AI Assistant Samsung

AI Assistant Samsung — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  Attack path management

  Attack path management is a cybersecurity technique that involves the continuous discovery, mapping, and risk assessment of identity-based attack paths. Attack path management is distinct from other computer security mitigation strategies in that it does not rely on finding individual attack paths through vulnerabilities, exploits, or offensive testing. Rather, attack path management techniques analyze all attack paths present in an environment based on active identity management policies, authentication configurations, and active authenticated "sessions" between objects. == Overview == Attack path management relies on concepts such as mapping and removing attack paths, identifying attack path choke points, and remediation of attack paths. Identity-based attacks are present in most publicly disclosed breaches, whether through social engineering to gain initial access to Active Directories or lateral movement for privilege escalation. Attackers require privileges to attack an environment’s most sensitive segments. Attack path management often involves removing out-of-date privileges and privilege assignments given to overly large groups. In attack path management, attack graphs are used to represent how a network of machines’ security is vulnerable to attack. The nodes in an attack graph represent principals and other objects such as machines, accounts, and security groups. The edges in an attack graph represent the links and relationships between nodes. Some nodes are easy to penetrate due to short paths from regular users to domain admins, resulting in focal points of concentrated network traffic, which are known as attack path choke points. Attack graphs are often analyzed using algorithms and visualization. Attack path management also identifies tier 0 assets, which are considered the most vulnerable because they have direct or indirect control of an Active Directory or Microsoft Entra ID environment.

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  Plaintext

  In cryptography, plaintext usually means unencrypted information pending input into cryptographic algorithms, usually encryption algorithms. This usually refers to data that is transmitted or stored unencrypted. == Overview == With the advent of computing, the term plaintext expanded beyond human-readable documents to mean any data, including binary files, in a form that can be viewed or used without requiring a key or other decryption device. Information—a message, document, file, etc.—if to be communicated or stored in an unencrypted form is referred to as plaintext. Plaintext is used as input to an encryption algorithm; the output is usually termed ciphertext, particularly when the algorithm is a cipher. Codetext is less often used, and almost always only when the algorithm involved is actually a code. Some systems use multiple layers of encryption, with the output of one encryption algorithm becoming "plaintext" input for the next. == Secure handling == Insecure handling of plaintext can introduce weaknesses into a cryptosystem by letting an attacker bypass the cryptography altogether. Plaintext is vulnerable in use and in storage, whether in electronic or paper format. Physical security means the securing of information and its storage media from physical, attack—for instance by someone entering a building to access papers, storage media, or computers. Discarded material, if not disposed of securely, may be a security risk. Even shredded documents and erased magnetic media might be reconstructed with sufficient effort. If plaintext is stored in a computer file, the storage media, the computer and its components, and all backups must be secure. Sensitive data is sometimes processed on computers whose mass storage is removable, in which case physical security of the removed disk is vital. In the case of securing a computer, useful (as opposed to handwaving) security must be physical (e.g., against burglary, brazen removal under cover of supposed repair, installation of covert monitoring devices, etc.), as well as virtual (e.g., operating system modification, illicit network access, Trojan programs). Wide availability of keydrives, which can plug into most modern computers and store large quantities of data, poses another severe security headache. A spy (perhaps posing as a cleaning person) could easily conceal one, and even swallow it if necessary. Discarded computers, disk drives and media are also a potential source of plaintexts. Most operating systems do not actually erase anything— they simply mark the disk space occupied by a deleted file as 'available for use', and remove its entry from the file system directory. The information in a file deleted in this way remains fully present until overwritten at some later time when the operating system reuses the disk space. With even low-end computers commonly sold with many gigabytes of disk space and rising monthly, this 'later time' may be months later, or never. Even overwriting the portion of a disk surface occupied by a deleted file is insufficient in many cases. Peter Gutmann of the University of Auckland wrote a celebrated 1996 paper on the recovery of overwritten information from magnetic disks; areal storage densities have gotten much higher since then, so this sort of recovery is likely to be more difficult than it was when Gutmann wrote. Modern hard drives automatically remap failing sectors, moving data to good sectors. This process makes information on those failing, excluded sectors invisible to the file system and normal applications. Special software, however, can still extract information from them. Some government agencies (e.g., US NSA) require that personnel physically pulverize discarded disk drives and, in some cases, treat them with chemical corrosives. This practice is not widespread outside government, however. Garfinkel and Shelat (2003) analyzed 158 second-hand hard drives they acquired at garage sales and the like, and found that less than 10% had been sufficiently sanitized. The others contained a wide variety of readable personal and confidential information. See data remanence. Physical loss is a serious problem. The US State Department, Department of Defense, and the British Secret Service have all had laptops with secret information, including in plaintext, lost or stolen. Appropriate disk encryption techniques can safeguard data on misappropriated computers or media. On occasion, even when data on host systems is encrypted, media that personnel use to transfer data between systems is plaintext because of poorly designed data policy. For example, in October 2007, HM Revenue and Customs lost CDs that contained the unencrypted records of 25 million child benefit recipients in the United Kingdom. Modern cryptographic systems resist known plaintext or even chosen plaintext attacks, and so may not be entirely compromised when plaintext is lost or stolen. Older systems resisted the effects of plaintext data loss on security with less effective techniques—such as padding and Russian copulation to obscure information in plaintext that could be easily guessed.

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  Social trading

  Social trading is a form of investing that allows investors to observe the trading behavior of their peers and expert traders. The primary objective is to follow their investment strategies using copy trading or mirror trading. Social trading requires little or no knowledge about financial markets. == History == One of the first social trading platforms was Collective2] which began offering a social trading functionality to retail traders as early as 2003 (preceding ZuluTrade by four years). In 2010, social trading started to achieve a greater degree of mainstream appeal with eToro, followed by Wikifolio in 2012. Europe-based NAGA, listed on Frankfurt Stock Exchange since 2017, claims more than EUR 27 billion was traded on its platform in the second half of 2019. Some of the other contemporary social trading platforms and tech providers are Trading Motion, Brokeree Solutions, iSystems, and FX Junction, among others. === Research === MIT Computer Scientist and researcher Yaniv Altshuler described social trading networks as complex adaptive systems, and in his 2014 research on eToro's OpenBook, wrote that "Having the inherent ability to share ideas and information between each others, OpenBook's users are given a new source of information they can use in order to enhance their trading performance. As the users are not playing against each other but rather – against the market, this situation becomes a non zero-sum game, hence incentivizing the users to share as much information as possible." His paper concludes that "social trading provides much better opportunities for profiting compared with individual trading," but that users make "excellent but sometimes not optimal decisions in selecting experts when they can see others' choices." A 2015 World Economic Forum report described social trading networks as disruptors, which "have emerged to provide low-cost, sophisticated alternatives to traditional wealth managers. These solutions cater to a broader customer base and empower customers to have more control of their wealth management," and "pose a tangible threat to the traditional practices of the wealth management industry". Economist Nouriel Roubini's thinktank predicted in 2016 that "newer forms of investment, such as socially responsible investments and social trading will bring some of the largest industry growth in the coming years." A 2017 St. John's University study found that 'leader' traders, or those with followers, are more susceptible to the disposition effect than investors that are not being followed by any other traders, with the authors suggesting the observation may be explained by "leaders feeling responsible towards their followers and an urge to not let them down, by fear of losing followers when admitting a bad investment decision and signaling confidence in their initial investment choice, or by an attempt of newly appointed leaders to manage their self-image." Social trading may potentially also change how much risk investors take. A recent experimental study argues that merely providing information on the success of others may lead to a significant increase in risk taking. This increase in risk taking may even be larger when subjects are provided with the option to directly copy others. == Characteristics == Social trading is an alternative way of analyzing financial data by looking at what other traders are doing and comparing and copying their techniques and strategies. Prior to the advent of social trading, investors and traders were relying on fundamental or technical analysis to form their investment decisions. Using social trading investors and traders could integrate into their investment decision-process social indicators from trading data-feeds of other traders. Social trading platforms or networks can be considered a subcategory of social networking services. Social trading allows traders to trade online with the help of others and some have claimed shortens the learning curve from novice to experienced trader. Traders can interact with others, watch others take trades, then duplicate their trades and learn what prompted the top performer to take a trade in the first place. By copying trades, traders can learn which strategies work and which do not work. Social trading is used to do speculation; in the moral context speculative practices are considered negatively and to be avoided by each individual. who conversely should maintain a long-term horizon avoiding any types of short term speculation. Social Media has permeated the trading world such that two main types of trading has evolved: Traditional Trades Single (or non-social) trade: Trader A places a normal trade by himself or herself; This can by manual or automated Social Trading There are two main types of social trading: Copy trade: Trader A places exactly the same trade as trader B's one single trade; (iii) Mirror trade: Trader A automatically executes trader B's every single trade, i.e., trader A follows exactly trader B's trading activities. Other variations offered on some platforms allow users to copy another trader's portfolio (copy portfolio), and follow a trader's dividends (copy dividends), where whenever a followed trader withdraws money from his or her account, a proportional amount of money will be withdrawn from the balance of their follower, in real time. === Key features === Information flow: Unencumbered access to information is important in financial markets and that makes the free exchange of information of interest to small scale as well as individual investors. Cooperative trading: Social trading offers traders the opportunity to work together in trading teams which can trade the markets collaboratively, whether by pooling funds, dividing research or through sharing information. Monetization: As with social networks in the broader sense, monetization strategies are not always clear. As with social networks in general, it is possible, however, that the long-term worth of such websites may come from the variety and depth of data about their users which their active communities are likely to generate. Transparency: Social trading platforms reveal traders' performance stats, open and past positions, and market sentiment, giving members complete information to assess the credibility of the contributors they follow on the platform.

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  HKDF

  HKDF is a multi-purpose key derivation function (KDF) based on the HMAC message authentication code. HKDF follows "extract-then-expand" paradigm, where the KDF logically consists of two modules: the first stage takes the input keying material and "extracts" from it a fixed-length pseudorandom key, and then the second stage "expands" this key into several additional, independent pseudorandom keys as the output of the KDF. == Mechanism == HKDF is the composition of two functions, HKDF-Extract and HKDF-Expand: HKDF(salt, IKM, info, length) = HKDF-Expand(HKDF-Extract(salt, IKM), info, length) === HKDF-Extract === HKDF-Extract (XTR) takes "input key material" or "source key material" (IKM or SKM) such as a shared secret generated using Diffie-Hellman; an optional, non-secret, random or pseudorandom salt (r); and generates a cryptographic key called the PRK ("pseudorandom key"). HKDF-Extract acts as a "randomness extractor", specifically a "computational extractor", taking a potentially non-uniform value of sufficient min-entropy and generating a value indistinguishable from a uniform random value (pseudorandom). Computational extractors assume attackers are computationally bounded and source entropy may only exist in a computational sense. Such extractors can be built using cryptographic functions under suitable assumptions, modeled as universal hash function (in the generic case) or a random oracle (in constrained scenarios like sources with weak entropy). Salt (r) acts as a "source-independent extractor", strengthening HKDF's security guarantees. Using a fixed public r is safe for multiple invocations of HKDF (on "independent" but secret IKMs which may or may not be derived from the same source), provided r isn't chosen or manipulated by an attacker. Ideally, r is a random string of hash function's output length. Even low quality r (weak entropy or shorter length) is recommended as they contribute "significantly" to the security of the OKM. Without or with a low-entropy, non-secret r, if an attacker can influence the IKMs source in a way that specifically exploits HKDF-Extract's underlying hash function (finding a collision or a specific bias), XTR provides no protection. A random r, even if fixed by the application (for example, random number generators using r as seed), would strengthen protections for that specific extractor session. In such a setting, sufficiently long IKMs also provide better entropy extraction. However, allowing the attacker to influence enough of the IKM after seeing r may result in a completely insecure KDF. HKDF-Extract is the result of HMAC with r as the key (all zeros up to length of the underlying extractor hash function, if not provided) and the IKM as the message. The underlying hash function used for HKDF-Extract step may be different to the one used by HKDF-Expand. It is recommended that HKDF-Extract uses strongest hash function available to the application, as it "concentrates" the entropy already present in IKM but may not necessarily "add" to it. Truncated output from a stronger underlying hash function for XTR (for example, SHA512/256) offers stronger extraction properties. The attacker is assumed to have partial knowledge about IKM (publicly known values in the case of Diffie-Hellman) or partial control over it (entropy pools). HKDF-Extract may be skipped if the IKM is itself a cryptographically strong key (and hence can assume the role of PRK), though it is recommended that HKDF-Extract be applied for the sake of compatibility with the general case, especially if r is available to the application. === HKDF-Expand === HKDF-Expand (PRF) takes the PRK (or any random key-derivation key if HKDF-Extract step is skipped), optional info (CTXinfo), and a length (L), to generate output key material (OKM) of length L. Multiple OKMs can be generated from a single PRK by using different values for CTXinfo, which must be "independent" of the IKM passed in HKDF-Extract. Even if an attacker, who knows r and some auxillary information about the secret IKM, can force the use of the same IKM (and PRK, by extension), in two or more HKDF-Expand contexts (represented by CTXinfo), the OKMs output are computationally independent (leak no useful information on each other). HKDF-Expand, acting as a variable-output-length pseudorandom function (PRF) keyed on PRK, calls HMAC on CTXinfo as the message (empty string, if unspecified) appended to a 8-bit counter i initialized to 1. Subsequent calls to HMAC are chained in "feedback mode" by prepending the previous HMAC output to CTXinfo and incrementing i. OKM is a function of the output size (k bits) of HMAC's underlying hash function; i.e., SHA-256 outputs OKM in segments of k=256 bits for up to a maximum of length i × k bits (255 × 256 bits = 8160 bytes) truncated to desired length L. HKDF-Expand may be skipped if PRK is at least desired length L, though it is recommended that HKDF-Expand be applied for additional "smoothing" of the OKM. == Standardization == HKDF was proposed as a building block in various protocols and applications, as well as to discourage the proliferation of multiple KDF mechanisms by its authors. It is formally described in RFC 5869 with detailed analysis in a paper published in 2010. NIST SP800-56Cr2 specifies a parameterizable extract-then-expand scheme, noting that RFC 5869 HKDF is a version of it and citing its paper for the rationale for the recommendations' extract-and-expand mechanisms. == Applications == HKDF is used in the Signal Protocol for end-to-end encrypted messaging where it generates the message keys, in conjunction with the triple Elliptic-curve Diffie-Hellman handshake (X3DH) key agreement protocol. Signal's "Secure Value Recovery" and "Sealed Sender" are based on HKDF. HKDF is a main component in the Noise Protocol Framework, Message Layer Security, and is used in widely deployed protocols like IPsec Internet Key Exchange and TLS 1.3. The "multi-purpose" nature of HKDF is meant to serve applications that require key extraction, key expansion, and key hierarchies in key wrapping, key exchange, PRNG, and password-based key derivation schemes. == Implementations == There are implementations of HKDF for C#, Go, Java, JavaScript, Perl, PHP, Python, Ruby, Rust, and other programming languages. RFC6234 lays out a reference C implementation of HKDF based on the Secure Hash Standard. === Example in Python ===

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  Jeremy Renner Official

  Jeremy Renner Official (or Jeremy Renner on the Google Play Store) was a mobile app created by American actor Jeremy Renner. He created the app in March 2017 to hear the input and comments of his fans. The app was shut down in September 2019 in part due to the frequent bullying and trolling that the platform had experienced. The app featured optional microtransactions, with some ranging up to roughly US$400 despite the app itself being free. Upon shutting down the app, Renner issued a mass-refund for the collectible "stars" in the app for purchases made within the last ninety days, from the day the announcement was posted. He then posted an apology to the app itself, and the app was deleted from both the Google Play Store and the App Store shortly after. == Usage == Upon downloading the app, the user was faced with a video of Renner speaking about his fans and superfans, regular giveaways, and real-life updates. While the app was active, Renner posted regular questions and comments for fans. Renner occasionally livestreamed about his work and day-to-day life. The community developed to include memes, selfies, and a "Happy Rennsday" event on Wednesdays. == History == === 2017–2019 === The app launched in March 2017 with a promotional contest. Renner's fans were encouraged to download the app and create comments about being Renner's biggest fan; Renner would then choose a winner and transport the winner and a guest to have lunch with him at the Calgary Expo. In the first few months Renner teased behind-the-scenes of projects he was working on, which he now sporadically does on Instagram. The app was similarly designed to Instagram as well, with a near identically styled layout. Around midway through 2019, a hoax account of Renner was made to mock the celebrity, joking about masturbating to porn and defending another hoax account of Casey Anthony. FastCompany wrote extensively about Renner's app in April 2019, calling it "a surprising new kind of social media". The Ringer stated "Jeremy Renner's Jeremy Renner app is the Jeremy Renner of apps." === After deletion (2019–2020) === After the shutdown of the app, a comedy-based pseudo-app with modular endings was released, called "The Jeremy Renner App Experience", in which the player plays as Jeremy Renner on the day of the Jeremy Renner Official app's shutdown. The app details several different choices on how Renner handles the situation. A six-part podcast was also created to mock the app's deletion, called The Renner Files, featuring Carolyn Goldfarb and Sarah Ramos. == Controversies == === Marketing === One of the main controversies of Renner's app was its marketing. The app's developers, Escapex, specialized in and grew famous for making similar monetized apps for celebrities. The marketing campaign was based on direct contact with Renner, whose chances were increased with regular payments for "stars", although very few encounters seemed to happen with Renner himself. The multiple problems with the app led the CEO of Escapex, Sephi Shapira, to call the app a "freak situation", and added "Am I concerned about this? Not more than I'm concerned about 50 other things I'm dealing with as a startup company." Along with the marketing failures, the app was seen as misrepresenting itself as seemingly erotic with some advertisements featuring Renner suggestively staring at the camera, despite the actual app being initially considered safe for children. === Harassment === After its release in 2017, the app was met with waves of harassment and bullying by many users on the app, most frequently by using impersonation — referenced in Renner's apology/deletion notice. Some death threats were made across the app by fraud accounts pretending to be several controversial celebrities, including O. J. Simpson and Casey Anthony. As early as October 2017, there were claims of censorship, bullying, and "contest-rigging". In September 2019, comedian Stefan Heck publicized his discovery of the fact that replies through the app appeared as if they were sent by Renner himself in push notifications. After several users abused this feature, Renner asked Escapex to shut down the app.

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  Data product

  In data management and product management, a data product is a reusable, active, and standardized data asset designed to deliver measurable value to its users, whether internal or external, by applying the rigorous principles of product thinking and management. It comprises one or more data artifacts (e.g., datasets, models, pipelines) and is enriched with metadata, including governance policies, data quality rules, data contracts, and, where applicable, a software bill of materials (SBOM) to document its dependencies and components. Ownership of a data product is aligned to a specific domain or use case, ensuring accountability, stewardship, and its continuous evolution throughout its lifecycle. Adhering to the FAIR principles – findable, accessible, interoperable, and reusable – a data product is designed to be discoverable, scalable, reusable, and aligned with both business and regulatory standards, driving innovation and efficiency in modern data ecosystems. == History == In 2012, DJ Patil proposed the first documented definition: a data product is a product that facilitates an end goal through the use of data. In 2019, Zhamak Dehghani introduced Data Mesh, with a strong focus on domain-oriented data products. Later, in 2020, she solidifies Data Mesh around four principles, one being Data as a Product, in which she defines Data Product as the node on the mesh that encapsulates three structural components required for its function, providing access to the domain's analytical data as a product. In 2024, Andrea Gioia published one of the first books specifically on data products post Data Mesh announcement. In his book, Gioia defines the concept of pure data product. In 2025, during the Data Day Texas conference, Jean-Georges Perrin and a collective of product managers and data engineers got together to craft the current definition and make it available to the public domain. In July 2025, Bitol, a project of The Linux Foundation, released and early version of the Open Data Product Standard (ODPS) aiming at normalizing data products

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  Consumer relationship system

  Consumer relationship systems (CRS) are specialized customer relationship management (CRM) software applications that are used to handle a company's dealings with its customers. Current consumer relationship systems integrate the software with telephone and call recording systems as well as with corporate systems for input and reporting. Customers can provide input from the company's website directly into the CRS. These systems are popular because they can deliver the 'voice of the consumer' that contributes to product quality improvement and that ultimately increases corporate profits. Consumer relationship systems that provide automated support as well as advanced systems may have artificial intelligence (AI) interfaces that can extract and analyse data collected, or handle basic questions and complaints. == History == The first CRS was developed in the 1980s. In 1981 Michael Wilke and Robert Thornton founded Wilke/Thornton, Inc in Columbus, Ohio, to develop new CRS software.

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  Point-to-point encryption

  Point-to-point encryption (P2PE) is a standard established by the PCI Security Standards Council. Payment solutions that offer similar encryption but do not meet the P2PE standard are referred to as end-to-end encryption (E2EE) solutions. The objective of P2PE and E2EE is to provide a payment security solution that instantaneously converts confidential payment card (credit and debit card) data and information into indecipherable code at the time the card is swiped, in order to prevent hacking and fraud. It is designed to maximize the security of payment card transactions in an increasingly complex regulatory environment. == The standard == The P2PE Standard defines the requirements that a "solution" must meet in order to be accepted as a PCI-validated P2PE solution. A "solution" is a complete set of hardware, software, gateway, decryption, device handling, etc. Only "solutions" can be validated; individual pieces of hardware such as card readers cannot be validated. It is also a common mistake to refer to P2PE validated solutions as "certified"; there is no such certification. The determination of whether or not a solution meets the P2PE standard is the responsibility of a P2PE Qualified Security Assessor (P2PE-QSA). P2PE-QSA companies are independent third-party companies who employ assessors that have met the PCI Security Standards Council's requirements for education and experience, and have passed the requisite exam. The PCI Security Standards Council does not validate solutions. == How it works == As a payment card is swiped through a card reading device, referred to as a point of interaction (POI) device, at the merchant location or point of sale, the device immediately encrypts the card information. A device that is part of a PCI-validated P2PE solution uses an algorithmic calculation to encrypt the confidential payment card data. From the POI, the encrypted, indecipherable codes are sent to the payment gateway or processor for decryption. The keys for encryption and decryption are never available to the merchant, making card data entirely invisible to the retailer. Once the encrypted codes are within the secure data zone of the payment processor, the codes are decrypted to the original card numbers and then passed to the issuing bank for authorization. The bank either approves or rejects the transaction, depending upon the card holder's payment account status. The merchant is then notified if the payment is accepted or rejected to complete the process along with a token that the merchant can store. This token is a unique number reference to the original transaction that the merchant can use should they ever be needed to perform research or refund the customer without ever knowing the customer's card information (tokenization). There are also Qualified Integrator and Reseller (QIR) Companies, which are businesses authorized to "implement, configure, and/or support validated" PA-DSS Payment Applications, and perform qualified installations. == Solution providers == According to the PCI Security Standards Council:The P2PE solution provider is a third-party entity (for example, a processor, acquirer, or payment gateway) that has overall responsibility for the design and implementation of a specific P2PE solution, and manages P2PE solutions for its merchant customers. The solution provider has overall responsibility for ensuring that all P2PE requirements are met, including any P2PE requirements performed by third-party organizations on behalf of the solution provider (for example, certification authorities and key-injection facilities). == Benefits == === Customer benefits === P2PE significantly reduces the risk of payment card fraud by instantaneously encrypting confidential cardholder data at the moment a payment card is swiped or "dipped" if it is a chip card at the card reading device (payment terminal) or POI. === Merchant benefits === P2PE significantly facilitates merchant responsibilities: With a P2PE validated solution, merchants save significant time and money as PCI requirements may be greatly reduced. Payment Card Industry Data Security Standard (PCI DSS). For organizations who use a P2PE validated solution provider, the PCI Self Assessment Questionnaire is reduced from 12 sections to 4 sections and the controls are reduced from 329 questions to just 35. In the event of fraud, the P2PE Solution Provider, not the merchant, is held accountable for data loss and resulting fines that may be assessed by the card brands (American Express, Visa, MasterCard, Discover, and JCB). The PCI Security Standards Council does not assess penalties on Solution Providers or Merchants. The payment process with P2PE is quicker than other transaction processes, thus creating simpler and faster customer–merchant transactions. == Point-to-point encryption versus end-to-end encryption == === Point-to-point === A point-to-point connection directly links system 1 (the point of payment card acceptance) to system 2 (the point of payment processing). A true P2PE solution is determined with three main factors: The solution uses a hardware-to-hardware encryption and decryption process along with a POI device that has SRED (Secure Reading and Exchange of Data) listed as a function. The solution has been validated to the PCI P2PE Standard which includes specific POI device requirements such as strict controls regarding shipping, receiving, tamper-evident packaging, and installation. A solution includes merchant education in the form of a P2PE Instruction Manual, which guides the merchant on POI device use, storage, return for repairs, and regular PCI reporting. === End-to-end === End-to-end encryption as the name suggests has the advantage over P2PE that card details are not unencrypted between the two endpoints. If the endpoints are a PCI PED validated PIN pad and a POS acquirer, there is no opportunity for the card details to be intercepted. It is obviously important that the endpoints (the PED and gateway) are provided by PCI accredited organisations. == PCI point-to-point encryption requirements == The requirements include: Secure encryption of payment card data at the point of interaction (POI), P2PE validated application(s) at the point of interaction, Secure management of encryption and decryption devices, Management of the decryption environment and all decrypted account data, Use of secure encryption methodologies and cryptographic key operations, including key generation, distribution, loading/injection, administration, and usage.

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  Rule induction

  Rule induction is an area of machine learning in which formal rules are extracted from a set of observations. The rules extracted may represent a full scientific model of the data, or merely represent local patterns in the data. Data mining in general and rule induction in detail are trying to create algorithms without human programming but with analyzing existing data structures. In the easiest case, a rule is expressed with “if-then statements” and was created with the ID3 algorithm for decision tree learning. Rule learning algorithm are taking training data as input and creating rules by partitioning the table with cluster analysis. A possible alternative over the ID3 algorithm is genetic programming which evolves a program until it fits to the data. Creating different algorithm and testing them with input data can be realized in the WEKA software. Additional tools are machine learning libraries for Python, like scikit-learn. == Paradigms == Some major rule induction paradigms are: Association rule learning algorithms (e.g., Agrawal) Decision rule algorithms (e.g., Quinlan 1987) Hypothesis testing algorithms (e.g., RULEX) Horn clause induction Version spaces Rough set rules Inductive Logic Programming Boolean decomposition (Feldman) == Algorithms == Some rule induction algorithms are: Charade Rulex Progol CN2

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  NATGRID

  The National Intelligence Grid or NATGRID is an integrated intelligence master database structure for counter-terrorism purposes which connects databases of various core security agencies under the Government of India. It collects and analyses comprehensive patterns procured from 21 different organizations that can be readily accessed by security agencies round the clock. As of September 2025 its CEO is Hirdesh Kumar. NATGRID came into existence after the 2008 Mumbai attacks. The Government of India in July 2016 appointed Ashok Patnaik as the Chief Executive Officer (CEO) of NATGRID. The appointment is being seen as the government's effort to revive the project. Patnaik's appointment was valid till 31 December 2018. As of 2019, NATGRID is headed by an Indian Police Service (IPS) officer Ashish Gupta. The Ministry of Home Affairs on 5 February 2020 announced in Parliament that Project NATGRID with all its required physical infrastructures been completed as of 31 March 2020 and the NATGRID solution went live as of 31 December 2020. == Reason for establishment == The landscape of Terrorism in India and the subsequent response by Law enforcement in India have necessitated a sophisticated data-integration framework, positioning NATGRID as a vital tool for national security agencies. This shift towards Mass surveillance in India is rooted in a broader policy evolution of state monitoring, which is technologically enabled by the India Stack—the foundational digital infrastructure providing the API-based backbone for government service delivery and identity verification. This ecosystem is further bolstered by advanced Signal intelligence capabilities and the implementation of SIM binding, a security protocol that anchors a user’s digital identity to a specific mobile device and verified SIM card to prevent identity fraud and unauthorized access. Collectively, these elements form a 360-degree surveillance and authentication grid designed to preemptively identify threats by synthesizing historical, financial, and real-time communication data across disparate platforms. === Terror attacks in India === The 2008 Mumbai attacks led to the exposure of several weaknesses in India's intelligence gathering and action networks. NATGRID is part of the radical overhaul of the security and intelligence apparatuses of India that was mooted by the then Home Minister P. Chidambaram in 2009. The National Investigation Agency (NIA) and the National Counter Terrorism Centre (NCTC) are two organisations established in the aftermath of the Mumbai attacks of 2008. Before the Mumbai attacks, a Pakistani origin American Lashkar-e-Taiba (LeT) operative David Coleman Headley had visited India several times and done a recce of the places that came under attack on 26/11. Despite having travelled to India several times and having returned to the US through Pakistan or West Asia, his trips failed to raise the suspicion of Indian agencies as they lacked a system that could reveal a pattern in his unusual travel itineraries and trips to the country. It was argued that if they had a system like the NATGRID in place, Headley would have been apprehended well before the attacks. === Need for the integrated intelligence system === During the inauguration of NATGRID campus in Bengaluru, the Minister of Home Affairs, Amit Shah stated that a new national database is in the process of being made which will bring a change in the current ways of functioning of agencies once it's ready also adding that the government has entrusted the task of developing and operating a state-of-the-art and innovative technology system. It is accessible to 11 central agencies in the first phase and in later phases will be made accessible to police of all States and Union Territories and only authorized personnel are allowed access to the platform on a case-to-case basis for investigations into suspected cases of terrorism. NATGRID has a total fund allocation of ₹3,400 crore (US$355 million). d == Legal framework == Relevant legal framework: Digital Personal Data Protection Act, 2023 – The legislative framework governing how digital data is handled. Information Technology Act - Interception Rules, 2002 – The specific regulations under the Information Technology Act that govern these agencies. National Security Act of 1980, evidence-based preventative detention of suspects Right to Information Act, 2005, for obtaining information from the government and used by activists and whistleblowers == Structure and functions == === Multi-agency integrated intelligence database === NATGRID is an intelligence sharing network that collates data from the standalone databases of the various agencies and ministries of the Indian government. It is a counter terrorism measure that collects and collates a host of information from government databases including tax and bank account details, credit/debit card transactions, visa and immigration records and itineraries of rail and air travel. It also has access to the Crime and Criminal Tracking Network and Systems, a database that links crime information, including First Information Reports, across 14,000 police stations in India. This combined data will be made available to 11 central agencies, which are: the Research and Analysis Wing (R&AW), Intelligence Bureau (IB), National Investigation Agency (NIA), Central Bureau of Investigation (CBI), Narcotics Control Bureau (NCB), Financial Intelligence Unit (India) (FIU), Enforcement Directorate (ED), Central Board of Direct Taxes (CBDT), Central Board of Indirect Taxes and Customs (CBIC), Directorate of Revenue Intelligence (DRI) and Directorate General of GST Intelligence. Also as stated by the MHA, NATGRID will have an in-built mechanism for continuous upgradation. In the later phases of NATGRID integration, the central government further plans to integrate 950 additional organizations into it. === Key components and users === ==== Some important backend data feeds to the NATGRID (middleware) ==== National Crime Records Bureau's Crime and Criminal Tracking Network and Systems (CCTNS) national-integrated law-and-order database for the state-level police forces: CCTNS is a mission-mode project under the National e-Governance Plan that interconnects over 15,000 police stations across India. It serves as the primary source for NATGRID to access digitized FIR (First Information Report) data and criminal history records from state-level law enforcement. NSA's National Technical Research Organisation (NTRO) national security-based database feed to NATGRID: NTRO serves as a primary technical data provider to NATGRID, offering specialized intercepts and satellite imagery. While NATGRID functions as a centralized data-integration middleware under the Ministry of Home Affairs, NTRO reports to the National Security Advisor within the Prime Minister's Office. DRDO's NETRA (Network Traffic Analysis) ELINT-based mass surveillance system for monitor internal internet traffic for keywords related to terrorism and criminal activity within Indian borders: Developed by the Centre for Artificial Intelligence and Robotics (CAIR), NETRA is an internet monitoring system capable of scanning traffic for specific trigger words. It provides digital behavioral triggers that NATGRID can cross-reference against structural data like financial or travel records. NETRA is a massive software network used to intercept and analyze internet traffic (emails, social media, blogs) for keywords like "bomb," "attack," or "kill." The intelligence gathered by NETRA regarding suspicious digital patterns or "keyword hits" can be fed into NATGRID. This allows an investigator to see if a person flagged by NETRA also has suspicious travel (from airline databases) or financial records (from bank databases) linked within NATGRID. Department of Telecommunications (DoT's Central Monitoring System (CMS) for lawfully intercepting national and international telecomm data: CMS is the centralized system for lawful interception of all telecommunications (phone calls, SMS, and data) in India, managed by the Department of Telecommunications (DoT). While CMS focuses on the content and metadata of real-time communication, NATGRID focuses on historical/structural data (tax, travel, identity). They represent two halves of a 360-degree surveillance profile: CMS listens to what a suspect says, while NATGRID tracks where they go and what they own. The CMS allows for the lawful interception of telecommunications metadata and content in real-time. In the broader surveillance architecture, CMS provides the "active" communication profile while NATGRID provides the "static" historical profile. Telecom Enforcement Resource and Monitoring (TERM) - Telecomm Regulatory & Verification Node for telecomm KYC: TERM cells verify subscriber identity (KYC) and maintain the integrity of telecom databases. NATGRID relies on these audited records to ensure the accuracy of telephone-to-identity mapping. TERM

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  Social advertising (social relationships)

  Social advertising is advertising that relies on social information or networks in generating, targeting, and delivering marketing communications. Many current examples of social advertising use a particular Internet service to collect social information, establish and maintain relationships with consumers, and for delivering communications. For example, the advertising platforms provided by Google, Twitter, and Facebook involve targeting and presenting ads based on relationships articulated on those same services. Social advertising can be part of a broader social media marketing strategy designed to connect with consumers. == Social targeting == Since a pair of consumers connected via a relationship are more likely to be similar than an unconnected pair, information about such relationships can be used to infer characteristics of consumers useful for targeting. For example, predictions of an individual's home location can be improved using geographic information about their peers. Existing advertising platforms can allow advertisers to explicitly target the peers (e.g., Facebook friends, Twitter followers) of consumers who have a known affiliation with their brand. Thus, one way social advertising is expected to be effective is because social networks encode information about unobserved characteristics of consumers, including their susceptibility to adopt a product and to influence their peers to adopt. Social advertisement targets audiences' demographics based on customers browsing histories. This helped companies understand users' interests and target a specific group of users. Whether it is location or personal interest, different categories of companies can make the consumers on social media rely heavily on their advertisements. This is one of the reasons why social advertising has grown over time. Targeting their audience to real life stakeholders generally increase the attention of the advertised deal which brings up more profits for companies. Subsequently, the psychological effects that social media gives off to its users play a huge role in advertisement companies keeping their customers online. One of the main reasons users rely on social media is because it's a source of entertainment that provides them with a feeling of inclusiveness. In making the customers feel the inclusiveness, social advertising targeting a specific group of users is presented as if these advertisements are customized for the users in their perspective making them feel the attention that they do not often feel in the real world. You can use Social signals checker tool to find more information about links. Social signals are metrics that measure how much people interact with your content on social media. From likes, to shares, to comments; each of these signals contributes to an overall number that tells search engines like Google how much people like your content. The more social signals your website gets, the more likely it is to rank higher in Google. The reason for this is two-fold. First, social media is used by millions of people every day, and if your content is being shared and interacted with on these sites, it shows that it’s worthy of being seen. And second, social media sites are highly trusted by Google. So if you can get your content seen and interacted with on these platforms, you’ll be off to a great start. == Social cues in advertisements == Social ads often include information about the affiliation of a peer with an advertised entity. For example, a social ad might indicate a friend has endorsed a product, highly rated a restaurant, or watched a particular film. In fact, some definitions make these personalized social signals a necessary condition for the advertising being social advertising. Inclusion of personalized social signals creates a channel for social influence. Experiments that remove peers' names or images from social advertisements provide evidence that their presence increases proximal outcomes (e.g., clicks on advertisements). This is technically how trends are started on social media. Since social media links a single profile to thousands of other accounts some being real-life friends or even acquaintances, the opinions and the bias a user has for other users who are also a customer of an advertisement on the feed can heavily affect whether to click on the advertisement or not. Once this pattern continues, the brand benefits from increased customers, profit, and attention. Social networking can spread rapidly because 71 percent of the world's population contributes and uses social media which means social advertising gives companies a better marketing technique than a physical poster advertisement. == Word of mouth == Advertisers often attempt to use word of mouth to affect consumers and their decisions to adopt products and services. Ads and other inducements targeted at a seed set of individuals can be designed to produce a larger cascade of adoption through influence. Businesses are also using social media to attempt to identify and persuade influential consumers to spread positive messages about their products or services. Consequently, not only on social platforms but also in physical settings, users start talking to each other. When individuals develop an intimate relationship with each other, it is quite heavily based on shared characteristics, interests, and personalities. If one social media user becomes a regular customer to a well-known company that advertises often, there is a higher chance that all the other people who have intimate relationships with that one customer will be exposed to the online advertisement more than another user who might be completely new to a brand that is being advertised on screen. In reality, this happens to not only one user but to most of the users which mean a single brand advertisement online can have to potential of being talked about between billions and trillions of people all around the globe. == Relationship marketing == To accurately conduct relationship marketing, businesses must develop and manage six marketplaces: internal, customer, referral, supplier, influencer and employee. To maintain relationship marketing, customers often see social media influencers getting free sponsorships or PR boxes just to advertise their products. At times, users who become customers through these social influencers will get a better deal than regular customers which stands as a very commonly used marketing technique. By doing this, users think they are receiving special treatment when in reality it very much benefits social influencers and brands. Especially for brands that are just starting, they use this marketing technique so that their names can be out there, and people will start talking, which is their initial goal.

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  Content-oriented workflow models

  In data management, a content-oriented workflow model seeks to articulate workflow progression by the presence of content units (like data-records/objects/documents). Most content-oriented workflow approaches provide a life-cycle model for content units, such that workflow progression can be qualified by conditions on the state of the units. Most approaches are research and work in progress and the content models and life-cycle models are more or less formalized. The term content-oriented workflows is an umbrella term for several scientific workflow approaches, namely "data-driven", "resource-driven", "artifact-centric", "object-aware", and "document-oriented". Thus, the meaning of "content" ranges from simple data attributes to self-contained documents; the term "content-oriented workflows" appeared at first in as an umbrella term. Such a general term, independent from a specific approach, is necessary to contrast the content-oriented modelling principle with traditional activity-oriented workflow models (like Petri nets or BPMN) where a workflow is driven by a control flow and where the content production perspective is neglected or even missing. The term "content" was chosen to subsume the different levels in granularity of the content units in the respective workflow models; it was also chosen to make associations with content management. Both terms "artifact-centric" and "data-driven" would also be good candidates for an umbrella term, but each is closely related to a specific approach of a single working group. The "artifact-centric" group itself (i.e. IBM Research) has generalized the characteristics of their approach and has used "information-centric" as an umbrella term in. Yet, the term information is too unspecific in the context of computer science, thus, "content-orientated workflows" is considered as good compromise. == Workflow Model Approaches == === Data-driven === The data-driven process structures provides a sophisticated workflow model being specialized on hierarchical write-and-review-processes. The approach provides interleaved synchronization of sub-processes and extends activity diagrams. Unfortunately, the COREPRO prototype implementation is not publicly available. Research on the project had been ceased. The general idea has been continued by Reichert in form of the #Object-aware approach. Synonyms data-driven process structures / data-driven modeling and coordination Protagonists Dr. Dominic Müller (University of Twente), Joachim Herbst (DaimlerChrysler Research), and Manfred Reichert (at this time Assoc. Prof. at Univ. of Twente, currently Prof. at Ulm Univ.) Organization(s) University of Twente, DaimlerChrysler Period 2005 - 2007 Selected publications Implementation COREPRO === Resource-driven === The resource-driven workflow system is an early approach that considered workflows from a content-oriented perspective and emphasizes on the missing support for plain document-driven processes by traditional activity-oriented workflow engines. The resource-driven approach demonstrated the application of database triggers for handling workflow events. Still the system implementation is centralized and the workflow schema is statically defined. The project appeared in 2005 but many aspects are considered future work by the authors. Research did not continue on the project. Wang completed his PhD thesis in 2009, yet, his thesis does not mention the resource-driven approach to workflow modelling but is about discrete event simulation. Synonyms Resource-based Workflows / Document-Driven Workflow Systems Protagonists Jianrui Wang and Prof. Akhil Kumar Organization Pennsylvania State University Period 2005 - today Selected publications Implementation N/A === Artifact-centric === The artifact-centric approach provides a framework for content-oriented workflows. In this model, the enterprise application landscape includes distributed business services, while the workflow engine is centralized. Process enactment is integrated with database management system infrastructure, and the project is funded by IBM. Synonyms artifact-centric business process models / artifact-based business process (ACP) / artifact-centric workflows Protagonists Richard Hull and Dr. Kamal Bhattacharya as well as Cagdas E. Gerede and Jianwen Su Organization IBM (T.J. Watson Research Center, NY) Period 2007 - today Selected publications Implementation ArtiFact === Object-aware === The object-aware approach manages a set of object types and generates forms for creating object instances. The form completion flow is controlled by transitions between object configurations each describing a progressing set of mandatory attributes. Each object configuration is named by an object state. The data production flow is user-shifting and it is discrete by defining a sequence of object states. The discussion is currently limited to a centralized system, without any workflows across different organizations. However, the approach is of great relevance to many domains like concurrent engineering. Finally, the object-aware approach and its PHILharmonicFlows system are going to provide general-purpose workflow systems for generic enactment of data production processes. Synonyms object-aware process management / datenorientiertes Prozess-Management-System Protagonists Vera Künzle and Prof. Manfred Reichert Organization Ulm University Period 2009 - today Selected publications Implementation PHILharmonicFlows === Distributed Document-oriented === Distributed document-oriented process management (dDPM) enables distributed case handling in heterogeneous system environments and it is based on document-oriented integration. The workflow model reflects the paper-based working practice in inter-institutional healthcare scenarios. It targets distributed knowledge-driven ad hoc workflows, wherein distributed information systems are required to coordinate work with initially unknown sets of actors and activities. The distributed workflow engine supports process planning & process history as well as participant management and process template creation with import/export. The workflow engine embeds a functional fusion of 1) group-based instant messaging 2) with a shared work list editor 3) with version control. The software implementation of dDPM is α-Flow which is available as open source. dDPM and α-Flow provide a content-oriented approach to schema-less workflows. The complete distributed case handling application is provided in form of a single active Document ("α-Doc"). The α-Doc is a case file (as information carrier) with an embedded workflow engine (in form of active properties). Inviting process participants is equivalent to providing them with a copy of an α-Doc, copying it like an ordinary desktop file. All α-Docs that belong to the same case can synchronize each other, based on the participant management, electronic postboxes, store-and-forward messaging, and an offline-capable synchronization protocol. Synonyms distributed document-oriented process management (dDPM), distributed case handling via active documents Protagonists Christoph P. Neumann and Prof. Richard Lenz Organization Friedrich-Alexander-Universität Erlangen-Nürnberg Period 2009 - 2012 Selected Publications and a PhD thesis Implementation α-Flow (open source) == Related Concepts == === Content Management === The bandwidth of Content management systems (CMS) reaches from Web content management systems (WCMS) and Document management system (DMS) to Enterprise Content Management (ECM). Mature DMS products support document production workflows in a basic form, primarily focusing on review cycle workflows concerning a single document. === Groupware and Computer-Supported Cooperative Work === Groupware focuses on messaging (like E-Mail, Chat, and Instant Messaging), shared calendars (e.g. Lotus Notes, Microsoft Outlook with Exchange Server), and conferencing (e.g. Skype). Groupware overlaps with Computer-supported cooperative work (CSCW), that originated from shared multimedia editors (for live drawing/sketching) and synchronous multi-user applications like desktop sharing. The extensive conceptual claim of CSWC must be put into perspective by its actual solution scope, that is available as the CSCW Matrix. === Case Handling === The case handling paradigm stems from Prof. van der Aalst and gained momentum in 2005. The core features are: (a) provide all information available, i.e. present the case as a whole rather than showing bits and pieces, (b) decide about activities on the basis of the information available rather than the activities already executed, (c) separate work distribution from authorization and allow for additional types of roles, not just the execute role, and (d) allow workers to view and add/modify data before or after the corresponding activities have been executed. In healthcare, the flow of a patient between healthcare professionals is considered as a workflow - with activities that inc

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  Structured sparsity regularization

  Structured sparsity regularization is a class of methods, and an area of research in statistical learning theory, that extend and generalize sparsity regularization learning methods. Both sparsity and structured sparsity regularization methods seek to exploit the assumption that the output variable Y {\displaystyle Y} (i.e., response, or dependent variable) to be learned can be described by a reduced number of variables in the input space X {\displaystyle X} (i.e., the domain, space of features or explanatory variables). Sparsity regularization methods focus on selecting the input variables that best describe the output. Structured sparsity regularization methods generalize and extend sparsity regularization methods, by allowing for optimal selection over structures like groups or networks of input variables in X {\displaystyle X} . Common motivation for the use of structured sparsity methods are model interpretability, high-dimensional learning (where dimensionality of X {\displaystyle X} may be higher than the number of observations n {\displaystyle n} ), and reduction of computational complexity. Moreover, structured sparsity methods allow to incorporate prior assumptions on the structure of the input variables, such as overlapping groups, non-overlapping groups, and acyclic graphs. Examples of uses of structured sparsity methods include face recognition, magnetic resonance image (MRI) processing, socio-linguistic analysis in natural language processing, and analysis of genetic expression in breast cancer. == Definition and related concepts == === Sparsity regularization === Consider the linear kernel regularized empirical risk minimization problem with a loss function V ( y i , f ( x ) ) {\displaystyle V(y_{i},f(x))} and the ℓ 0 {\displaystyle \ell _{0}} "norm" as the regularization penalty: min w ∈ R d 1 n ∑ i = 1 n V ( y i , ⟨ w , x i ⟩ ) + λ ‖ w ‖ 0 , {\displaystyle \min _{w\in \mathbb {R} ^{d}}{\frac {1}{n}}\sum _{i=1}^{n}V(y_{i},\langle w,x_{i}\rangle )+\lambda \|w\|_{0},} where x , w ∈ R d {\displaystyle x,w\in \mathbb {R^{d}} } , and ‖ w ‖ 0 {\displaystyle \|w\|_{0}} denotes the ℓ 0 {\displaystyle \ell _{0}} "norm", defined as the number of nonzero entries of the vector w {\displaystyle w} . f ( x ) = ⟨ w , x i ⟩ {\displaystyle f(x)=\langle w,x_{i}\rangle } is said to be sparse if ‖ w ‖ 0 = s < d {\displaystyle \|w\|_{0}=s 0 {\displaystyle w_{j}>0} . However, as in this case groups may overlap, we take the intersection of the complements of those groups that are not set to zero. This intersection of complements selection criteria implies the modeling choice that we allow some coefficients within a particular group g {\displaystyle g} to be set to zero, while others within the same group g {\displaystyle g} may remain positive. In other words, coefficients within a group may differ depending on the several group memberships that each variable within the group may have. ==== Union of groups: latent group Lasso ==== A different approach is to consider union of groups for variable selection. This approach captures the modeling situation where variables can be selected as long as they belong at least to one group with positive coefficients. This modeling perspective implies that we want to preserve group structure. The formulation of the union of groups approach is also referred to as latent group Lasso, and requires to modify the group ℓ 2 {\displaystyle \ell _{2}} norm considered above and introduce the following regularizer R ( w ) = i n f { ∑ g ‖ w g ‖ g : w = ∑ g = 1 G w ¯ g } {\displaystyle R(w)=inf\left\{\sum _{g}\|w_{g}\|_{g}:w=\sum _{g=1}^{G}{\bar {w}}_{g}\right\}} where w ∈ R d {\displaystyle w\in {\mathbb {R^{d}} }} , w g ∈ G g {\displaystyle w_{g}\in G_{g}} is the vector of coefficients of group g, and w ¯ g ∈ R d {\displaystyle {\bar {w}}_{g}\in {\mathbb {R^{d}} }} is a vector with coefficients w g j {\displaystyle w_{g}^{j}} for all variables j {

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  Data custodian

  In data governance groups, responsibilities for data management are increasingly divided between the business process owners and information technology (IT) departments. Two functional titles commonly used for these roles are data steward and data custodian. Data Stewards are commonly responsible for data content, context, and associated business rules. Data custodians are responsible for the safe custody, transport, storage of the data and implementation of business rules. Simply put, Data Stewards are responsible for what is stored in a data field, while data custodians are responsible for the technical environment and database structure. Common job titles for data custodians are database administrator (DBA), data modeler, ETL developer and data engineer. == Data custodian responsibilities == A data custodian ensures: Access to the data is authorized and controlled Data stewards are identified for each data set Technical processes sustain data integrity Processes exist for data quality issue resolution in partnership with data stewards Technical controls safeguard data Data added to data sets are consistent with the common data model Versions of master data are maintained along with the history of changes Change management practices are applied in maintenance of the database Data content and changes can be audited

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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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