Web-based simulation (WBS) is the invocation of computer simulation services over the World Wide Web, specifically through a web browser. Increasingly, the web is being looked upon as an environment for providing modeling and simulation applications, and as such, is an emerging area of investigation within the simulation community. == Application == Web-based simulation is used in several contexts: In e-learning, various principles can quickly be illustrated to students by means of interactive computer animations, for example during lecture demonstrations and computer exercises. In distance learning, web-based simulation may provide an alternative to installing expensive simulation software on the student computer, or an alternative to expensive laboratory equipment. In software engineering, web-based emulation allows application development and testing on one platform for other target platforms, for example for various mobile operating systems or mobile web browsers, without the need of target hardware or locally installed emulation software. In online computer games, 3D environments can be simulated, and old home computers and video game consoles can be emulated, allowing the user to play old computer games in the web browser. In medical education, nurse education and allied health education (like sonographer training), web-based simulations can be used for learning and practicing clinical healthcare procedures. Web-based procedural simulations emphasize the cognitive elements such as the steps of the procedure, the decisions, the tools/devices to be used, and the correct anatomical location. == Client-side vs server-side approaches == Web-based simulation can take place either on the server side or on the client side. In server-side simulation, the numerical calculations and visualization (generation of plots and other computer graphics) is carried out on the web server, while the interactive graphical user interface (GUI) often partly is provided by the client-side, for example using server-side scripting such as PHP or CGI scripts, interactive services based on Ajax or a conventional application software remotely accessed through a VNC Java applet. In client-side simulation, the simulation program is downloaded from the server side but completely executed on the client side, for example using Java applets, Flash animations, JavaScript, or some mathematical software viewer plug-in. Server-side simulation is not scalable for many simultaneous users, but places fewer demands on the user computer performance and web-browser plug-ins than client-side simulation. The term on-line simulation sometimes refers to server-side web-based simulation, sometimes to symbiotic simulation, i.e. a simulation that interacts in real-time with a physical system. The upcoming cloud-computing technologies can be used for new server-side simulation approaches. For instance, there are multi-agent-simulation applications which are deployed on cloud-computing instances and act independently. This allows simulations to be highly scalable. == Existing tools == AgentSheets – graphically programmed tool for creating web-based The Sims-like simulation games, and for teaching beginner students programming. AnyLogic – a graphically programmed tool that generates Java code for discrete-event simulation, system dynamics and agent-based models Easy Java Simulations – a tool for modelling and visualization of physical phenomenons, that automatically generates Java code from mathematical expressions. ExploreLearning Gizmos – a large library of interactive online simulations for math and science education in grades 3–12. FreeFem++ Javascript Version – FreeFem++ is a free and open source PDE solver using the finite element method. GNU Octave web interfaces – MATLAB compatible open-source software Lanner Group Ltd L-SIM Server – Java-based discrete-event simulation engine which supports model standards such as BPMN 2.0 Nanohub – web 2.0 in-browser interactive simulation of nanotechnology NetLogo – a multi-agent programming language and integrated modeling environment that runs on the Java Virtual Machine OpenPlaG – PHP-based function graph plotter for the use on websites OpenEpi – web-based packet of tools for biostatistics Recursive Porous Agent Simulation Toolkit (Repast) – agent-based modeling and simulation toolkit implemented in Java and many other languages SageMath – open-source numerical-analysis software with web interface, based on the Python programming language SimScale – web-based simulation platform supporting computational fluid dynamics, solid mechanics, and thermodynamics StarLogo – agent-based simulation language written in Java. VisSim viewer – graphically programmed data-flow diagrams for simulation of dynamical systems webMathematica and Mathematica Player – a computer algebra system and programming language. VisualSim Architect – VisualSim Explorer enables system-level models to be embedded in documents for viewing, simulation and analysis from within a web browser without any local software installation.
CLAWS (linguistics)
The Constituent Likelihood Automatic Word-tagging System (CLAWS) is a program that performs part-of-speech tagging. It was developed in the 1980s at Lancaster University by the University Centre for Computer Corpus Research on Language. It has an overall accuracy rate of 96–97% with the latest version (CLAWS4) tagging around 100 million words of the British National Corpus. == History == A Part-Of-Speech Tagger (POS Tagger) is a piece of software that reads text in some language and assigns parts of speech to each word (and other token), such as noun, verb, adjective, etc., although generally computational applications use more fine-grained POS tags like 'noun-plural'. Developed in the early 1980s, CLAWS was built to fill the ever-growing gap created by always-changing POS necessities. Originally created to add part-of-speech tags to the LOB corpus of British English, the CLAWS tagset has since been adapted to other languages as well, including Urdu and Arabic. Since its inception, CLAWS has been hailed for its functionality and adaptability. Still, it is not without flaws, and though it boasts an error-rate of only 1.5% when judged in major categories, CLAWS still remains with c.3.3% ambiguities unresolved. Ambiguity arises in cases such as with the word flies, and whether it should be classified as a noun or a verb. It's these ambiguities that will require the various upgrades and tagsets that CLAWS will endure. == Rules and processing == CLAWS uses a Hidden Markov model to determine the likelihood of sequences of words in anticipating each part-of-speech label. === Sample output === This excerpt from Bram Stoker's Dracula (1897) has been tagged using both the CLAWS C5 and C7 tagsets. This is what a CLAWS output will generally look like, with the most likely part-of-speech tag following each word. == Tagsets == === CLAWS1 tagset === The first tagset developed in CLAWS, CLAWS1 tagset, has 132 word tags. In terms of form and application, C1 tagset is similar to Brown Corpus tags. See Table of tags in C1 tagset here. === CLAWS2 tagset === From 1983 to 1986, updated versions leading to CLAWS2 were part of a larger attempt to deal with aspects such as recognizing sentence breaks, in order to avoid the need for manual pre-processing of a text before the tags were applied, moving instead to optional manual post-editing to adjust the output of the automatic annotation, if needed. The CLAWS2 tagset has 166 word tags. See Table of tags in C2 tagset here. === CLAWS4 tagset === The CLAWS4 was used for the 100-million-word British National Corpus (BNC). A general-purpose grammatical tagger, it is a successor of the CLAWS1 tagger. In tagging the BNC, the many rounds of work that went into CLAWS4 focused on making the CLAWS program independent from the tagsets. For example, the BNC project used two tagset versions: "a main tagset (C5) with 62 tags with which the whole of the corpus has been tagged, and a larger (C7) tagset with 152 tags, which has been used to make a selected 'core' sample corpus of two million words." The latest version of CLAWS4 is offered by UCREL, a research center of Lancaster University. === CLAWS5 tagset === The CLAWS5 tagset, which was used for BNC, has over 60 tags. See Table of tags in C5 tagset here. === CLAWS6 tagset === The CLAWS6 tagset was used for the BNC sampler corpus and the COLT corpus. It has over 160 tags, including 13 determiner subtypes. See Table of tags in C6 tagset here. === CLAWS7 tagset === The standard CLAWS7 tagset is used currently. It is only different in the punctuation tags when compared to the CLAWS6 tagset. See Table of tags in C7 tagset here. === CLAWS8 tagset === CLAWS8 tagset was extended from C7 tagset with further distinctions in the determiner and pronoun categories, as well as 37 new auxiliary tags for forms of be, do, and have. See Table of tags in C8 tagset here
Memory-hard function
In cryptography, a memory-hard function (MHF) is a function that costs a significant amount of memory to efficiently evaluate. It differs from a memory-bound function, which incurs cost by slowing down computation through memory latency. MHFs have found use in key stretching and proof of work as their increased memory requirements significantly reduce the computational efficiency advantage of custom hardware over general-purpose hardware compared to non-MHFs. == Introduction == MHFs are designed to consume large amounts of memory on a computer in order to reduce the effectiveness of parallel computing. In order to evaluate the function using less memory, a significant time penalty is incurred. As each MHF computation requires a large amount of memory, the number of function computations that can occur simultaneously is limited by the amount of available memory. This reduces the efficiency of specialised hardware, such as application-specific integrated circuits and graphics processing units, which utilise parallelisation, in computing a MHF for a large number of inputs, such as when brute-forcing password hashes or mining cryptocurrency. == Motivation and examples == Bitcoin's proof-of-work uses repeated evaluation of the SHA-256 function, but modern general-purpose processors, such as off-the-shelf CPUs, are inefficient when computing a fixed function many times over. Specialized hardware, such as application-specific integrated circuits (ASICs) designed for Bitcoin mining, can use 30,000 times less energy per hash than x86 CPUs whilst having much greater hash rates. This led to concerns about the centralization of mining for Bitcoin and other cryptocurrencies. Because of this inequality between miners using ASICs and miners using CPUs or off-the shelf hardware, designers of later proof-of-work systems utilised hash functions for which it was difficult to construct ASICs that could evaluate the hash function significantly faster than a CPU. As memory cost is platform-independent, MHFs have found use in cryptocurrency mining, such as for Litecoin, which uses scrypt as its hash function. They are also useful in password hashing because they significantly increase the cost of trying many possible passwords against a leaked database of hashed passwords without significantly increasing the computation time for legitimate users. == Measuring memory hardness == There are various ways to measure the memory hardness of a function. One commonly seen measure is cumulative memory complexity (CMC). In a parallel model, CMC is the sum of the memory required to compute a function over every time step of the computation. Other viable measures include integrating memory usage against time and measuring memory bandwidth consumption on a memory bus. Functions requiring high memory bandwidth are sometimes referred to as "bandwidth-hard functions". == Variants == MHFs can be categorized into two different groups based on their evaluation patterns: data-dependent memory-hard functions (dMHF) and data-independent memory-hard functions (iMHF). As opposed to iMHFs, the memory access pattern of a dMHF depends on the function input, such as the password provided to a key derivation function. Examples of dMHFs are scrypt and Argon2d, while examples of iMHFs are Argon2i and catena. Many of these MHFs have been designed to be used as password hashing functions because of their memory hardness. A notable problem with dMHFs is that they are prone to side-channel attacks such as cache timing. This has resulted in a preference for using iMHFs when hashing passwords. However, iMHFs have been mathematically proven to have weaker memory hardness properties than dMHFs.
Talim (textiles)
Talim (Kashmiri: تعليم, Kashmiri pronunciation: [t̪əːliːm], Urdu: تَعْلِیم, Arabic: تعليم, pronounced [taʕ.liːm] ) in textiles is a symbolic code and system of notation that facilitates the creation of intricate patterns in fabrics, such as shawls and carpets, and the written coded plans that include colour schemes and weaving instructions. The term is used in traditional hand-weaving in the Indian subcontinent. Talim was initially used to create certain types of patterns in Kashmiri shawls, and later came to be applied in the production of carpets. == Etymology and origin == The term talim, which refers to a symbolic code and system of notation used by shawl and carpet artisans in their weaving processes, came to the Urdu language from the Arabic noun taʻlim (تعليم), which means "authoritative instruction", "teaching", or "edification". It means the same in Urdu and Kashmiri. The Arabic noun originated from the second form of the Arabic root verb ʻalima (علم), which means "to know". According to a local belief in Kashmir, talim was introduced to them by Persian scholar and Sufi Muslim saint Mir Sayyid Ali Hamadani. The belief notwithstanding, talim might have originated from Kashmir; Amritsar was the only place outside of Srinagar where talim was used, by migrated Kashmiri artisans. == Technique == Whereas carpets are generally woven horizontally, providing weavers with a clear view of the progress they are making in creating designs, in Kashmir, carpets are woven vertically, so the weaver is reliant on the talim. The talim technique forms fabrics by passing the weft thread as per a given script that has design codes. Weavers use talim to weave the desired pattern with planned colours. Talim involves teamwork when applying the technique, as the process of creating intricate fabric designs in weaving begins with the Naqash (designer, who designs using pencils on graphs) meticulously crafting the design on a blank sheet of paper called a naska, and the master, Talim guru, making the colour codes and symbols for weft yarns that would interlace the warp to construct the desired design. He writes on a long strip of paper, in specific symbols, the colour codes, and the number of knots to be woven with each colour. Taraha guru collaborates with talim guru and is known as the artisan responsible for determining the colours. Talim uthana is a process or the act of "picking the codes" from the graph. A clerk called the Talim Navis would record the step-by-step instructions for these numbers and colours, and thousands of low-paid and interchangeable weavers would read or recite the record to carry out the design. Afterward, a talim copyist makes copies, which are needed when multiple looms weave the same product. The script, which has been encoded, is deciphered and translated according to the specific guidelines of weavers in order to incorporate the design that is included within it. Talim has been compared to "hieroglyphics" or as a "notational-cum-cryptographic system", as it is challenging to decipher and is unique to the shawls of Kashmir, which requires expertise to comprehend. According to researcher Gagan Deep Kaur, "The talim is widely held to be a trade secret of the community and has always been fiercely guarded by the owners." Those who use talim for shawl-making do not assign important tasks to women, because of the fear that the technique and knowledge may be divulged to other communities when the women are sent there to be married. The coded cards known as talim in the Kashmiri language were used for creating certain types of patterns in shawl weaving. The talim technique is employed in the creation of kani shawls, which originated from the Kanihama region of the Kashmir valley. Carpet weaving adapted the technique from shawl making. When Kashmiri artisans started to create carpets, they chose to continue using the talim rather than switching to a different method. The resurgence of the carpet industry in Amritsar during the last century resulted in the prevalent use of the talim technique among the local weavers, a majority of whom hailed from the region of Kashmir. === Recitation of codes === Talim was also communicated through recitation accompanied by a melodic chant or song. In traditional weaving practices, the use of chanting was common. The movement of the shuttles was synchronised with the song of the weaver, adding a musical rhythm to the instructions represented through hieroglyphics. The weaver's chant, "Two blue, one red, three yellow, two blue," served as a guide as they wove and replicated the designated pattern. == Usage == The first factories established in Amritsar around 1860 utilised Bokhara designs. However, Kashmiri weavers maintained their traditional techniques and employed the talim, instead of a cartoon, for tying knots. As a result, Amritsar became the second location in the Indian subcontinent to use the talim. The traditional weaving practices are still carried out in some parts of the Indian subcontinent. The exact date when talim was last used in the subcontinent varies depending on the region and the specific weaving community. Indian textile historian Jasleen Dhamija wrote in her 1989 book Handwoven Fabrics of India that there were still some weavers in the Kashmiri village of Kanihama who applied talim in weaving shawls. As of 2022, the carpet weavers in Kashmir were the only remaining users of talim in carpets, according to Zubair Ahmed, director of the Indian Institute of Carpet Technology. The institute aims to preserve traditional Kashmiri carpet designs by digitising talim and training weavers in the technique. == Gallery ==
VK (service)
VK (short for its original name VKontakte; Russian: ВКонтакте, lit. 'InContact') is a Russian online social media and social networking service based in Saint Petersburg. VK is available in multiple languages but it is predominantly used by Russian speakers. VK users can message each other publicly or privately, edit messages, create groups, public pages, and events; share and tag images, audio, and video; and play browser-based games. As of August 2018, VK had at least 500 million accounts. As of November 2022, it was the sixth most popular website in Russia. The network was also popular in Ukraine until it was banned by the Verkhovna Rada in 2017. According to Semrush, in 2024, VK was the 30th most visited website in the world; as YouTube is subject to blocking in Russia, VK Video overtook Google's top position in monthly web traffic for the first time in December 2024, as part of the major substitution to domestic business. == History == VKontakte was conceived in 2006 when Pavel Durov, creator of the popular student forum spbgu.ru, met his former classmate Vyacheslav Mirilashvili in St. Petersburg after graduating from the Faculty of Philology at St Petersburg State University. Vyacheslav showed Durov the increasingly popular Facebook, after which the friends decided to create a new Russian social network. Lev Leviev, an Israeli classmate of Vyacheslav Mirilashivili, became the third co-founder. Vyacheslav Mirilashvili borrowed the money from his billionaire father and became the largest shareholder. Lev Leviev took over operational management, and Durov became CEO. Pavel Durov convinced his older brother Nikolai, a multiple winner of international math and programming competitions, to develop the site. Durov launched VKontakte for beta testing in September 2006. The following month, the domain name Vkontakte.ru was registered. The new project was incorporated on 19 January 2007 as a Russian private limited company. In February 2007 the site reached a user base of over 100,000 and was recognized as the second largest company in Russia's nascent social network market. In the same month, the site was subjected to a severe DDoS attack, which briefly put it offline. The user base reached 1 million in July 2007, and 10 million in April 2008. In December 2008 VK overtook rival Odnoklassniki as Russia's most popular social networking service. == Website == Similar to many social networks, the platform's fundamental features revolve around private messaging, sharing photos, posting status updates, and exchanging links with friends. VK also provides tools for administering online communities and managing celebrity pages. The site allows its users to upload, search and stream media content, such as videos and music. VK features an advanced search engine, that allows complex queries for finding friends, as well as a real-time news search. VK updated its features and design in April 2016. === Features === Messaging. VK Private Messages can be exchanged between groups of 2 to 500 people. An email address can also be specified as the recipient. Each message may contain up to 10 attachments: Photos, Videos, Audio Files, Maps (an embedded map with a manually placed marker), and Documents. News. VK users can post on their profile walls, each post may contain up to 10 attachments – media files, maps, and documents (see above). User mentions and hashtags are supported. In the case of multiple photo attachments, the previews are automatically scaled and arranged in a magazine-style layout. The news feed can be switched between all news (default) and most interesting modes. The site features a news-recommendation engine, global real-time search, and individual search for posts and comments on specific users' walls. Communities. VK features three types of communities. Groups are better suited for decentralized communities (discussion boards, wiki-style articles, editable by all members, etc.). Public pages is a news feed-orientated broadcasting tool for celebrities and businesses. The two types are largely interchangeable, the main difference being in the default settings. The third type of community is called Events, which are used for appropriately organizing concerts and events in an appropriate way. Like buttons. VK like buttons for posts, comments, media, and external sites operate differently from Facebook. Liked content doesn't get automatically pushed to the user's wall, but is saved in the private Favorites section instead. The user has to press a second 'share with friends' button to share an item on their wall or send it via private message to a friend. Privacy. Users can control the availability of their content within the network and on the Internet. Blanket and granular privacy settings are available for pages and individual content. Synchronization with other social networks. Any news published on the VK wall will appear on Facebook or Twitter. Certain news may not be published by clicking on the logo next to the "Send" button. Editing a post in VK does not change the post in Facebook or Twitter and vice versa. However, removing the news in VK will remove it from other social networks. SMS service. Russian users can receive and reply to a private message or leave a comment for community news using SMS. Music. Users have access to the audio files uploaded by other users. In addition, users can upload the audio files themselves, create playlists and share audios with others by attaching to messages and wall posts. The uploaded audio files cannot violate copyright laws. === Popularity === As of May 2017, according to Alexa Internet ranking, VK is one of the most visited websites in some Eurasian countries. It is: 4th most visited in Russia; 3rd most visited in Belarus; 6th most visited in Kazakhstan; 8th most visited in Kyrgyzstan and Moldova; 12th most visited in Latvia. It was the fourth most viewed site in Ukraine until, in May 2017, the Ukrainian government banned the use of VK in Ukraine. According to a study for May 2018 conducted by Factum Group Ukraine VK remained the fourth most viewed site in Ukraine, but Facebook was twice as much visited. For 2019, VK appeared as the most visited social network in Ukraine according to Alexa. According to the Internet Association of Ukraine the share of Ukrainian Internet users who visit VK daily had fallen from 54% to 10% from September 2016 to September 2019. They also claimed in November 2019 that Facebook was the most popular social network. VK was expected to gain most of the users lost by Facebook and Instagram after they were blocked in Russia in 2022, according to a Calltouch poll. == Ownership == Initially, founder and CEO Pavel Durov owned 20% of shares (although he had majority voting power through proxy votes), and a trio of Russian-Israeli investors Yitzchak Mirilashvili, his father Mikhael Mirilashvili, and Lev Leviev owned 60%, 10%, and 10% respectively. In 2007, Digital Sky Technologies, an investment company managed by Yuri Milner, acquired a total of 24.99% of the shares from shareholders, investing $16.3 million. In preparation for the IPO in September 2010, DST separated international and Russian assets: the former formed the DST Global fund, while the latter, including VKontakte and rival social network Odnoklassniki, were merged into Mail.ru Group. Mail.ru Group used part of the money to acquire 7.5% of the social network for $112.5 million at a valuation of the entire project of 1.5 billion dollars. After exercising a 7.5% option in July 2011 for $111.7 million, Mail.ru Group accumulated a 39.99% stake in VKontakte. The head of Mail.ru Group, Dmitry Grishin, voiced the company's intention to gain 100% control over VKontakte. MRG was discussing with shareholders to buy out shares from the valuation of the entire company in $2-3 billion. In the summer of 2011, Mirilashvili and Leviev were ready to accept in payment owned by Mail.ru Group shares of Facebook, Groupon, and Zynga, but the deal failed due to Durov's unwillingness to sell a stake on MRG terms. Later, the co-founders considered VKontakte's IPO as an alternative. In March 2012, Durov "accidentally" became plugged into the negotiations where Mirilashvili and Leviev discussed selling their stakes directly to Mail.ru Group's main investor, Alisher Usmanov. On the same day, Durov deleted the pages of the first co-investors, stopped contacting them, and soon announced that VKontakte would postpone its IPO indefinitely. On 29 May 2012, Mail.ru Group announced its decision to yield control of the company to Durov by offering him the voting rights on its shares. Combined with Durov's personal 12% stake, this gave him 52% of the votes. In April 2013, the Mirilashvili family sold its 40% share in VK to United Capital Partners for $1.12 billion, while Lev Leviev sold his 8% share in the same deal, giving United Capital Partners 48% ownership. In January 2014, VK's founder Pavel Durov sold his 12% stake in the company to I
LanguageWare
LanguageWare is a natural language processing (NLP) technology developed by IBM, which allows applications to process natural language text. It comprises a set of Java libraries that provide a range of NLP functions: language identification, text segmentation/tokenization, normalization, entity and relationship extraction, and semantic analysis and disambiguation. The analysis engine uses a finite-state machine approach at multiple levels, which aids its performance characteristics while maintaining a reasonably small footprint. The behaviour of the system is driven by a set of configurable lexico-semantic resources which describe the characteristics and domain of the processed language. A default set of resources comes as part of LanguageWare and these describe the native language characteristics, such as morphology, and the basic vocabulary for the language. Supplemental resources have been created that capture additional vocabularies, terminologies, rules and grammars, which may be generic to the language or specific to one or more domains. A set of Eclipse-based customization tooling, LanguageWare Resource Workbench, is available on IBM's alphaWorks site, and allows domain knowledge to be compiled into these resources and thereby incorporated into the analysis process. LanguageWare can be deployed as a set of UIMA-compliant annotators, Eclipse plug-ins or Web Services.
Hybrid argument (cryptography)
In cryptography, the hybrid argument is a proof technique used to show that two distributions are computationally indistinguishable. == History == Hybrid arguments had their origin in a papers by Andrew Yao in 1982 and Shafi Goldwasser and Silvio Micali in 1983. == Formal description == Formally, to show two distributions D1 and D2 are computationally indistinguishable, we can define a sequence of hybrid distributions D1 := H0, H1, ..., Ht =: D2 where t is polynomial in the security parameter n. Define the advantage of any probabilistic efficient (polynomial-bounded time) algorithm A as A d v H i , H i + 1 d i s t ( A ) := | Pr [ x ← $ H i : A ( x ) = 1 ] − Pr [ x ← $ H i + 1 : A ( x ) = 1 ] | , {\displaystyle {\mathsf {Adv}}_{H_{i},H_{i+1}}^{\mathsf {dist}}(\mathbf {A} ):=\left|\Pr[x{\stackrel {\$}{\gets }}H_{i}:\mathbf {A} (x)=1]-\Pr[x{\stackrel {\$}{\gets }}H_{i+1}:\mathbf {A} (x)=1]\right|,} where the dollar symbol ($) denotes that we sample an element from the distribution at random. By triangle inequality, it is clear that for any probabilistic polynomial time algorithm A, A d v D 1 , D 2 d i s t ( A ) ≤ ∑ i = 0 t − 1 A d v H i , H i + 1 d i s t ( A ) . {\displaystyle {\mathsf {Adv}}_{D_{1},D_{2}}^{\mathsf {dist}}(\mathbf {A} )\leq \sum _{i=0}^{t-1}{\mathsf {Adv}}_{H_{i},H_{i+1}}^{\mathsf {dist}}(\mathbf {A} ).} Thus there must exist some k s.t. 0 ≤ k < t(n) and A d v H k , H k + 1 d i s t ( A ) ≥ A d v D 1 , D 2 d i s t ( A ) / t ( n ) . {\displaystyle {\mathsf {Adv}}_{H_{k},H_{k+1}}^{\mathsf {dist}}(\mathbf {A} )\geq {\mathsf {Adv}}_{D_{1},D_{2}}^{\mathsf {dist}}(\mathbf {A} )/t(n).} Since t is polynomial-bounded, for any such algorithm A, if we can show that it has a fixed negligible advantage function ε(n) between distributions Hi and Hi+1 for every i, so in particular, ϵ ( n ) ≥ A d v H k , H k + 1 d i s t ( A ) ≥ A d v D 1 , D 2 d i s t ( A ) / t ( n ) , {\displaystyle \epsilon (n)\geq {\mathsf {Adv}}_{H_{k},H_{k+1}}^{\mathsf {dist}}(\mathbf {A} )\geq {\mathsf {Adv}}_{D_{1},D_{2}}^{\mathsf {dist}}(\mathbf {A} )/t(n),} then it immediately follows that its advantage to distinguish the distributions D1 = H0 and D2 = Ht must also be negligible. == Applications == The hybrid argument is extensively used in cryptography. Some simple proofs using hybrid arguments are: If one cannot efficiently predict the next bit of the output of some number generator, then this generator is a pseudorandom number generator (PRG). We can securely expand a PRG with 1-bit output into a PRG with n-bit output.