In applied mathematical analysis, shearlets are a multiscale framework which allows efficient encoding of anisotropic features in multivariate problem classes. Originally, shearlets were introduced in 2006 for the analysis and sparse approximation of functions f ∈ L 2 ( R 2 ) {\displaystyle f\in L^{2}(\mathbb {R} ^{2})} . They are a natural extension of wavelets, to accommodate the fact that multivariate functions are typically governed by anisotropic features such as edges in images, since wavelets, as isotropic objects, are not capable of capturing such phenomena. Shearlets are constructed by parabolic scaling, shearing, and translation applied to a few generating functions. At fine scales, they are essentially supported within skinny and directional ridges following the parabolic scaling law, which reads length² ≈ width. Similar to wavelets, shearlets arise from the affine group and allow a unified treatment of the continuum and digital situation leading to faithful implementations. Although they do not constitute an orthonormal basis for L 2 ( R 2 ) {\displaystyle L^{2}(\mathbb {R} ^{2})} , they still form a frame allowing stable expansions of arbitrary functions f ∈ L 2 ( R 2 ) {\displaystyle f\in L^{2}(\mathbb {R} ^{2})} . One of the most important properties of shearlets is their ability to provide optimally sparse approximations (in the sense of optimality in ) for cartoon-like functions f {\displaystyle f} . In imaging sciences, cartoon-like functions serve as a model for anisotropic features and are compactly supported in [ 0 , 1 ] 2 {\displaystyle [0,1]^{2}} while being C 2 {\displaystyle C^{2}} apart from a closed piecewise C 2 {\displaystyle C^{2}} singularity curve with bounded curvature. The decay rate of the L 2 {\displaystyle L^{2}} -error of the N {\displaystyle N} -term shearlet approximation obtained by taking the N {\displaystyle N} largest coefficients from the shearlet expansion is in fact optimal up to a log-factor: ‖ f − f N ‖ L 2 2 ≤ C N − 2 ( log N ) 3 , N → ∞ , {\displaystyle \|f-f_{N}\|_{L^{2}}^{2}\leq CN^{-2}(\log N)^{3},\quad N\to \infty ,} where the constant C {\displaystyle C} depends only on the maximum curvature of the singularity curve and the maximum magnitudes of f {\displaystyle f} , f ′ {\displaystyle f'} and f ″ . {\displaystyle f''.} This approximation rate significantly improves the best N {\displaystyle N} -term approximation rate of wavelets providing only O ( N − 1 ) {\displaystyle O(N^{-1})} for such class of functions. Shearlets are to date the only directional representation system that provides sparse approximation of anisotropic features while providing a unified treatment of the continuum and digital realm that allows faithful implementation. Extensions of shearlet systems to L 2 ( R d ) , d ≥ 2 {\displaystyle L^{2}(\mathbb {R} ^{d}),d\geq 2} are also available. A comprehensive presentation of the theory and applications of shearlets can be found in. == Definition == === Continuous shearlet systems === The construction of continuous shearlet systems is based on parabolic scaling matrices A a = [ a 0 0 a 1 / 2 ] , a > 0 {\displaystyle A_{a}={\begin{bmatrix}a&0\\0&a^{1/2}\end{bmatrix}},\quad a>0} as a means to change the resolution, on shear matrices S s = [ 1 s 0 1 ] , s ∈ R {\displaystyle S_{s}={\begin{bmatrix}1&s\\0&1\end{bmatrix}},\quad s\in \mathbb {R} } as a means to change the orientation, and finally on translations to change the positioning. In comparison to curvelets, shearlets use shearings instead of rotations, the advantage being that the shear operator S s {\displaystyle S_{s}} leaves the integer lattice invariant in case s ∈ Z {\displaystyle s\in \mathbb {Z} } , i.e., S s Z 2 ⊆ Z 2 . {\displaystyle S_{s}\mathbb {Z} ^{2}\subseteq \mathbb {Z} ^{2}.} This indeed allows a unified treatment of the continuum and digital realm, thereby guaranteeing a faithful digital implementation. For ψ ∈ L 2 ( R 2 ) {\displaystyle \psi \in L^{2}(\mathbb {R} ^{2})} the continuous shearlet system generated by ψ {\displaystyle \psi } is then defined as SH c o n t ( ψ ) = { ψ a , s , t = a 3 / 4 ψ ( S s A a ( ⋅ − t ) ) ∣ a > 0 , s ∈ R , t ∈ R 2 } , {\displaystyle \operatorname {SH} _{\mathrm {cont} }(\psi )=\{\psi _{a,s,t}=a^{3/4}\psi (S_{s}A_{a}(\cdot -t))\mid a>0,s\in \mathbb {R} ,t\in \mathbb {R} ^{2}\},} and the corresponding continuous shearlet transform is given by the map f ↦ S H ψ f ( a , s , t ) = ⟨ f , ψ a , s , t ⟩ , f ∈ L 2 ( R 2 ) , ( a , s , t ) ∈ R > 0 × R × R 2 . {\displaystyle f\mapsto {\mathcal {SH}}_{\psi }f(a,s,t)=\langle f,\psi _{a,s,t}\rangle ,\quad f\in L^{2}(\mathbb {R} ^{2}),\quad (a,s,t)\in \mathbb {R} _{>0}\times \mathbb {R} \times \mathbb {R} ^{2}.} === Discrete shearlet systems === A discrete version of shearlet systems can be directly obtained from SH c o n t ( ψ ) {\displaystyle \operatorname {SH} _{\mathrm {cont} }(\psi )} by discretizing the parameter set R > 0 × R × R 2 . {\displaystyle \mathbb {R} _{>0}\times \mathbb {R} \times \mathbb {R} ^{2}.} There are numerous approaches for this but the most popular one is given by { ( 2 j , k , A 2 j − 1 S k − 1 m ) ∣ j ∈ Z , k ∈ Z , m ∈ Z 2 } ⊆ R > 0 × R × R 2 . {\displaystyle \{(2^{j},k,A_{2^{j}}^{-1}S_{k}^{-1}m)\mid j\in \mathbb {Z} ,k\in \mathbb {Z} ,m\in \mathbb {Z} ^{2}\}\subseteq \mathbb {R} _{>0}\times \mathbb {R} \times \mathbb {R} ^{2}.} From this, the discrete shearlet system associated with the shearlet generator ψ {\displaystyle \psi } is defined by SH ( ψ ) = { ψ j , k , m = 2 3 j / 4 ψ ( S k A 2 j ⋅ − m ) ∣ j ∈ Z , k ∈ Z , m ∈ Z 2 } , {\displaystyle \operatorname {SH} (\psi )=\{\psi _{j,k,m}=2^{3j/4}\psi (S_{k}A_{2^{j}}\cdot {}-m)\mid j\in \mathbb {Z} ,k\in \mathbb {Z} ,m\in \mathbb {Z} ^{2}\},} and the associated discrete shearlet transform is defined by f ↦ S H ψ f ( j , k , m ) = ⟨ f , ψ j , k , m ⟩ , f ∈ L 2 ( R 2 ) , ( j , k , m ) ∈ Z × Z × Z 2 . {\displaystyle f\mapsto {\mathcal {SH}}_{\psi }f(j,k,m)=\langle f,\psi _{j,k,m}\rangle ,\quad f\in L^{2}(\mathbb {R} ^{2}),\quad (j,k,m)\in \mathbb {Z} \times \mathbb {Z} \times \mathbb {Z} ^{2}.} == Examples == Let ψ 1 ∈ L 2 ( R ) {\displaystyle \psi _{1}\in L^{2}(\mathbb {R} )} be a function satisfying the discrete Calderón condition, i.e., ∑ j ∈ Z | ψ ^ 1 ( 2 − j ξ ) | 2 = 1 , for a.e. ξ ∈ R , {\displaystyle \sum _{j\in \mathbb {Z} }|{\hat {\psi }}_{1}(2^{-j}\xi )|^{2}=1,{\text{for a.e. }}\xi \in \mathbb {R} ,} with ψ ^ 1 ∈ C ∞ ( R ) {\displaystyle {\hat {\psi }}_{1}\in C^{\infty }(\mathbb {R} )} and supp ψ ^ 1 ⊆ [ − 1 2 , − 1 16 ] ∪ [ 1 16 , 1 2 ] , {\displaystyle \operatorname {supp} {\hat {\psi }}_{1}\subseteq [-{\tfrac {1}{2}},-{\tfrac {1}{16}}]\cup [{\tfrac {1}{16}},{\tfrac {1}{2}}],} where ψ ^ 1 {\displaystyle {\hat {\psi }}_{1}} denotes the Fourier transform of ψ 1 . {\displaystyle \psi _{1}.} For instance, one can choose ψ 1 {\displaystyle \psi _{1}} to be a Meyer wavelet. Furthermore, let ψ 2 ∈ L 2 ( R ) {\displaystyle \psi _{2}\in L^{2}(\mathbb {R} )} be such that ψ ^ 2 ∈ C ∞ ( R ) , {\displaystyle {\hat {\psi }}_{2}\in C^{\infty }(\mathbb {R} ),} supp ψ ^ 2 ⊆ [ − 1 , 1 ] {\displaystyle \operatorname {supp} {\hat {\psi }}_{2}\subseteq [-1,1]} and ∑ k = − 1 1 | ψ ^ 2 ( ξ + k ) | 2 = 1 , for a.e. ξ ∈ [ − 1 , 1 ] . {\displaystyle \sum _{k=-1}^{1}|{\hat {\psi }}_{2}(\xi +k)|^{2}=1,{\text{for a.e. }}\xi \in \left[-1,1\right].} One typically chooses ψ ^ 2 {\displaystyle {\hat {\psi }}_{2}} to be a smooth bump function. Then ψ ∈ L 2 ( R 2 ) {\displaystyle \psi \in L^{2}(\mathbb {R} ^{2})} given by ψ ^ ( ξ ) = ψ ^ 1 ( ξ 1 ) ψ ^ 2 ( ξ 2 ξ 1 ) , ξ = ( ξ 1 , ξ 2 ) ∈ R 2 , {\displaystyle {\hat {\psi }}(\xi )={\hat {\psi }}_{1}(\xi _{1}){\hat {\psi }}_{2}\left({\tfrac {\xi _{2}}{\xi _{1}}}\right),\quad \xi =(\xi _{1},\xi _{2})\in \mathbb {R} ^{2},} is called a classical shearlet. It can be shown that the corresponding discrete shearlet system SH ( ψ ) {\displaystyle \operatorname {SH} (\psi )} constitutes a Parseval frame for L 2 ( R 2 ) {\displaystyle L^{2}(\mathbb {R} ^{2})} consisting of bandlimited functions. Another example are compactly supported shearlet systems, where a compactly supported function ψ ∈ L 2 ( R 2 ) {\displaystyle \psi \in L^{2}(\mathbb {R} ^{2})} can be chosen so that SH ( ψ ) {\displaystyle \operatorname {SH} (\psi )} forms a frame for L 2 ( R 2 ) {\displaystyle L^{2}(\mathbb {R} ^{2})} . In this case, all shearlet elements in SH ( ψ ) {\displaystyle \operatorname {SH} (\psi )} are compactly supported providing superior spatial localization compared to the classical shearlets, which are bandlimited. Although a compactly supported shearlet system does not generally form a Parseval frame, any function f ∈ L 2 ( R 2 ) {\displaystyle f\in L^{2}(\mathbb {R} ^{2})} can be represented by the shearlet expansion due to its frame property. == Cone-adapted shearlets == One drawback of shearlets defined as above is the directional bias of shearlet elements associated with large shearing parameters. This effect is already r
Read Along
Read Along, formerly known as Bolo, is an Android language-learning app for children developed by Google for the Android operating system. The application was released on the Play Store on March 7, 2019. It features a character named Diya helping children learn to read through illustrated stories. It has the facility to learn English and Indian major languages i.e. Hindi, Bengali, Tamil, Telugu, Marathi and Urdu, as well as Spanish, Portuguese and Arabic. == Technology == The app uses text-to-speech technology, through which the character named Dia reads the story, as well as speech-to-text technology, which mechanically identifies the matches between the text and the reading of the user. The story of Chhota Bheem and Katha Kids was added in September 2019. In April 2020, a new version of the application was released. In September 2020, it added Arabic language to its language option. A web version was launched in August 2022.
Data custodian
In data governance groups, responsibilities for data management are increasingly divided between the business process owners and information technology (IT) departments. Two functional titles commonly used for these roles are data steward and data custodian. Data Stewards are commonly responsible for data content, context, and associated business rules. Data custodians are responsible for the safe custody, transport, storage of the data and implementation of business rules. Simply put, Data Stewards are responsible for what is stored in a data field, while data custodians are responsible for the technical environment and database structure. Common job titles for data custodians are database administrator (DBA), data modeler, ETL developer and data engineer. == Data custodian responsibilities == A data custodian ensures: Access to the data is authorized and controlled Data stewards are identified for each data set Technical processes sustain data integrity Processes exist for data quality issue resolution in partnership with data stewards Technical controls safeguard data Data added to data sets are consistent with the common data model Versions of master data are maintained along with the history of changes Change management practices are applied in maintenance of the database Data content and changes can be audited
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.
Instant messaging
Instant messaging (IM) technology is a type of synchronous computer-mediated communication involving the immediate (real-time) transmission of messages between two or more parties over the Internet or another computer network. Originally involving simple text message exchanges, modern instant messaging applications and services (also variously known as instant messenger, messaging app, chat app, chat client, or simply a messenger) tend to also feature the exchange of multimedia, emojis, file transfer, VoIP (voice calling), and video chat capabilities. Instant messaging systems facilitate connections between specified known users (often using a contact list also known as a "buddy list" or "friend list") or in chat rooms, and can be standalone apps or integrated into a wider social media platform, or in a website where it can, for instance, be used for conversational commerce. Originally the term "instant messaging" was distinguished from "text messaging" by being run on a computer network instead of a cellular/mobile network, being able to write longer messages, real-time communication, presence ("status"), and being free (only cost of access instead of per SMS message sent). Instant messaging was pioneered in the early Internet era; the IRC protocol was the earliest to achieve wide adoption. Later in the 1990s, ICQ was among the first closed and commercialized instant messengers, and several rival services appeared afterwards as it became a popular use of the Internet. Beginning with its first introduction in 2005, BlackBerry Messenger became the first popular example of mobile-based IM, combining features of traditional IM and mobile SMS. Instant messaging remains very popular today; IM apps are the most widely used smartphone apps: in 2018 for instance there were 980 million monthly active users of WeChat and 1.3 billion monthly users of WhatsApp, the largest IM network. == Overview == Instant messaging (IM), sometimes also called "messaging" or "texting", consists of computer-based human communication between two users (private messaging) or more (chat room or "group") in real-time, allowing immediate receipt of acknowledgment or reply. This is in direct contrast to email, where conversations are not in real-time, and the perceived quasi-synchrony of the communications by the users (although many systems allow users to send offline messages that the other user receives when logging in). Earlier IM networks were limited to text-based communication, not dissimilar to mobile text messaging. As technology has moved forward, IM has expanded to include voice calling using a microphone, videotelephony using webcams, file transfer, location sharing, image and video transfer, voice notes, and other features. IM is conducted over the Internet or other types of networks (see also LAN messenger). Depending on the IM protocol, the technical architecture can be peer-to-peer (direct point-to-point transmission) or client–server (when all clients have to first connect to the central server). Primary IM services are controlled by their corresponding companies and usually follow the client-server model. At one point, the term "Instant Messenger" was a service mark of AOL Time Warner and could not be used in software not affiliated with AOL in the United States. For this reason, in April 2007, the instant messaging client formerly named Gaim (or gaim) announced that they would be renamed "Pidgin". === Clients === Modern IM services generally provide their own client, either a separately installed application or a browser-based client. They are normally centralised networks run by the servers of the platform's operators, unlike peer-to-peer protocols like XMPP. These usually only work within the same IM network, although some allow limited function with other services (see #Interoperability). Third-party client software applications exist that will connect with most of the major IM services. There is the class of instant messengers that uses the serverless model, which doesn't require servers, and the IM network consists only of clients. There are several serverless messengers: RetroShare, Tox, Bitmessage, Ricochet. See also: LAN messenger. Some examples of popular IM services today include Signal, Telegram, WhatsApp Messenger, WeChat, QQ Messenger, Viber, Line, and Snapchat. The popularity of certain apps greatly differ between different countries. Certain apps have an emphasis on certain uses - for example, Skype focuses on video calling, Slack focuses on messaging and file sharing for work teams, and Snapchat focuses on image messages. Some social networking services offer messaging services as a component of their overall platform, such as Facebook's Facebook Messenger, who also own WhatsApp. Others have a direct IM function as an additional adjunct component of their social networking platforms, like Instagram, Reddit, Tumblr, TikTok, Clubhouse and Twitter; this also includes for example dating websites, such as OkCupid or Plenty of Fish, and online gaming chat platforms. === Features === ==== Private and group messaging ==== Private chat allows users to converse privately with another person or a group. Privacy can also be enhanced in several ways, such as end-to-end encryption by default. Public and group chat features allow users to communicate with multiple people simultaneously. ==== Calling ==== Many major IM services and applications offer a call feature for user-to-user voice calls, conference calls, and voice messages. The call functionality is useful for professionals who utilize the application for work purposes and as a hands-free method. Videotelephony using a webcam is also possible by some. ==== Games and entertainment ==== Some IM applications include in-app games for entertainment. Yahoo! Messenger, for example, introduced these where users could play a game and viewed by friends in real-time. MSN Messenger featured a number of playable games within the interface. Facebook's Messenger has had a built-in option to play games with people in a chat, including games like Tetris and Blackjack. Discord features multiple games built inside the "activities" tab in voice channels. ==== Payments ==== A relatively new feature to instant messaging, peer-to-peer payments are available for financial tasks on top of communication. The lack of a service fee also makes these advantageous to financial applications. IM services such as Facebook Messenger and the WeChat 'super-app' for example offer a payment feature. == History == === Early systems === Though the term dates from the 1990s, instant messaging predates the Internet, first appearing on multi-user operating systems like Compatible Time-Sharing System (CTSS) and Multiplexed Information and Computing Service (Multics) in the mid-1960s. Initially, some of these systems were used as notification systems for services like printing, but quickly were used to facilitate communication with other users logged into the same machine. CTSS facilitated communication via text message for up to 30 people. Parallel to instant messaging were early online chat facilities, the earliest of which was Talkomatic (1973) on the PLATO system, which allowed 5 people to chat simultaneously on a 512 x 512 plasma display (5 lines of text + 1 status line per person). During the bulletin board system (BBS) phenomenon that peaked during the 1980s, some systems incorporated chat features which were similar to instant messaging; Freelancin' Roundtable was one prime example. The first such general-availability commercial online chat service (as opposed to PLATO, which was educational) was the CompuServe CB Simulator in 1980, created by CompuServe executive Alexander "Sandy" Trevor in Columbus, Ohio. As networks developed, the protocols spread with the networks. Some of these used a peer-to-peer protocol (e.g. talk, ntalk and ytalk), while others required peers to connect to a server (see talker and IRC). The Zephyr Notification Service (still in use at some institutions) was invented at MIT's Project Athena in the 1980s to allow service providers to locate and send messages to users. Early instant messaging programs were primarily real-time text, where characters appeared as they were typed. This includes the Unix "talk" command line program, which was popular in the 1980s and early 1990s. Some BBS chat programs (i.e. Celerity BBS) also used a similar interface. Modern implementations of real-time text also exist in instant messengers, such as AOL's Real-Time IM as an optional feature. In the latter half of the 1980s and into the early 1990s, the Quantum Link online service for Commodore 64 computers offered user-to-user messages between concurrently connected customers, which they called "On-Line Messages" (or OLM for short), and later "FlashMail." Quantum Link later became America Online and made AOL Instant Messenger (AIM, discussed later). While the Quantum Link client software ran on a Commodore 64, using only
Sentence extraction
Sentence extraction is a technique used for automatic summarization of a text. In this shallow approach, statistical heuristics are used to identify the most salient sentences of a text. Sentence extraction is a low-cost approach compared to more knowledge-intensive deeper approaches which require additional knowledge bases such as ontologies or linguistic knowledge. In short, sentence extraction works as a filter that allows only meaningful sentences to pass. The major downside of applying sentence-extraction techniques to the task of summarization is the loss of coherence in the resulting summary. Nevertheless, sentence extraction summaries can give valuable clues to the main points of a document and are frequently sufficiently intelligible to human readers. == Procedure == Usually, a combination of heuristics is used to determine the most important sentences within the document. Each heuristic assigns a (positive or negative) score to the sentence. After all heuristics have been applied, the highest-scoring sentences are included in the summary. The individual heuristics are weighted according to their importance. === Early approaches and some sample heuristics === Seminal papers which laid the foundations for many techniques used today have been published by Hans Peter Luhn in 1958 and H. P Edmundson in 1969. Luhn proposed to assign more weight to sentences at the beginning of the document or a paragraph. Edmundson stressed the importance of title-words for summarization and was the first to employ stop-lists in order to filter uninformative words of low semantic content (e.g. most grammatical words such as of, the, a). He also distinguished between bonus words and stigma words, i.e. words that probably occur together with important (e.g. the word form significant) or unimportant information. His idea of using key-words, i.e. words which occur significantly frequently in the document, is still one of the core heuristics of today's summarizers. With large linguistic corpora available today, the tf–idf value which originated in information retrieval, can be successfully applied to identify the key words of a text: If for example the word cat occurs significantly more often in the text to be summarized (TF = "term frequency") than in the corpus (IDF means "inverse document frequency"; here the corpus is meant by document), then cat is likely to be an important word of the text; the text may in fact be a text about cats.
Malleability (cryptography)
Malleability is a property of some cryptographic algorithms. An encryption algorithm is said to be malleable if it is possible to transform a ciphertext into another ciphertext which decrypts to a related plaintext. That is, given an encryption of a plaintext m {\displaystyle m} , it is possible to generate another ciphertext which decrypts to f ( m ) {\displaystyle f(m)} , for a known function f {\displaystyle f} , without necessarily knowing or learning m {\displaystyle m} . Malleability is often an undesirable property in a general-purpose cryptosystem, since it allows an attacker to modify the contents of a message. For example, suppose that a bank uses a stream cipher to hide its financial information, and a user sends an encrypted message containing, say, "TRANSFER $0000100.00 TO ACCOUNT #199." If an attacker can modify the message on the wire, and can guess the format of the unencrypted message, the attacker could change the amount of the transaction, or the recipient of the funds, e.g. "TRANSFER $0100000.00 TO ACCOUNT #227". Malleability does not refer to the attacker's ability to read the encrypted message. Both before and after tampering, the attacker cannot read the encrypted message. On the other hand, some cryptosystems are malleable by design. In other words, in some circumstances it may be viewed as a feature that anyone can transform an encryption of m {\displaystyle m} into a valid encryption of f ( m ) {\displaystyle f(m)} (for some restricted class of functions f {\displaystyle f} ) without necessarily learning m {\displaystyle m} . Such schemes are known as homomorphic encryption schemes. A cryptosystem may be semantically secure against chosen-plaintext attacks or even non-adaptive chosen-ciphertext attacks (CCA1) while still being malleable. However, security against adaptive chosen-ciphertext attacks (CCA2) is equivalent to non-malleability. == Example malleable cryptosystems == In a stream cipher, the ciphertext is produced by taking the exclusive or of the plaintext and a pseudorandom stream based on a secret key k {\displaystyle k} , as E ( m ) = m ⊕ S ( k ) {\displaystyle E(m)=m\oplus S(k)} . An adversary can construct an encryption of m ⊕ t {\displaystyle m\oplus t} for any t {\displaystyle t} , as E ( m ) ⊕ t = m ⊕ t ⊕ S ( k ) = E ( m ⊕ t ) {\displaystyle E(m)\oplus t=m\oplus t\oplus S(k)=E(m\oplus t)} . In the RSA cryptosystem, a plaintext m {\displaystyle m} is encrypted as E ( m ) = m e mod n {\displaystyle E(m)=m^{e}{\bmod {n}}} , where ( e , n ) {\displaystyle (e,n)} is the public key. Given such a ciphertext, an adversary can construct an encryption of m t {\displaystyle mt} for any t {\displaystyle t} , as E ( m ) ⋅ t e mod n = ( m t ) e mod n = E ( m t ) {\textstyle E(m)\cdot t^{e}{\bmod {n}}=(mt)^{e}{\bmod {n}}=E(mt)} . For this reason, RSA is commonly used together with padding methods such as OAEP or PKCS1. In the ElGamal cryptosystem, a plaintext m {\displaystyle m} is encrypted as E ( m ) = ( g b , m A b ) {\displaystyle E(m)=(g^{b},mA^{b})} , where ( g , A ) {\displaystyle (g,A)} is the public key. Given such a ciphertext ( c 1 , c 2 ) {\displaystyle (c_{1},c_{2})} , an adversary can compute ( c 1 , t ⋅ c 2 ) {\displaystyle (c_{1},t\cdot c_{2})} , which is a valid encryption of t m {\displaystyle tm} , for any t {\displaystyle t} . In contrast, the Cramer-Shoup system (which is based on ElGamal) is not malleable. In the Paillier, ElGamal, and RSA cryptosystems, it is also possible to combine several ciphertexts together in a useful way to produce a related ciphertext. In Paillier, given only the public key and an encryption of m 1 {\displaystyle m_{1}} and m 2 {\displaystyle m_{2}} , one can compute a valid encryption of their sum m 1 + m 2 {\displaystyle m_{1}+m_{2}} . In ElGamal and in RSA, one can combine encryptions of m 1 {\displaystyle m_{1}} and m 2 {\displaystyle m_{2}} to obtain a valid encryption of their product m 1 m 2 {\displaystyle m_{1}m_{2}} . Block ciphers in the cipher block chaining mode of operation, for example, are partly malleable: flipping a bit in a ciphertext block will completely mangle the plaintext it decrypts to, but will result in the same bit being flipped in the plaintext of the next block. This allows an attacker to 'sacrifice' one block of plaintext in order to change some data in the next one, possibly managing to maliciously alter the message. This is essentially the core idea of the padding oracle attack on CBC, which allows the attacker to decrypt almost an entire ciphertext without knowing the key. For this and many other reasons, a message authentication code is required to guard against any method of tampering. == Complete non-malleability == Fischlin, in 2005, defined the notion of complete non-malleability as the ability of the system to remain non-malleable while giving the adversary additional power to choose a new public key which could be a function of the original public key. In other words, the adversary shouldn't be able to come up with a ciphertext whose underlying plaintext is related to the original message through a relation that also takes public keys into account.