers are alerted to changes in content The ability to track and manage multiple versions of a single instance of content The ability to publish the content to a repository to support access The ability to personalize content based on a set of rules Increasingly, the repository is an inherent part of the system, and incorporates enterprise search and retrieval. Content management systems take the following forms: Web content management system—software for web site management (often what content management implicitly means) Output of a newspaper editorial staff organization Workflow for article publication Document management systems Knowledge management software Single source content management system—content stored in chunks within a relational database Variant management system—where personnel tag source content (usually text and graphics) to represent variants stored as single source "master" content modules, resolved to the desired variant at publication (for example: automobile owners manual content for 12 model years stored as single master content files and "called" by model year as needed)—often used in concert with database chunk storage (see above) for large content objects == Governance structures == Content management expert Marc Feldman defines three primary content management governance structures: localized, centralized, and federated—each having its unique strengths and weaknesses. === Localized governance === By putting control in the hands of those closest to the content, the context experts, localized governance models empower and unleash creativity. These benefits come, however, at the cost of a partial-to-total loss of managerial control and oversight. === Centralized governance === When the levers of control are strongly centralized, content management systems are capable of delivering an exceptionally clear and unified brand message. Moreover, centralized content management governance structures allow for a large number of cost-savings opportunities in large enterprises, realized, for example, through (1) the avoidance of duplicated efforts in creating, editing, formatting, repurposing and archiving content; (2) process management and the streamlining of all content related labor; and/or (3) an orderly deployment or updating of the content management system. === Federated governance === Federated governance models potentially realize the benefits of both localized and centralized control while avoiding the weaknesses of both. While content management software systems are inherently structured to enable federated governance models, realizing these benefits can be difficult because it requires, for example, negotiating the boundaries of control with local managers and content creators. In the case of larger enterprises, in particular, the failure to fully implement or realize a federated governance structure equates to a failure to realize the full return on investment and cost savings that content management systems enable. == Implementation == Content management implementations must be able to manage content distributions and digital rights in content life cycle. Content management systems are usually involved with digital rights management in order to control user access and digital rights. In this step, the read-only structures of digital rights management systems force some limitations on content management, as they do not allow authors to change protected content in their life cycle. Creating new content using managed (protected) content is also an issue that gets protected contents out of management controlling systems. A few content management implementations cover all these issues.

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  • Visual cryptography

    Visual cryptography

    Visual cryptography is a cryptographic technique which allows visual information (pictures, text, etc.) to be encrypted in such a way that the decrypted information appears as a visual image. One of the best-known techniques has been credited to Moni Naor and Adi Shamir, who developed it in 1994. They demonstrated a visual secret sharing scheme, where a binary image was broken up into n shares so that only someone with all n shares could decrypt the image, while any n − 1 shares revealed no information about the original image. Each share was printed on a separate transparency, and decryption was performed by overlaying the shares. When all n shares were overlaid, the original image would appear. There are several generalizations of the basic scheme including k-out-of-n visual cryptography, and using opaque sheets but illuminating them by multiple sets of identical illumination patterns under the recording of only one single-pixel detector, which exposed the image. Using a similar idea, transparencies can be used to implement a one-time pad encryption, where one transparency is a shared random pad, and another transparency acts as the ciphertext. Normally, there is an expansion of space requirement in visual cryptography. But if one of the two shares is structured recursively, the efficiency of visual cryptography can be increased to 100%. Some antecedents of visual cryptography are in patents from the 1960s. Other antecedents are in the work on perception and secure communication. Visual cryptography can be used to protect biometric templates in which decryption does not require any complex computations. == Example == In this example, the binary image has been split into two component images. Each component image has a pair of pixels for every pixel in the original image. These pixel pairs are shaded black or white according to the following rule: if the original image pixel was black, the pixel pairs in the component images must be complementary; randomly shade one ■□, and the other □■. When these complementary pairs are overlapped, they will appear dark gray. On the other hand, if the original image pixel was white, the pixel pairs in the component images must match: both ■□ or both □■. When these matching pairs are overlapped, they will appear light gray. So, when the two component images are superimposed, the original image appears. However, without the other component, a component image reveals no information about the original image; it is indistinguishable from a random pattern of ■□ / □■ pairs. Moreover, if you have one component image, you can use the shading rules above to produce a counterfeit component image that combines with it to produce any image at all. == (2, n) visual cryptography sharing case == Sharing a secret with an arbitrary number of people, n, such that at least 2 of them are required to decode the secret is one form of the visual secret sharing scheme presented by Moni Naor and Adi Shamir in 1994. In this scheme we have a secret image which is encoded into n shares printed on transparencies. The shares appear random and contain no decipherable information about the underlying secret image, however if any 2 of the shares are stacked on top of one another the secret image becomes decipherable by the human eye. Every pixel from the secret image is encoded into multiple subpixels in each share image using a matrix to determine the color of the pixels. In the (2, n) case, a white pixel in the secret image is encoded using a matrix from the following set, where each row gives the subpixel pattern for one of the components: {all permutations of the columns of} : C 0 = [ 1 0 . . . 0 1 0 . . . 0 . . . 1 0 . . . 0 ] . {\displaystyle \mathbf {C_{0}=} {\begin{bmatrix}1&0&...&0\\1&0&...&0\\...\\1&0&...&0\end{bmatrix}}.} While a black pixel in the secret image is encoded using a matrix from the following set: {all permutations of the columns of} : C 1 = [ 1 0 . . . 0 0 1 . . . 0 . . . 0 0 . . . 1 ] . {\displaystyle \mathbf {C_{1}=} {\begin{bmatrix}1&0&...&0\\0&1&...&0\\...\\0&0&...&1\end{bmatrix}}.} For instance in the (2,2) sharing case (the secret is split into 2 shares and both shares are required to decode the secret) we use complementary matrices to share a black pixel and identical matrices to share a white pixel. Stacking the shares we have all the subpixels associated with the black pixel now black while 50% of the subpixels associated with the white pixel remain white. == Cheating the (2, n) visual secret sharing scheme == Horng et al. proposed a method that allows n − 1 colluding parties to cheat an honest party in visual cryptography. They take advantage of knowing the underlying distribution of the pixels in the shares to create new shares that combine with existing shares to form a new secret message of the cheaters choosing. We know that 2 shares are enough to decode the secret image using the human visual system. But examining two shares also gives some information about the 3rd share. For instance, colluding participants may examine their shares to determine when they both have black pixels and use that information to determine that another participant will also have a black pixel in that location. Knowing where black pixels exist in another party's share allows them to create a new share that will combine with the predicted share to form a new secret message. In this way a set of colluding parties that have enough shares to access the secret code can cheat other honest parties. == Visual steganography == 2×2 subpixels can also encode a binary image in each component image. For example, each white pixel of each component image could be represented by two black subpixels, while each black pixel represented by three black subpixels. When overlaid, each white pixel of the secret image is represented by three black subpixels, while each black pixel is represented by all four subpixels black. Each corresponding pixel in the component images is randomly rotated to avoid orientation leaking information about the secret image. == In popular culture == In "Do Not Forsake Me Oh My Darling", a 1967 episode of TV series The Prisoner, the protagonist uses a visual cryptography overlay of multiple transparencies to reveal a secret message – the location of a scientist friend who had gone into hiding.

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  • Steerable filter

    Steerable filter

    In image processing, a steerable filter is an orientation-selective filter that can be computationally rotated to any direction. Rather than designing a new filter for each orientation, a steerable filter is synthesized from a linear combination of a small, fixed set of "basis filters". This approach is efficient and is widely used for tasks that involve directionality, such as edge detection, texture analysis, and shape-from-shading. The principle of steerability has been generalized in deep learning to create equivariant neural networks, which can recognize features in data regardless of their orientation or position. == Example == A common example of a steerable filter is the first derivative of a two-dimensional Gaussian function. This filter responds strongly to oriented image features like edges. It is constructed from two basis filters: the partial derivative of the Gaussian with respect to the horizontal direction ( x {\displaystyle x} ) and the vertical direction ( y {\displaystyle y} ). If G ( x , y ) {\displaystyle G(x,y)} is the Gaussian function, and G x {\displaystyle G_{x}} and G y {\displaystyle G_{y}} are its partial derivatives (which measure the rate of change in the x {\displaystyle x} and y {\displaystyle y} directions, respectively), a new filter G θ {\displaystyle G_{\theta }} oriented at an angle θ {\displaystyle \theta } can be synthesized with the formula: G θ = cos ⁡ ( θ ) G x + sin ⁡ ( θ ) G y {\displaystyle G_{\theta }=\cos(\theta )G_{x}+\sin(\theta )G_{y}} Here, the basis filters G x {\displaystyle G_{x}} and G y {\displaystyle G_{y}} are weighted by cos ⁡ ( θ ) {\displaystyle \cos(\theta )} and sin ⁡ ( θ ) {\displaystyle \sin(\theta )} to "steer" the filter's sensitivity to the desired orientation. This is equivalent to taking the dot product of the direction vector ( cos ⁡ θ , sin ⁡ θ ) {\displaystyle (\cos \theta ,\sin \theta )} with the filter's gradient, ( G x , G y ) {\displaystyle (G_{x},G_{y})} . == Generalization in deep learning: Equivariant neural networks == The concept of steerability is foundational to equivariant neural networks, a class of models in deep learning designed to understand symmetries in data. A network is considered equivariant to a transformation (like a rotation) if transforming the input and then passing it through the network produces the same result as passing the input through the network first and then transforming the output. Formally, for a transformation T {\displaystyle T} and a network f {\displaystyle f} , this property is defined as f ( T ( input ) ) = T ( f ( input ) ) {\displaystyle f(T({\text{input}}))=T(f({\text{input}}))} . This built-in understanding of geometry makes models more data-efficient. For example, a network equivariant to rotation does not need to be shown an object in multiple orientations to learn to recognize it; it inherently understands that a rotated object is still the same object. This leads to better generalization and performance, particularly in scientific applications. === Mathematical foundation === Equivariant neural networks use principles from group theory to create operations that respect geometric symmetries, such as the SO(3) group for 3D rotations or the E(3) group for rotations and translations. Instead of learning standard filter kernels, these networks learn how to combine a fixed set of basis kernels. These basis functions are chosen so that they have well-defined behaviors under transformation groups. Spherical harmonics are frequently used as basis functions because they form a complete set of functions that behave predictably under rotation, making them ideal for creating steerable 3D kernels. Features within the network are treated as geometric tensors, which are mathematical objects (like scalars or vectors) that are "typed" by their behavior under transformations. These types correspond to the irreducible representations (irreps) of the group. The tensor product is the fundamental operation used to combine these typed features in a way that preserves equivariance, guaranteeing that the network as a whole respects the desired symmetry. Frameworks like e3nn simplify the construction of these networks by automating the complex mathematics of irreducible representations and tensor products. === Applications === Steerable and equivariant models are highly effective for problems with inherent geometric symmetries. Examples include: Protein structure analysis: SE(3)-equivariant networks can process 3D molecular structures while respecting their rotational and translational symmetries. 3D Point cloud processing: Rotation-equivariant filters built from steerable spherical functions can perform tasks like 3D shape classification. Computational chemistry: E(3)-equivariant graph neural networks are used to model interatomic potentials for molecular dynamics simulations, creating highly accurate and data-efficient models of physical systems.

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  • Group key

    Group key

    In cryptography, a group key is a cryptographic key that is shared between a group of users. Typically, group keys are distributed by sending them to individual users, either physically, or encrypted individually for each user using either that user's pre-distributed private key. A common use of group keys is to allow a group of users to decrypt a broadcast message that is intended for that entire group of users, and no one else. For example, in the Second World War, group keys (known as "iodoforms", a term invented by a classically educated non-chemist, and nothing to do with the chemical of the same name) were sent to groups of agents by the Special Operations Executive. These group keys allowed all the agents in a particular group to receive a single coded message. In present-day applications, group keys are commonly used in conditional access systems, where the key is the common key used to decrypt the broadcast signal, and the group in question is the group of all paying subscribers. In this case, the group key is typically distributed to the subscribers' receivers using a combination of a physically distributed secure cryptoprocessor in the form of a smartcard and encrypted over-the-air messages.

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  • Copyright

    Copyright

    A copyright is a type of intellectual property that gives its owner the exclusive legal right to copy, distribute, adapt, display, and perform a creative work, usually for a limited time. The creative work may be in a literary, artistic, educational, or musical form. Copyright is intended to protect the original expression of an idea in the form of a creative work, but not the idea itself. A copyright is subject to limitations based on public interest considerations, such as the fair use doctrine in the United States and fair dealing doctrine in the United Kingdom. Some jurisdictions require "fixing" copyrighted works in a tangible form. It is often shared among multiple authors, each of whom holds a set of rights to use or license the work, and who are commonly referred to as rights holders. These rights normally include reproduction, control over derivative works, distribution, public performance, and moral rights such as attribution. Copyrights can be granted by public law and are in that case considered "territorial rights". This means that copyrights granted by the law of a certain state do not extend beyond the territory of that specific jurisdiction. Copyrights of this type vary by country; many countries, and sometimes a large group of countries, have made agreements with other countries on procedures applicable when works "cross" national borders or national rights are inconsistent. Typically, the public law duration of a copyright expires 50 to 100 years after the creator dies, depending on the jurisdiction. Some countries require certain copyright formalities to establishing copyright, others recognize copyright in any completed work, without a formal registration. When the copyright of a work expires, it enters the public domain. == History == === Background === The concept of copyright developed after the printing press came into use in Europe in the 15th and 16th centuries. It was associated with a common law and rooted in the civil law system. The printing press made it much cheaper to produce works, but as there was initially no copyright law, anyone could buy or rent a press and print any text. Popular new works were immediately re-set and re-published by competitors, so printers needed a constant stream of new material. Fees paid to authors for new works were high and significantly supplemented the incomes of many academics. Printing brought profound social changes. The rise in literacy across Europe led to a dramatic increase in the demand for reading matter. Prices of reprints were low, so publications could be bought by poorer people, creating a mass audience. In German-language markets before the advent of copyright, technical materials, like academic papers and handbooks, were inexpensive and widely available; it has been suggested this contributed to Germany's industrial and economic success. === Conception === The concept of copyright first developed in England. In reaction to the printing of "scandalous books and pamphlets", the English Parliament passed the Licensing of the Press Act 1662, which required all intended publications to be registered with the government-approved Stationers' Company, giving the Stationers the right to regulate what material could be printed. The Statute of Anne, enacted in 1710 in England and Scotland, provided the first legislation to protect copyrights (but not authors' rights). The Copyright Act 1814 extended more rights for authors but did not protect British publications from being reprinted in the US. The Berne International Copyright Convention of 1886 finally provided protection for authors among the countries who signed the agreement, although the US did not join the Berne Convention until 1989. In the US, the Constitution grants Congress the right to establish copyright and patent laws. Shortly after the Constitution was passed, Congress enacted the Copyright Act of 1790, modeling it after the Statute of Anne. While the national law protected authors' published works, authority was granted to the states to protect authors' unpublished works. The most recent major overhaul of copyright in the US, the Copyright Act of 1976, extended federal copyright to works as soon as they are created and "fixed", without requiring publication or registration. State law continues to apply to unpublished works that are not otherwise copyrighted by federal law. This act also changed the calculation of copyright term from a fixed term (then a maximum of fifty-six years) to "life of the author plus 50 years". These changes brought the US closer to conformity with the Berne Convention, and in 1989 the United States further revised its copyright law and joined the Berne Convention officially. Copyright laws allow products of creative human activities, such as literary and artistic production, to be preferentially exploited and thus incentivized. Different cultural attitudes, social organizations, economic models and legal frameworks are seen to account for why copyright emerged in Europe and not, for example, in Asia. In the Middle Ages in Europe, there was generally a lack of any concept of literary property due to the general relations of production, the specific organization of literary production and the role of culture in society. The latter refers to the tendency of oral societies, such as that of Europe in the medieval period, to view knowledge as the product and expression of the collective, rather than to see it as individual property. However, with copyright laws, intellectual production comes to be seen as a product of an individual, with attendant rights. The most significant point is that patent and copyright laws support the expansion of the range of creative human activities that can be commodified. This parallels the ways in which capitalism led to the commodification of many aspects of social life that earlier had no monetary or economic value perse. Copyright has developed into a concept that has a significant effect on nearly every modern industry, including not just literary work, but also forms of creative work such as sound recordings, films, photographs, software, and architecture. === National copyrights === Often seen as the first real copyright law, the 1709 British Statute of Anne gave authors and the publishers to whom they did chose to license their works, the right to publish the author's creations for a fixed period, after which the copyright expired. It was "An Act for the Encouragement of Learning, by Vesting the Copies of Printed Books in the Authors or the Purchasers of such Copies, during the Times therein mentioned." The act also alluded to individual rights of the artist. It began: "Whereas Printers, Booksellers, and other Persons, have of late frequently taken the Liberty of Printing ... Books, and other Writings, without the Consent of the Authors ... to their very great Detriment, and too often to the Ruin of them and their Families:". A right to benefit financially from the work is articulated, and court rulings and legislation have recognized a right to control the work, such as ensuring that the integrity of it is preserved. An irrevocable right to be recognized as the work's creator appears in some countries' copyright laws. The Copyright Clause of the United States, Constitution (1787) authorized copyright legislation: "To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries." That is, by guaranteeing them a period of time in which they alone could profit from their works, they would be enabled and encouraged to invest the time required to create them, and this would be good for society as a whole. A right to profit from the work has been the philosophical underpinning for much legislation extending the duration of copyright, to the life of the creator and beyond, to their heirs. Yet scholars like Lawrence Lessig have argued that copyright terms have been extended beyond the scope imagined by the Framers. Lessig refers to the Copyright Clause as the "Progress Clause" to emphasize the social dimension of intellectual property rights. The original length of copyright in the United States was 14 years, and it had to be explicitly applied for. If the author wished, they could apply for a second 14‑year monopoly grant, but after that the work entered the public domain, so it could be used and built upon by others. === Continental law === In many jurisdictions of the European continent, comparable legal concepts to copyright did exist from the 16th century on but did change under Napoleonic rule into another legal concept: authors' rights or creator's right laws, from French: droits d'auteur and German Urheberrecht. In many modern-day publications the terms copyright and authors' rights are being mixed, or used as translations, but in a juridical sense the legal concepts do essentially differ. Authors' rights are, generally speaking,

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