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  MobileNet

  MobileNet is a family of convolutional neural network (CNN) architectures designed for image classification, object detection, and other computer vision tasks. They are designed for small size, low latency, and low power consumption, making them suitable for on-device inference and edge computing on resource-constrained devices like mobile phones and embedded systems. They were originally designed to be run efficiently on mobile devices with TensorFlow Lite. The need for efficient deep learning models on mobile devices led researchers at Google to develop MobileNet. As of June 2025, the family has five versions, each improving upon the previous one in terms of performance and efficiency. == Features == === V1 === MobileNetV1 was published in April 2017. Its main architectural innovation was incorporation of depthwise separable convolutions. It was first developed by Laurent Sifre during an internship at Google Brain in 2013 as an architectural variation on AlexNet to improve convergence speed and model size. The depthwise separable convolution decomposes a single standard convolution into two convolutions: a depthwise convolution that filters each input channel independently and a pointwise convolution ( 1 × 1 {\displaystyle 1\times 1} convolution) that combines the outputs of the depthwise convolution. This factorization significantly reduces computational cost. The MobileNetV1 has two hyperparameters: a width multiplier α {\displaystyle \alpha } that controls the number of channels in each layer. Smaller values of α {\displaystyle \alpha } lead to smaller and faster models, but at the cost of reduced accuracy, and a resolution multiplier ρ {\displaystyle \rho } , which controls the input resolution of the images. Lower resolutions result in faster processing but potentially lower accuracy. === V2 === MobileNetV2 was published in March 2019. It uses inverted residual layers and linear bottlenecks. Inverted residuals modify the traditional residual block structure. Instead of compressing the input channels before the depthwise convolution, they expand them. This expansion is followed by a 1 × 1 {\displaystyle 1\times 1} depthwise convolution and then a 1 × 1 {\displaystyle 1\times 1} projection layer that reduces the number of channels back down. This inverted structure helps to maintain representational capacity by allowing the depthwise convolution to operate on a higher-dimensional feature space, thus preserving more information flow during the convolutional process. Linear bottlenecks removes the typical ReLU activation function in the projection layers. This was rationalized by arguing that that nonlinear activation loses information in lower-dimensional spaces, which is problematic when the number of channels is already small. === V3 === MobileNetV3 was published in 2019. The publication included MobileNetV3-Small, MobileNetV3-Large, and MobileNetEdgeTPU (optimized for Pixel 4). They were found by a form of neural architecture search (NAS) that takes mobile latency into account, to achieve good trade-off between accuracy and latency. It used piecewise-linear approximations of swish and sigmoid activation functions (which they called "h-swish" and "h-sigmoid"), squeeze-and-excitation modules, and the inverted bottlenecks of MobileNetV2. === V4 === MobileNetV4 was published in September 2024. The publication included a large number of architectures found by NAS. Inspired by Vision Transformers, the V4 series included multi-query attention. It also unified both inverted residual and inverted bottleneck from the V3 series with the "universal inverted bottleneck", which includes these two as special cases. === V5 === MobileNetV5's architecture was published shortly after the release of Gemma 3n in June 2025. While the announcement stated a technical report on MobileNetV5 would be available soon, this has not yet materialised. The network is 10 times larger than the largest V4 variant.

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  Blocknots

  Blocknots were random sequences of numbers contained in a book and organized by numbered rows and columns and were used as additives in the reciphering of Soviet Union codes, during World War II. The Blocknot consisted of a booklet of fifty sheets of 5-figure random additive, 100 additive groups to a sheet. No sheet was used more than once, thus the blocknots were in effect a form of one-time pad. The Soviet Unions highest grade ciphers that were used in the East, were the 5-figure codebook enciphered with the Blocknot book, and were generally considered unbreakable. == Technical Description == Blocknots were distributed centrally from an office in Moscow. Every Blocknot contained 5-figure groups in a number of sheets, for the enciphering of 5-figure messages. The encipherment was effected by applying additives taken from the pad, of which 50-100 5-figure groups appeared. Each pad had a 5-figure number and each sheet had a 2-figure number running consecutively. There were 5 different types of Blocknots, in two different categories The Individual in which each table of random numbers was used only once. The General in which each page of the Blocknot was valid for one day. The security of the additive sequence rested on the choice of different starting points for each message. In 5-figure messages, the blocknot was one of the first 10 Groups in the message. Its position changed at long intervals, but was always easy to re-identify. The Russians differentiated between three types of blocks: The 3-block, DRIERBLOCK. I-block for Individual Block: 50 pages, additive read off in one direction only. The messages could be used and read only between 2 wireless telegraphy stations on one net. The 6-block, SECHSERBLOCK. Z-block for Circular Block: 30 pages, additive read off in either direction. The messages could be used and read, between all W/T stations in a net. The 2-block, ZWEIERBLOCK. OS-block. Used only in traffic from lower to higher formations. Two other types were used, in lower echelons. Notblock: Used in an emergency. Blocknot used for passing on traffic. The distribution of Blocknots was carried out centrally from Moscow to Army Groups then to Armies. The Army was responsible for their distribution throughout the lower levels of the army down to company level. Independent units took their cipher material with them. Occasionally the same blocknot was distributed to two units on different parts of the front, which enabled Depth to be established. Records of all Blocknots used were kept in Berlin and when a repeat was noticed a BLOCKNOT ANGEBOT message was sent out to all German Signals units, to indicate that it may have been possible to break the code using it. There was no certainty in this. A cryptanalyst with the General der Nachrichtenaufklärung stated while being interrogated by TICOM: It seems that depths of up to 8 were established at the beginning of the Russian Campaign but that no 5-figure code was broken after May 1943 German cryptanalysts who were prisoners of war stated under interrogation, that each of the figures 0 to 9 were placed en clair usually within the first ten groups of the text or sometimes at the end. One indicator was the Blocknot number and the consisted of two random figures, the figure representing the type, and the remaining two, the page of the Blocknot being used. In long messages, 000000 was placed in the message when the end of a page had been reached. == Chi number == The Chi-number was the serial numbering of all 5-figure messages passing through the hands of the Cipher Officer, starting on the first of January and ending on thirty-first December of the current year. It always appeared as the last group in an intercepted message, e.g. 00001 on the 1st January, or when the unit was newly set up. The progression of Chi-numbers was carefully observed and recorded in the form of a graph. A Russian corps had about 10 5-figure messages per day, and Army about 20-30 and a Front about 60–100. After only a relatively short time, the individual curves separated sharply and the type of formation could be recognized by the height of the Chi-number alone. == Monitoring == Blocknots were tracked in a card index, that was maintained by the Signal Intelligence Evaluation Centre (NAAS). The NAAS functionality included evaluation and traffic analysis, cryptanalysis, collation and dissemination of intelligence. The card index, which was one amongst several Card Indexes. A careful recording and study of blocks provided the positive clues in the identification and tracking of formations using 5-figure ciphers. The index was subdivided into two files: Search card index, contained all blocknots and chi-numbers whether or not they were known. Unit card index, contained only known Block and Chi-numbers. Inspector Berger, who was the chief cryptanalyst of NAAS 1 stated that the two files formed: The most important and surest instruments for identifying Russian radio nets, known to him. The Blocknots were also used in the Stationary Intercept Company (Feste), the military unit that were designed to work at a lower level to the NAAS, at the Army level and were semi-motorized, and closer to the front. The Feste used the Blocknot value along with several other parameters to build a network diagram. The network diagram was studied extensively, as part of a 6-stage process, that involved several departments within the Feste. The outcome was a metric which determined the most interesting circuit for traffic monitoring, and least interesting, where monitoring of traffic should cease. == Analysis == Johannes Marquart was a mathematician and cryptanalyst who initially worked for Inspectorate 7/VI and later led Referat Ia of Group IV of the General der Nachrichtenaufklärung. Marquart was assigned the study of the Soviet Union Blocknot traffic. Marquart and his unit conducted extensive research in an attempt to discover the method by which they were produced. All the counts which they made, however, failed to reveal any non-random characteristics in the design of the tables, and while they thought the Blocknots must have been generated by machine, they were never able to draw any concrete deductions as a result of their research. == Example == The Soviet 3rd Guard Tank Army transmits a 5-figure message with the Blocknot of 37581 (one of the first 10 groups in the message). On the same day the Block 37582 was used by the same formation. The next day 37583 appeared. Thereafter, for a period, the Army was not heard by German Wireless telegraphy intercept operators, as it was maintaining wireless silence. After a few days, an unidentified net with the Blocknot 37588 is picked up. This message net is claimed, because of the proximity of the blocks (88/83) to be the 3rd Guard Tank Army. The missing Blocknots 84-87 were presumably used in telegraphic, telephonic or courier communications. The Chi number provides confirmation of the first assumption, based on proximity of blocknots in most cases.

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  Cambridge Analytica

  Cambridge Analytica Ltd. (CA), previously known as SCL USA, was a British political consulting firm that came to prominence through the Facebook–Cambridge Analytica data scandal. It was founded in 2013, as a subsidiary of the private intelligence company and self-described "global election management agency" SCL Group by long-time SCL executives Nigel Oakes, Alexander Nix and Alexander Oakes, with Nix as CEO. Cambridge Analytica was hired by a variety of political actors, including the Trinidadian government in 2010 and the 2016 presidential campaigns of Ted Cruz and Donald Trump. The firm maintained offices in London, New York City, and Washington, D.C. The company closed operations in 2018 due to backlash from the scandal, although firms related to both Cambridge Analytica and its parent firm SCL still exist. == History == Cambridge Analytica was founded in 2013 as a subsidiary of the private intelligence company SCL Group, which describes itself as providing "data, analytics and strategy to governments and military organisations worldwide". The company was part of "an international web of companies" headed by the London-based SCL Group. Cambridge Analytica (SCL USA) was incorporated in January 2013 with its registered office being in Westferry Circus, London and consisting of just one staff member, director and CEO Alexander Nix (also appointed in January 2015). Nix was also the director of nine similar companies sharing the same registered offices in London, including Firecrest technologies, Emerdata and six SCL Group companies including "SCL elections limited". Nigel Oakes, known as the former boyfriend of Lady Helen Windsor, had founded the predecessor SCL Group in the 1990s, and in 2005 Oakes established SCL Group together with his brother Alexander Oakes and Alexander Nix; SCL Group was the parent company of Cambridge Analytica. Former Conservative minister and MP Sir Geoffrey Pattie was the founding chairman of SCL; Lord Ivar Mountbatten also joined Oakes as a director of the company. As a result of the Facebook–Cambridge Analytica data scandal, Nix was removed as CEO and replaced by Julian Wheatland before the company closed. Several of the company's executives were Old Etonians. The company's owners included several of the Conservative Party's largest donors such as billionaire Vincent Tchenguiz, former British Conservative minister Jonathan Marland, Baron Marland and the family of American hedge fund manager Robert Mercer. The company combined misappropriation of digital assets, data mining, data brokerage, and data analysis with strategic communication during electoral processes. While its parent SCL had focused on influencing elections in developing countries since the 1990s, Cambridge Analytica focused more on the western world, including the United Kingdom and the United States; CEO Alexander Nix has said CA was involved in 44 U.S. political races in 2014. In 2015, CA performed data analysis services for Ted Cruz's presidential campaign. In 2016, CA worked for Donald Trump's presidential campaign as well as for Leave.EU (one of the organisations campaigning in the United Kingdom's referendum on European Union membership). CA's role in those campaigns has been controversial and is the subject of ongoing inquiries in both countries. Political scientists question CA's claims about the effectiveness of its methods of targeting voters. == Data scandal == In March 2018, media outlets broke news of Cambridge Analytica's business practices. The New York Times and The Observer reported that the company had acquired and used personal data about Facebook users from an external researcher who had told Facebook he was collecting it for academic purposes. Shortly afterwards, Channel 4 News aired undercover investigative videos showing Nix boasting about using prostitutes, bribery sting operations, and honey traps to discredit politicians on whom it had conducted opposition research, and saying that the company "ran all of (Donald Trump's) digital campaign". In response to the media reports, the Information Commissioner's Office (ICO) of the UK pursued a warrant to search the company's servers. Facebook banned Cambridge Analytica from advertising on its platform, saying that it had been deceived. On 23 March 2018, the British High Court granted the ICO a warrant to search Cambridge Analytica's London offices. As a result, Nix was suspended as CEO, and replaced by Julian Wheatland. The personal data of up to 87 million Facebook users were acquired via the 270,000 Facebook users who used a Facebook app created by Aleksandr Kogan called "This Is Your Digital Life". This was a personality profiling app and asked simple personality questions similar to other Facebook quizzes. Kogan was a scientist and psychologist, also being an employed lecturer for the University of Cambridge from 2012 to 2018. Alexander Nix claimed they had close to five thousand data points on each person who participated. They also gathered information through other data brokers ending with them acquiring millions of data points from American citizens. Kogan's app exploited a feature of Facebook's Graph API (version 1.0), which permitted any third-party app to access not only the app user's data, but also the full profile data of all of that user's Facebook friends, without those friends' knowledge or consent. This platform-wide design was available to all developers and was used by tens of thousands of apps; Facebook CEO Mark Zuckerberg later told the House Energy and Commerce Committee that the company was auditing "tens of thousands" of apps that had had access to large amounts of user data. Because the average Facebook user at the time had approximately 300 friends, the 270,000 users who installed Kogan's app yielded data on up to 87 million people. Facebook deprecated the friends-data API in April 2014 and shut it down entirely in April 2015, but data already collected by apps remained in developers' possession. Kogan passed this data to Cambridge Analytica, breaching Facebook's terms of service. On 1 May 2018, Cambridge Analytica and its parent company SCL filed for insolvency proceedings and closed operations. Alexander Tayler, a former director for Cambridge Analytica, was appointed director of Emerdata on 28 March 2018. Rebekah Mercer, Jennifer Mercer, Alexander Nix and Johnson Chun Shun Ko, who has links to American businessman Erik Prince, are in leadership positions at Emerdata. The Russo brothers are producing an upcoming film on Cambridge Analytica. In 2019 the Federal Trade Commission filed an administrative complaint against Cambridge Analytica for misuse of data. In 2020, the British Information Commissioner's Office closed a three-year inquiry into the company, concluded that Cambridge Analytica was "not involved" in the 2016 Brexit referendum and found no additional evidence for Russia's alleged interference during the campaign. US sensitive polling and election data, however, were passed to Russian Intelligence via a Cambridge Analytica contractor Sam Patten, Trump campaign manager Paul Manafort, and Russian agent Konstantin Kilimnik, who was indicted during the affair. Publicly, parent company SCL Group called itself a "global election management agency", Politico reported it was known for involvement "in military disinformation campaigns to social media branding and voter targeting". SCL gained work on a large number of campaigns for the US and UK governments' war on terror advancing their model of behavioral conflict during the 2000s. SCL's involvement in the political world has been primarily in the developing world where it has been used by the military and politicians to study and manipulate public opinion and political will. Slate writer Sharon Weinberger compared one of SCL's hypothetical test scenarios to fomenting a coup. Among the investors in Cambridge Analytica were some of the Conservative Party's largest donors such as billionaire Vincent Tchenguiz, former Conservative minister Jonathan Marland, Baron Marland, Roger Gabb, the family of American hedge fund manager Robert Mercer, and Steve Bannon. A minimum of 15 million dollars has been invested into the company by Mercer, according to The New York Times. Bannon's stake in the company was estimated at 1 to 5 million dollars, but he divested his holdings in April 2017 as required by his role as White House Chief Strategist. In March 2018, Jennifer Mercer and Rebekah Mercer became directors of Emerdata limited. In March 2018 it became public by Christopher Wylie, that Cambridge Analytica's first activities were founded on a data set, which its parent company SCL bought 2014 from a company named Global Science Research founded by Aleksandr Kogan and his team present across the world who worked as a psychologist at Cambridge. During Boris Johnson's tenure as foreign secretary, the Foreign Office sought advice from Cambridge Analytica and Boris Johnson had a meeting with Alexander N

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  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 →

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  Protocol engineering

  Protocol engineering is the application of systematic methods to the development of communication protocols. It uses many of the principles of software engineering, but it is specific to the development of distributed systems. == History == When the first experimental and commercial computer networks were developed in the 1970s, the concept of protocols was not yet well developed. These were the first distributed systems. In the context of the newly adopted layered protocol architecture (see OSI model), the definition of the protocol of a specific layer should be such that any entity implementing that specification in one computer would be compatible with any other computer containing an entity implementing the same specification, and their interactions should be such that the desired communication service would be obtained. On the other hand, the protocol specification should be abstract enough to allow different choices for the implementation on different computers. It was recognized that a precise specification of the expected service provided by the given layer was important. It is important for the verification of the protocol, which should demonstrate that the communication service is provided if both protocol entities implement the protocol specification correctly. This principle was later followed during the standardization of the OSI protocol stack, in particular for the transport layer. It was also recognized that some kind of formalized protocol specification would be useful for the verification of the protocol and for developing implementations, as well as test cases for checking the conformance of an implementation against the specification. While initially mainly finite-state machine were used as (simplified) models of a protocol entity, in the 1980s three formal specification languages were standardized, two by ISO and one by ITU. The latter, called SDL, was later used in industry and has been merged with UML state machines. == Principles == The following are the most important principles for the development of protocols: Layered architecture: A protocol layer at the level n consists of two (or more) entities that have a service interface through which the service of the layer is provided to the users of the protocol, and which uses the service provided by a local entity of level (n-1). The service specification of a layer describes, in an abstract and global view, the behavior of the layer as visible at the service interfaces of the layer. The protocol specification defines the requirements that should be satisfied by each entity implementation. Protocol verification consists of showing that two (or more) entities satisfying the protocol specification will provide at their service interfaces the specified service of that layer. The (verified) protocol specification is used mainly for the following two activities: The development of an entity implementation. Note that the abstract properties of the service interface are defined by the service specification (and also used by the protocol specification), but the detailed nature of the interface can be chosen during the implementation process, separately for each entity. Test suite development for conformance testing. Protocol conformance testing checks that a given entity implementation conforms to the protocol specification. The conformance test cases are developed based on the protocol specification and are applicable to all entity implementations. Therefore standard conformance test suites have been developed for certain protocol standards. == Methods and tools == Tools for the activities of protocol verification, entity implementation and test suite development can be developed when the protocol specification is written in a formalized language which can be understood by the tool. As mentioned, formal specification languages have been proposed for protocol specification, and the first methods and tools where based on finite-state machine models. Reachability analysis was proposed to understand all possible behaviors of a distributed system, which is essential for protocol verification. This was later complemented with model checking. However, finite-state descriptions are not powerful enough to describe constraints between message parameters and the local variables in the entities. Such constraints can be described by the standardized formal specification languages mentioned above, for which powerful tools have been developed. It is in the field of protocol engineering that model-based development was used very early. These methods and tools have later been used for software engineering as well as hardware design, especially for distributed and real-time systems. On the other hand, many methods and tools developed in the more general context of software engineering can also be used of the development of protocols, for instance model checking for protocol verification, and agile methods for entity implementations. == Constructive methods for protocol design == Most protocols are designed by human intuition and discussions during the standardization process. However, some methods have been proposed for using constructive methods possibly supported by tools to automatically derive protocols that satisfy certain properties. The following are a few examples: Semi-automatic protocol synthesis: The user defines all message sending actions of the entities, and the tool derives all necessary reception actions (even if several messages are in transit). Synchronizing protocol: The state transitions of one protocol entity are given by the user, and the method derives the behavior of the other entity such that it remains in states that correspond to the former entity. Protocol derived from service specification: The service specification is given by the user and the method derives a suitable protocol for all entities. Protocol for control applications: The specification of one entity (called the plant - which must be controlled) is given, and the method derives a specification of the other entity such that certain fail states of the plant are never reached and certain given properties of the plant's service interactions are satisfied. This is a case of supervisory control. == Books == Ming T. Liu, Protocol Engineering, Advances in Computers, Volume 29, 1989, Pages 79–195. G.J. Holzmann, Design and Validation of Computer Protocols, Prentice Hall, 1991. H. König, Protocol Engineering, Springer, 2012. M. Popovic, Communication Protocol Engineering, CRC Press, 2nd Ed. 2018. P. Venkataram, S.S. Manvi, B.S. Babu, Communication Protocol Engineering, 2014.

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  Protecting Our Kids from Social Media Addiction Act

  Protecting Our Kids from Social Media Addiction Act also known as California SB 976 is a law that was enacted in September 2024 that is meant to address problematic social media usage among minors. The law prohibitions minors to have "addictive feeds" unless they have verifiable parental consent, minor's notifications are also restricted between 12 am to 6 am and during school hours between 8 am and 3 pm it also well requires minors to have default privacies settings and have social media companies to publicly disclose certain metrics about their users. The law was set to take effect in two steps the first being the restrictions on social media feeds, notifications, disclosures from social media companies and default settings which would have taken effect on January 1, 2025, and the age verification provision which would have taken effect on January 1, 2027. However, has faced legal challenges since its enactment delaying its enactment. == Legal Challenges == In November 2024 NetChoice a trade association representing many of the biggest social media companies such as YouTube, Facebook and Instagram sued the attorney general of California Rob Bonta hoping to get an injunction before the first set of the law's provisions would take effect in January of the next year. However, judge Edward Davila would only grant Netchoice's request as to the restrictions on notifications and public disclosures and would deny their request as to the rest of the law. The law was later fully enjoined temporarily by the District Court and Appellant Court pending appeal, and the case is now in the Ninth Circuit Court of Appeals and is pending a decision. === Social media platforms challenges to law === In November 2025 Meta, Google and TikTok filed lawsuits against the law arguing it violates the first amendment.

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  Symmetric Boolean function

  In mathematics, a symmetric Boolean function is a Boolean function whose value does not depend on the order of its input bits, i.e., it depends only on the number of ones (or zeros) in the input. For this reason they are also known as Boolean counting functions. There are 2n+1 symmetric n-ary Boolean functions. Instead of the truth table, traditionally used to represent Boolean functions, one may use a more compact representation for an n-variable symmetric Boolean function: the (n + 1)-vector, whose i-th entry (i = 0, ..., n) is the value of the function on an input vector with i ones. Mathematically, the symmetric Boolean functions correspond one-to-one with the functions that map n+1 elements to two elements, f : { 0 , 1 , . . . , n } → { 0 , 1 } {\displaystyle f:\{0,1,...,n\}\rightarrow \{0,1\}} . Symmetric Boolean functions are used to classify Boolean satisfiability problems. == Special cases == A number of special cases are recognized: Majority function: their value is 1 on input vectors with more than n/2 ones Threshold functions: their value is 1 on input vectors with k or more ones for a fixed k All-equal and not-all-equal function: their values is 1 when the inputs do (not) all have the same value Exact-count functions: their value is 1 on input vectors with k ones for a fixed k One-hot or 1-in-n function: their value is 1 on input vectors with exactly one one One-cold function: their value is 1 on input vectors with exactly one zero Congruence functions: their value is 1 on input vectors with the number of ones congruent to k mod m for fixed k, m Parity function: their value is 1 if the input vector has odd number of ones The n-ary versions of AND, OR, XOR, NAND, NOR and XNOR are also symmetric Boolean functions. == Properties == In the following, f k {\displaystyle f_{k}} denotes the value of the function f : { 0 , 1 } n → { 0 , 1 } {\displaystyle f:\{0,1\}^{n}\rightarrow \{0,1\}} when applied to an input vector of weight k {\displaystyle k} . === Weight === The weight of the function can be calculated from its value vector: | f | = ∑ k = 0 n ( n k ) f k {\displaystyle |f|=\sum _{k=0}^{n}{\binom {n}{k}}f_{k}} === Algebraic normal form === The algebraic normal form either contains all monomials of certain order m {\displaystyle m} , or none of them; i.e. the Möbius transform f ^ {\displaystyle {\hat {f}}} of the function is also a symmetric function. It can thus also be described by a simple (n+1) bit vector, the ANF vector f ^ m {\displaystyle {\hat {f}}_{m}} . The ANF and value vectors are related by a Möbius relation: f ^ m = ⨁ k 2 ⊆ m 2 f k {\displaystyle {\hat {f}}_{m}=\bigoplus _{k_{2}\subseteq m_{2}}f_{k}} where k 2 ⊆ m 2 {\displaystyle k_{2}\subseteq m_{2}} denotes all the weights k whose base-2 representation is covered by the base-2 representation of m (a consequence of Lucas’ theorem). Effectively, an n-variable symmetric Boolean function corresponds to a log(n)-variable ordinary Boolean function acting on the base-2 representation of the input weight. For example, for three-variable functions: f ^ 0 = f 0 f ^ 1 = f 0 ⊕ f 1 f ^ 2 = f 0 ⊕ f 2 f ^ 3 = f 0 ⊕ f 1 ⊕ f 2 ⊕ f 3 {\displaystyle {\begin{array}{lcl}{\hat {f}}_{0}&=&f_{0}\\{\hat {f}}_{1}&=&f_{0}\oplus f_{1}\\{\hat {f}}_{2}&=&f_{0}\oplus f_{2}\\{\hat {f}}_{3}&=&f_{0}\oplus f_{1}\oplus f_{2}\oplus f_{3}\end{array}}} So the three variable majority function with value vector (0, 0, 1, 1) has ANF vector (0, 0, 1, 0), i.e.: Maj ( x , y , z ) = x y ⊕ x z ⊕ y z {\displaystyle {\text{Maj}}(x,y,z)=xy\oplus xz\oplus yz} === Unit hypercube polynomial === The coefficients of the real polynomial agreeing with the function on { 0 , 1 } n {\displaystyle \{0,1\}^{n}} are given by: f m ∗ = ∑ k = 0 m ( − 1 ) | k | + | m | ( m k ) f k {\displaystyle f_{m}^{}=\sum _{k=0}^{m}(-1)^{|k|+|m|}{\binom {m}{k}}f_{k}} For example, the three variable majority function polynomial has coefficients (0, 0, 1, -2): Maj ( x , y , z ) = ( x y + x z + y z ) − 2 ( x y z ) {\displaystyle {\text{Maj}}(x,y,z)=(xy+xz+yz)-2(xyz)} == Examples ==

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  MIME Object Security Services

  MIME Object Security Services (MOSS) is a protocol that uses the multipart/signed and multipart/encrypted framework to apply digital signature and encryption services to MIME objects. == Details == The services are offered through the use of end-to-end cryptography between an originator and a recipient at the application layer. Asymmetric (public key) cryptography is used in support of the digital signature service and encryption key management. Symmetric (secret key) cryptography is used in support of the encryption service. The procedures are intended to be compatible with a wide range of public key management approaches, including both ad hoc and certificate-based schemes. Mechanisms are provided to support many public key management approaches. == Spreading == MOSS was never widely deployed and is now abandoned, largely due to the popularity of PGP.

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  Image destriping

  Image destriping is the process of removing stripes or streaks from images and videos without disrupting the original image/video. These artifacts plague a range of fields in scientific imaging including atomic force microscopy, light sheet fluorescence microscopy, and planetary satellite imaging. The most common image processing techniques to reduce stripe artifacts is with Fourier filtering. Unfortunately, filtering methods risk altering or suppressing useful image data. Methods developed for multiple-sensor imaging systems in planetary satellites use statistical-based methods to match signal distribution across multiple sensors. More recently, a new class of approaches leverage compressed sensing, to regularize an optimization problem, and recover stripe free images. In many cases, these destriped images have little to no artifacts, even at low signal to noise ratios.

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  Peñabot

  Peñabot is the nickname for automated social media accounts allegedly used by the Mexican government of Enrique Peña Nieto and the PRI political party to keep unfavorable news from reaching the Mexican public. Peñabot accusations are related to the broader issue of fake news in the 21st century. == History of disinformation in Mexican politics == The PRI political party has been reported to use fake news since before Peña Nieto. The main tactic originally was to spread such propaganda through open radio and television networks. Such tactic was effective in Mexico, because newspaper readership is low and cable TV is largely limited to the middle classes; consequently, the country's two major television networks – Televisa and TV Azteca – exert a significant influence in national politics. Televisa itself, not only owns around two-thirds of the programming on Mexico's TV channels, making it not only Mexico's largest television network, but also is the largest media network in the Spanish-speaking world. == Peñabots == Analysts have given the name Peñabots to a suspected network of automated accounts on social media used by the Mexican government to spread pro-government propaganda and to marginalize dissenting opinions in social media. The bots were first noticed in the 2012 elections when they were used to disseminate opinions in support of Enrique Peña Nieto on social networks such as Twitter and Facebook. According to Aristegui Noticias, their usage went against articles 6 and 134 of the Mexican Constitution. Those used by Peña Nieto's government cost an estimated 80 million pesos monthly, which news outlets argued only helped the government spread fake support towards the president, but did not have a benefit towards Mexican people (with whom EPN was highly unpopular). Facebook held approximately 640,321 Peñabots, while Twitter had less. As of July 2017, Oxford Internet Institute's Computational Propaganda Research Project claimed many western democracies, Mexico included, perform social media manipulation, thus saying the manipulation comes directly from the Mexican government itself. During Peña Nieto's subsequent presidency, analysts noted that Peñabots were used to overpower trending topics that critiqued government, to flood trending government critical hashtags with spam, to create fake trends by pushing alternative hashtags, and to push smear campaigns and threats against government-critical activists and journalists. Peñabots were distinguished as their pattern of activity was distinct from that of ordinary interaction on social networks. === Meadebots === On Twitter it was reported that about 94% of the followers of 2018 presidential candidate from the PRI Jose Antonio Meade were bots. When Antonio Meade presented himself as a candidate for the 2018 presidential election, his social media accounts such as "@MovimientoMEADE" (created by the PRI's official account @PRI_Nacional), obtained a huge quantity of followers in a short span of time. Some users noticed and brought it to attention, and after investigation it was reported 94% of such followers were bots (702,000 out of 747,000), and the account was eliminated from Twitter after 20 hours. The fake accounts used the hashtags #YoConMeade and #Meade18. It was further revealed was that Meade's official account on Twitter, @JoseAMeadeK had 25% bots (216,000 fake followers out of the 981,000). == Manipulation of news media in Mexico, through television == The Mexican government of Peña Nieto has been accused of using various means to keep unfavorable news from reaching the Mexican people. Many Mexicans have protested this practice as it clearly goes against the freedom of speech. The PRI has been reported to use fake news since before Peña Nieto. The main tactic has been to spread such propaganda through radio and television. This tactic is perceived as effective in Mexico, because newspaper readership is low and research on the Internet and cable TV is largely limited to the middle classes; consequently, the country's two major television networks – Televisa and TV Azteca – exert a significant influence in national politics. Televisa itself, owns around two-thirds of the programming on Mexico's TV channels, making it not only Mexico's largest television network, but also is the largest media network in the Spanish-speaking world. In June 2012, before the 2012 Mexican presidential elections, the British newspaper The Guardian published a series of allegations claiming Televisa, sold favorable coverage to top politicians in its news and entertainment shows, this scandal became known as the Televisa controversy. The documents published by 'The Guardian alleged that a secretive circle within Televisa manipulated news coverage to favor PRI presidential candidate Enrique Peña Nieto, who was poised as favorite to win. Televisa's secret circle supposedly commissioned videos to promote Peña Nieto and lash out his political rivals in 2009. The Guardian documents suggest that Televisa's secret team distributed such videos through e-mail, posting them posted them on Facebook and YouTube, some can still be seen there. Another document was a PowerPoint presentation, with a slide explicitly aimed at rival leftist candidate of the Party of the Democratic Revolution (PRD), Andrés Manuel López Obrador. Supposedly given to The Guardian by a Televisa employee. The document's authenticity was never possible to confirm– however dates, names, and events largely coincide. Televisa refused to talk the documents, and denied a relationship with the PRI or its presidential candidate, saying that they had provided equal media coverage to all parties. Televisa published an article supposedly showing discrepancies in The Guardian documents and denying accusations. Mexican citizens complained about the perceived favoritism towards Enrique Peña Nieto and the PRI, protesting through the Yo Soy 132 movement which Televisa covered in detail. However, Televisa's news media coverage is perceived to have been biased, by using a media coverage tactic Mexican citizens call cortinas de humo (smoke screens). These introduce a news scandal giving extensive coverage to distract citizens from a potential conflict-of-interest or controversy that could damage the image of the politician favored by the network. An example of a perceived smoke screen would be the news media coverage of "Caso Michoacán" and "Caso Paolette" distracting all the attention from the parallel "Yo soy 132" movement. A few years later, on the day of September 11, 2016; factual evidence of Televisa's performing media manipulation emerged, when a Televisa news anchor while live-on air reading a teleprompter, mistakenly read out loud that "try that Jaime "Ël Bronco" Rodríguez Calderón (Nuevo Leon's governor) is mentioned as little as possible". Newspaper El Universal caught it on video and published it social media. Televisa didn't mention the story and declined to comment. Lack of news coverage concerning Nuevo León's Governor Jaime Rodriguez, is perceived due to him being the first elected governor to not be part of any political party (Independent Governor), and because unlike the governors from the PRI preceding him, the independent governor "El Bronco" doesn't spend money on publicity at all, preferring to communicate all news by using social media such as Twitter and Facebook. While the incident may have proven Televisa's bias, there wasn't anything to incriminate the PRI political party or Enrique Peña Nieto, though it did further suspicion of Televisa manipulating news media. In contrast, a December 2017 article of The New York Times, reported Enrique Peña Nieto spending about 2000 million dollars on publicity, during his first 5 years as president, the largest publicity budget ever spent by a Mexican President. Additionally, 68 percent of news journalists admitted to not believe to have enough freedom of speech, and award-winning news reporter Carmen Aristegui was controversially fired shortly after revealing the Mexican White House scandals. == Violence and spying towards news journalists and civil rights activists == Far for only being receiving accusations of spreading fake news, the Mexican government of EPN (Enrique Peña Nieto) has also been accused of violence towards news journalists, and of spying on them, and also towards civil right leaders and their families. During his tenure as president, Peña Nieto has been accused of failing to protect news journalists, whose deaths are speculated to be politically triggered, by politicians attempting to prevent them from covering political scandals. The New York Times published a news report on the matter titled, "In Mexico it's easy to kill a journalist", on it mentioning how during EPN's government, Mexico became one of the worst countries on which to be a journalist. The assassination of journalist Javier Valdez on May 23, 2017, received national coverage, with multiple news journalists

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  Social collaboration

  Social collaboration refers to processes that help multiple people or groups interact and share information to achieve common goals. Such processes find their 'natural' environment on the Internet, where collaboration and social dissemination of information are made easier by current innovations and the proliferation of the web. Sharing concepts on a digital collaboration environment often facilitates a "brainstorming" process, where new ideas may emerge due to the varied contributions of individuals. These individuals may hail from different walks of life, different cultures and different age groups, their diverse thought processes help in adding new dimensions to ideas, dimensions that previously may have been missed. A crucial concept behind social collaboration is that 'ideas are everywhere.' Individuals are able to share their ideas in an unrestricted environment as anyone can get involved and the discussion is not limited to only those who have domain knowledge. Social collaboration is also known as enterprise social networking, and the products to support it are often branded enterprise social networks (ESNs). It is important that we understand the rhythm of social collaboration. There needs to be a balance, with ease to move from focused solitary work to brainstorming for problem solving in group work. This critical balance can be achieved by creating structures or a work environment where it is not too rigid to prevent brainstorming in group work nor too loose to result in total chaos. Social collaboration should happen at the edge of chaos. Work practices should support social collaboration. The most effective environment is one that supports opportunistic planning. Opportunistic planning provides a general plan but then gives enough room for flexibility to change activities and tasks until the last moment. This way, people are able to cope up with unforeseen developments and not throwing away everything with one grand plan. == Comparison to social networking == Social collaboration is related to social networking, with the distinction that while social networking is individual-centric, social collaboration is entirely group-centric. Generally speaking, social networking means socializing for personal, professional or entertainment purposes, for example, LinkedIn and Facebook. Social collaboration, on the other hand, means working socially to achieve a common goal, for example, GitHub and Quora. Social networking services generally focus on individuals sharing messages in a more-or-less undirected way and receiving messages from many sources into a single personalized activity feed. Social collaboration services, on the other hand, focus on the identification of groups and collaboration spaces in which messages are explicitly directed at the group and the group activity feed is seen the same way by everyone. Social collaboration may refer to time-bound collaborations with an explicit goal to be completed or perpetual collaborations in which the goal is knowledge sharing (e.g. community of practice, online community). == Comparison to crowdsourcing == Social collaboration is similar to crowdsourcing as it involves individuals working together towards a common goal. Crowdsourcing is a method for harnessing specific information from a large, diverse group of people. Unlike social collaboration, which involves much communication and cooperation among a large group of people, crowdsourcing is more like individuals working towards the common goal relatively independently. Therefore, the process of working involves less communication. Andrea Grover, curator of a crowdsourcing art show, explained that collaboration among individuals is an appealing experience, because participation is "a low investment, with the possibility of a high return." == Social collaboration software == Notable social collaboration software includes Glip messaging, Google Apps, Knowledge Plaza Electronic Document System and Social Intranet, Microsoft Lync social collaboration tool for businesses, Slack, Weekdone for managers, and Wrike. == Future == Social collaboration is going to be used as a tool in companies to enhance productivity. Social workers could be able to use social collaboration tools to manage personal tasks, professional projects and social networks with other colleagues within the same organization. Social collaboration will serve as a platform to get people involved and connected. This kind of platform provides a spiritual training practice for social workers. Social collaboration software could help enhance the communication between customers and employees and build trust in the organization. When we need real-time chat, it would be excellent to include every participant in a shared and archived forum which keeps a record of important information and logs. So collaborators need not worry about losing important records while working towards the common goal. The interactive communication and synchronous environment promote understanding among colleagues. Collaboration helps in building strong relationships between workers, which in turn leads to faster problem solving. The close connection between workers and customers creates a scalable organization which naturally increases the trust and faith that customers have in the company. Therefore, the interactive customer relationship levels up customer satisfaction in ways that traditional collaboration methods cannot. Apart from its effect on the way work will be conducted in the future, social collaboration will also affect society. In the coming years social collaboration will be the driving force in societal change as more and more people work together to get their vision across to governments and governing agencies. An example of this is Change.org, an online petition tool where users can help bring their government's attention to pressing social issues that need to be addressed.

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  Blocknots

  Blocknots were random sequences of numbers contained in a book and organized by numbered rows and columns and were used as additives in the reciphering of Soviet Union codes, during World War II. The Blocknot consisted of a booklet of fifty sheets of 5-figure random additive, 100 additive groups to a sheet. No sheet was used more than once, thus the blocknots were in effect a form of one-time pad. The Soviet Unions highest grade ciphers that were used in the East, were the 5-figure codebook enciphered with the Blocknot book, and were generally considered unbreakable. == Technical Description == Blocknots were distributed centrally from an office in Moscow. Every Blocknot contained 5-figure groups in a number of sheets, for the enciphering of 5-figure messages. The encipherment was effected by applying additives taken from the pad, of which 50-100 5-figure groups appeared. Each pad had a 5-figure number and each sheet had a 2-figure number running consecutively. There were 5 different types of Blocknots, in two different categories The Individual in which each table of random numbers was used only once. The General in which each page of the Blocknot was valid for one day. The security of the additive sequence rested on the choice of different starting points for each message. In 5-figure messages, the blocknot was one of the first 10 Groups in the message. Its position changed at long intervals, but was always easy to re-identify. The Russians differentiated between three types of blocks: The 3-block, DRIERBLOCK. I-block for Individual Block: 50 pages, additive read off in one direction only. The messages could be used and read only between 2 wireless telegraphy stations on one net. The 6-block, SECHSERBLOCK. Z-block for Circular Block: 30 pages, additive read off in either direction. The messages could be used and read, between all W/T stations in a net. The 2-block, ZWEIERBLOCK. OS-block. Used only in traffic from lower to higher formations. Two other types were used, in lower echelons. Notblock: Used in an emergency. Blocknot used for passing on traffic. The distribution of Blocknots was carried out centrally from Moscow to Army Groups then to Armies. The Army was responsible for their distribution throughout the lower levels of the army down to company level. Independent units took their cipher material with them. Occasionally the same blocknot was distributed to two units on different parts of the front, which enabled Depth to be established. Records of all Blocknots used were kept in Berlin and when a repeat was noticed a BLOCKNOT ANGEBOT message was sent out to all German Signals units, to indicate that it may have been possible to break the code using it. There was no certainty in this. A cryptanalyst with the General der Nachrichtenaufklärung stated while being interrogated by TICOM: It seems that depths of up to 8 were established at the beginning of the Russian Campaign but that no 5-figure code was broken after May 1943 German cryptanalysts who were prisoners of war stated under interrogation, that each of the figures 0 to 9 were placed en clair usually within the first ten groups of the text or sometimes at the end. One indicator was the Blocknot number and the consisted of two random figures, the figure representing the type, and the remaining two, the page of the Blocknot being used. In long messages, 000000 was placed in the message when the end of a page had been reached. == Chi number == The Chi-number was the serial numbering of all 5-figure messages passing through the hands of the Cipher Officer, starting on the first of January and ending on thirty-first December of the current year. It always appeared as the last group in an intercepted message, e.g. 00001 on the 1st January, or when the unit was newly set up. The progression of Chi-numbers was carefully observed and recorded in the form of a graph. A Russian corps had about 10 5-figure messages per day, and Army about 20-30 and a Front about 60–100. After only a relatively short time, the individual curves separated sharply and the type of formation could be recognized by the height of the Chi-number alone. == Monitoring == Blocknots were tracked in a card index, that was maintained by the Signal Intelligence Evaluation Centre (NAAS). The NAAS functionality included evaluation and traffic analysis, cryptanalysis, collation and dissemination of intelligence. The card index, which was one amongst several Card Indexes. A careful recording and study of blocks provided the positive clues in the identification and tracking of formations using 5-figure ciphers. The index was subdivided into two files: Search card index, contained all blocknots and chi-numbers whether or not they were known. Unit card index, contained only known Block and Chi-numbers. Inspector Berger, who was the chief cryptanalyst of NAAS 1 stated that the two files formed: The most important and surest instruments for identifying Russian radio nets, known to him. The Blocknots were also used in the Stationary Intercept Company (Feste), the military unit that were designed to work at a lower level to the NAAS, at the Army level and were semi-motorized, and closer to the front. The Feste used the Blocknot value along with several other parameters to build a network diagram. The network diagram was studied extensively, as part of a 6-stage process, that involved several departments within the Feste. The outcome was a metric which determined the most interesting circuit for traffic monitoring, and least interesting, where monitoring of traffic should cease. == Analysis == Johannes Marquart was a mathematician and cryptanalyst who initially worked for Inspectorate 7/VI and later led Referat Ia of Group IV of the General der Nachrichtenaufklärung. Marquart was assigned the study of the Soviet Union Blocknot traffic. Marquart and his unit conducted extensive research in an attempt to discover the method by which they were produced. All the counts which they made, however, failed to reveal any non-random characteristics in the design of the tables, and while they thought the Blocknots must have been generated by machine, they were never able to draw any concrete deductions as a result of their research. == Example == The Soviet 3rd Guard Tank Army transmits a 5-figure message with the Blocknot of 37581 (one of the first 10 groups in the message). On the same day the Block 37582 was used by the same formation. The next day 37583 appeared. Thereafter, for a period, the Army was not heard by German Wireless telegraphy intercept operators, as it was maintaining wireless silence. After a few days, an unidentified net with the Blocknot 37588 is picked up. This message net is claimed, because of the proximity of the blocks (88/83) to be the 3rd Guard Tank Army. The missing Blocknots 84-87 were presumably used in telegraphic, telephonic or courier communications. The Chi number provides confirmation of the first assumption, based on proximity of blocknots in most cases.

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  Curvelet

  Curvelets are a non-adaptive technique for multi-scale object representation. Being an extension of the wavelet concept, they are becoming popular in similar fields, namely in image processing and scientific computing. Wavelets generalize the Fourier transform by using a basis that represents both location and spatial frequency. For 2D or 3D signals, directional wavelet transforms go further, by using basis functions that are also localized in orientation. A curvelet transform differs from other directional wavelet transforms in that the degree of localisation in orientation varies with scale. In particular, fine-scale basis functions are long ridges; the shape of the basis functions at scale j is 2 − j {\displaystyle 2^{-j}} by 2 − j / 2 {\displaystyle 2^{-j/2}} so the fine-scale bases are skinny ridges with a precisely determined orientation. Curvelets are an appropriate basis for representing images (or other functions) which are smooth apart from singularities along smooth curves, where the curves have bounded curvature, i.e. where objects in the image have a minimum length scale. This property holds for cartoons, geometrical diagrams, and text. As one zooms in on such images, the edges they contain appear increasingly straight. Curvelets take advantage of this property, by defining the higher resolution curvelets to be more elongated than the lower resolution curvelets. However, natural images (photographs) do not have this property; they have detail at every scale. Therefore, for natural images, it is preferable to use some sort of directional wavelet transform whose wavelets have the same aspect ratio at every scale. When the image is of the right type, curvelets provide a representation that is considerably sparser than other wavelet transforms. This can be quantified by considering the best approximation of a geometrical test image that can be represented using only n {\displaystyle n} wavelets, and analysing the approximation error as a function of n {\displaystyle n} . For a Fourier transform, the squared error decreases only as O ( 1 / n ) {\displaystyle O(1/{\sqrt {n}})} . For a wide variety of wavelet transforms, including both directional and non-directional variants, the squared error decreases as O ( 1 / n ) {\displaystyle O(1/n)} . The extra assumption underlying the curvelet transform allows it to achieve O ( ( log ⁡ n ) 3 / n 2 ) {\displaystyle O({(\log n)}^{3}/{n^{2}})} . Efficient numerical algorithms exist for computing the curvelet transform of discrete data. The computational cost of the discrete curvelet transforms proposed by Candès et al. (Discrete curvelet transform based on unequally-spaced fast Fourier transforms and based on the wrapping of specially selected Fourier samples) is approximately 6–10 times that of an FFT, and has the same dependence of O ( n 2 log ⁡ n ) {\displaystyle O(n^{2}\log n)} for an image of size n × n {\displaystyle n\times n} . == Curvelet construction == To construct a basic curvelet ϕ {\displaystyle \phi } and provide a tiling of the 2-D frequency space, two main ideas should be followed: Consider polar coordinates in frequency domain Construct curvelet elements being locally supported near wedges The number of wedges is N j = 4 ⋅ 2 ⌈ j 2 ⌉ {\displaystyle N_{j}=4\cdot 2^{\left\lceil {\frac {j}{2}}\right\rceil }} at the scale 2 − j {\displaystyle 2^{-j}} , i.e., it doubles in each second circular ring. Let ξ = ( ξ 1 , ξ 2 ) T {\displaystyle {\boldsymbol {\xi }}=\left(\xi _{1},\xi _{2}\right)^{T}} be the variable in frequency domain, and r = ξ 1 2 + ξ 2 2 , ω = arctan ⁡ ξ 1 ξ 2 {\displaystyle r={\sqrt {\xi _{1}^{2}+\xi _{2}^{2}}},\omega =\arctan {\frac {\xi _{1}}{\xi _{2}}}} be the polar coordinates in the frequency domain. We use the ansatz for the dilated basic curvelets in polar coordinates: ϕ ^ j , 0 , 0 := 2 − 3 j 4 W ( 2 − j r ) V ~ N j ( ω ) , r ≥ 0 , ω ∈ [ 0 , 2 π ) , j ∈ N 0 {\displaystyle {\hat {\phi }}_{j,0,0}:=2^{\frac {-3j}{4}}W(2^{-j}r){\tilde {V}}_{N_{j}}(\omega ),r\geq 0,\omega \in [0,2\pi ),j\in N_{0}} To construct a basic curvelet with compact support near a ″basic wedge″, the two windows W {\displaystyle W} and V ~ N j {\displaystyle {\tilde {V}}_{N_{j}}} need to have compact support. Here, we can simply take W ( r ) {\displaystyle W(r)} to cover ( 0 , ∞ ) {\displaystyle (0,\infty )} with dilated curvelets and V ~ N j {\displaystyle {\tilde {V}}_{N_{j}}} such that each circular ring is covered by the translations of V ~ N j {\displaystyle {\tilde {V}}_{N_{j}}} . Then the admissibility yields ∑ j = − ∞ ∞ | W ( 2 − j r ) | 2 = 1 , r ∈ ( 0 , ∞ ) . {\displaystyle \sum _{j=-\infty }^{\infty }\left|W(2^{-j}r)\right|^{2}=1,r\in (0,\infty ).} see Window Functions for more information For tiling a circular ring into N {\displaystyle N} wedges, where N {\displaystyle N} is an arbitrary positive integer, we need a 2 π {\displaystyle 2\pi } -periodic nonnegative window V ~ N {\displaystyle {\tilde {V}}_{N}} with support inside [ − 2 π N , 2 π N ] {\displaystyle \left[{\frac {-2\pi }{N}},{\frac {2\pi }{N}}\right]} such that ∑ l = 0 N − 1 V ~ N 2 ( ω − 2 π l N ) = 1 {\displaystyle \sum _{l=0}^{N-1}{\tilde {V}}_{N}^{2}\left(\omega -{\frac {2\pi l}{N}}\right)=1} , for all ω ∈ [ 0 , 2 π ) {\displaystyle \omega \in \left[0,2\pi \right)} , V ~ N {\displaystyle {\tilde {V}}_{N}} can be simply constructed as 2 π {\displaystyle 2\pi } -periodizations of a scaled window V ( N ω 2 π ) {\displaystyle V\left({\frac {N\omega }{2\pi }}\right)} . Then, it follows that ∑ l = 0 N j − 1 | 2 3 j 4 ϕ ^ j , 0 , 0 ( r , ω − 2 π l N j ) | 2 = | W ( 2 − j r ) | 2 ∑ l = 0 N j − 1 V ~ N j 2 ( ω − 2 π l N ) = | W ( 2 − j r ) | 2 {\displaystyle \sum _{l=0}^{N_{j}-1}\left|2^{\frac {3j}{4}}{\hat {\phi }}_{j,0,0}\left(r,\omega -{\frac {2\pi l}{N_{j}}}\right)\right|^{2}=\left|W(2^{-j}r)\right|^{2}\sum _{l=0}^{N_{j}-1}{\tilde {V}}_{N_{j}}^{2}\left(\omega -{\frac {2\pi l}{N}}\right)=\left|W(2^{-j}r)\right|^{2}} For a complete covering of the frequency plane including the region around zero, we need to define a low pass element ϕ ^ − 1 := W 0 ( | ξ | ) {\displaystyle {\hat {\phi }}_{-1}:=W_{0}(\left|\xi \right|)} with W 0 2 ( r ) 2 := 1 − ∑ j = 0 ∞ W ( 2 − j r ) 2 {\displaystyle W_{0}^{2}(r)^{2}:=1-\sum _{j=0}^{\infty }W(2^{-j}r)^{2}} that is supported on the unit circle, and where we do not consider any rotation. == Applications == Image processing Seismic exploration Fluid mechanics PDEs solving Compressed sensing

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  Content repository

  A content repository or content store is a database of digital content with an associated set of data management, search and access methods allowing application-independent access to the content, rather like a digital library, but with the ability to store and modify content in addition to searching and retrieving. The content repository acts as the storage engine for a larger application such as a content management system or a document management system, which adds a user interface on top of the repository's application programming interface. == Advantages provided by repositories == Common rules for data access allow many applications to work with the same content without interrupting the data. They give out signals when changes happen, letting other applications using the repository know that something has been modified, which enables collaborative data management. Developers can deal with data using programs that are more compatible with the desktop programming environment. The data model is scriptable when users use a content repository. == Content repository features == A content repository may provide functionality such as: Add/edit/delete content Hierarchy and sort order management Query / search Versioning Access control Import / export Locking Life-cycle management Retention and holding / records management == Examples == Apache Jackrabbit ModeShape == Applications == Content management Document management Digital asset management Records management Revision control Social collaboration Web content management == Standards and specification == Content repository API for Java WebDAV Content Management Interoperability Services

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  Cipher device

  A cipher device was a term used by the US military in the first half of the 20th century to describe a manually operated cipher equipment that converted the plaintext into ciphertext or vice versa. A similar term, cipher machine, was used to describe the cipher equipment that required external power for operation. Cipher box or crypto box is a physical cryptographic device used to encrypt and decrypt messages between plaintext (unencrypted) and ciphertext (encrypted or secret) forms. The ciphertext is suitable for transmission over a channel, such as radio, that might be observed by an adversary the communicating parties wish to conceal the plaintext from.

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