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Closest point method
The closest point method (CPM) is an embedding method for solving partial differential equations on surfaces. The closest point method uses standard numerical approaches such as finite differences, finite element or spectral methods in order to solve the embedding partial differential equation (PDE) which is equal to the original PDE on the surface. The solution is computed in a band surrounding the surface in order to be computationally efficient. In order to extend the data off the surface, the closest point method uses a closest point representation. This representation extends function values to be constant along directions normal to the surface. == Definitions == Closest Point function: Given a surface S , c p ( x ) {\displaystyle {\mathcal {S}},cp(\mathbf {x} )} refers to a (possibly non-unique) point belonging to S {\displaystyle {\mathcal {S}}} , which is closest to x {\displaystyle \mathbf {x} } [SE]. Closest point extension: Let S {\displaystyle {\mathcal {S}}} , be a smooth surface in R d {\displaystyle \mathbb {R} ^{d}} . The closest point extension of a function u : S → R {\displaystyle u:{\mathcal {S}}\rightarrow \mathbb {R} } , to a neighborhood Ω {\displaystyle \Omega } of S {\displaystyle {\mathcal {S}}} , is the function v : Ω → R {\displaystyle v:\Omega \rightarrow \mathbb {R} } , defined by v ( x ) = u ( c p ( x ) ) {\displaystyle v(\mathbf {x} )=u(cp(\mathbf {x} ))} . == Closest point method == Initialization consists of these steps [EW]: If it is not already given, a closest point representation of the surface is constructed. A computational domain is chosen. Typically this is a band around the surface. Replace surface gradients by standard gradients in R 3 {\displaystyle \mathbb {R} ^{3}} . Solution is initialized by extending the initial surface data on to the computational domain using the closest point function. After initialization, alternate between the following two steps: Using the closest point function, extend the solution off the surface to the computational domain. Compute the solution to the embedding PDE on a Cartesian mesh in the computational domain for one time step. == Banding == The surface PDE is extended into R 3 {\displaystyle \mathbb {R} ^{3}} however it is only necessary to solve this new PDE near the surface. Hence, we solve the PDE in a band surrounding the surface for efficient computational purposes. Ω c x : ‖ x − c p ( x ) ‖ 2 ≤ λ {\displaystyle \Omega _{c}{x:\|x-cp(x)\|_{2}\leq \lambda }} where λ {\displaystyle \lambda } is the bandwidth. == Example: Heat equation on a circle == Using initial profile u S ( θ , t ) = sin ( θ ) {\displaystyle u_{S}(\theta ,t)=\sin(\theta )} leads to the solution u S ( θ , t ) = exp ( − t ) sin ( θ ) {\displaystyle u_{S}(\theta ,t)=\exp(-t)\sin(\theta )} for the heat equation. Forward Euler time-stepping is used with relation Δ t = 0.1 Δ x 2 {\displaystyle \Delta t=0.1\Delta x^{2}} and degree-four interpolation polynomials for the interpolations. Second-order centered differences are used for the spatial discretization. The CPM results in the expected second order error in the solution u {\displaystyle u} . == Applications == The closest point method can be applied to various PDEs on surfaces. Reaction–diffusion problems on point clouds [RD], eigenvalue problems [EV], and level set equations [LS] are a few examples.
Manhattan address algorithm
The Manhattan address algorithm is a series of formulas used to estimate the closest east–west cross street for building numbers on north–south avenues in the New York City borough of Manhattan. == Algorithm == To find the approximate number of the closest cross street, divide the building number by a divisor (generally 20) and add (or subtract) the "tricky number" from the table below: For the north–south avenues, there are typically 20 address numbers between consecutive east–west streets (10 on either side of the avenue). A standard land lot on each avenue was originally 20 feet (6.1 m) wide, and there is about 200 feet (61 m) between each pair of east–west streets, for ten land lots between each pair of streets. The exceptions are Riverside Drive, as well as Fifth Avenue and Central Park West between 59th and 110th streets, which use a divisor of 10. These avenues all have buildings only on one side of the street, with a park on the other side. The "tricky number" often corresponds to a street near the southern end of the avenue. There are some notable exceptions: York Avenue address numbers are continuations of Avenue A address numbers, since the avenue was originally called Avenue A. East End Avenue address numbers are continuations of Avenue B address numbers, since the avenue was originally called Avenue B. Sixth Avenue and Broadway start south of Houston Street, the southern boundary of the Manhattan street numbering system. Although Park Avenue's southern terminus is at 32nd Street, a homeowner at 34th Street wanted the address "1 Park Avenue" (this was later changed). === Examples === For example, if you are at 62 Avenue B, 62 ÷ 20 ≈ 3 {\displaystyle 62\div 20\approx 3} , then add the "tricky number" 3 {\displaystyle 3} to give 6 {\displaystyle 6} . The nearest cross street to 62 Avenue B is East 6th Street. If you are at 78 Riverside Drive, 78 ÷ 10 ≈ 8 {\displaystyle 78\div 10\approx 8} , then add the "tricky number" 72 {\displaystyle 72} to give 80 {\displaystyle 80} . The nearest cross street to 78 Riverside Drive is West 80th Street. If you are at 501 5th Avenue, 501 ÷ 20 ≈ 25 {\displaystyle 501\div 20\approx 25} , then add the "tricky number" 18 {\displaystyle 18} to give 43 {\displaystyle 43} . The nearest cross street to 501 5th Avenue is actually 42nd Street, not 43rd Street, as the Manhattan address algorithm only gives approximate answers.
Retention period
A retention period (associated with a retention schedule or retention program) is an aspect of records and information management (RIM) and the records life cycle that identifies the duration of time for which the information should be maintained or "retained", irrespective of format (paper, electronic, or other). Retention periods vary with different types of information, based on content and a variety of other factors, including internal organizational need, regulatory requirements for inspection or audit, legal statutes of limitation, involvement in litigation, and taxation and financial reporting needs, as well as other factors as defined by local, regional, state, national, and/or international governing entities. Once an applicable retention period has elapsed for a given type or series of information, and all holds/moratoriums have been released, the information is typically destroyed using an approved and effective destruction method, which renders the information completely and irreversibly unusable via any means. Alternatively, it may be converted from one form to another (e.g. from paper to electronic), depending on the defined retention period per format. Information with historical value beyond its "usable value" may be accessioned to the custody of an archive organization for permanent or extended long-term preservation. == Defensible disposition == Defensible disposition refers to the ability of an identified and applied retention period to effectively provide for the defense of the record, and its eventual destruction or accessioning when scrutinized within a court of law or by other review. It is commonly advised by records and information management (RIM) professionals that any and all retention periods applied to organizational information should be reviewed and approved for use by competent legal counsel, which represents the organization, and is familiar with the specific business needs and legal and regulatory requirements of the organization. Additionally, a practical approach to information assessment/classification, proper documentation of the disposition program, strategic review of disposition policy over time for efficacy are required for proper defensible disposition. == Guidance and education organizations == ARMA International Information and Records Management Society filerskeepers records retention FAQ
March algorithm
The March algorithm is a widely used algorithm that tests SRAM memory by filling all its entries test patterns. It carries out several passes through an SRAM checking the patterns and writing new patterns. The SRAM read and write operations performed on each pass are called a March element and each element is repeated for each entry. The March algorithm is often used to find functional faults in SRAM during testing such as: Stuck-at Faults (SAFs) Transition Faults (TFs) Address Decoder Faults (AFs) Coupling Faults (CFs), such as Inversion (CFin), Idempotent (CFid), and State (CFst) coupling faults It has been suggested to test SRAM modules using the algorithm before sale using a built-in self-test mechanism. == Notation == Each pass in a test sequence is represented by an "element". An element consists of a vertical arrow to indicate the direction in which the memory is scanned followed by a list of read/write operations to be applied to each memory cell. Multiple elements can be listed, separated by semicolons, to form a "test". For example, { ⇕ ( w 0 ) ; ⇑ ( r 0 , w 1 ) ; ⇓ ( r 1 , w 0 , r 0 ) } {\displaystyle \{\Updownarrow (w0);\Uparrow (r0,w1);\Downarrow (r1,w0,r0)\}} specifies to: Scan in both directions, writing 0. Scan from lowest to highest address, reading 0 and writing 1. Scan from highest to lowest address, reading 1, writing 0 and reading 0. == Variants == Many variants of the March algorithm exist with different sequences of tests. Each variant makes a different tradeoff between what faults it can detect and the complexity of the algorithm. Several variants have been given names:
Percept (artificial intelligence)
A percept is the input that an intelligent agent is perceiving at any given moment. It is essentially the same concept as a percept in psychology, except that it is being perceived not by the brain but by the agent. A percept is detected by a sensor, often a camera, processed accordingly, and acted upon by an actuator. Each percept is added to a "percept sequence", which is a complete history of each percept ever detected. The agent's action at any instant point may depend on the entire percept sequence up to that particular instant point. An intelligent agent chooses how to act not only based on the current percept, but the percept sequence. The next action is chosen by the agent function, which maps every percept to an action. For example, if a camera were to record a gesture, the agent would process the percepts, calculate the corresponding spatial vectors, examine its percept history, and use the agent program (the application of the agent function) to act accordingly. == Examples == Examples of percepts include inputs from touch sensors, cameras, infrared sensors, sonar, microphones, mice, and keyboards. A percept can also be a higher-level feature of the data, such as lines, depth, objects, faces, or gestures.
Non-personal data
Non-Personal Data (NPD) is electronic data that does not contain any information that can be used to identify a natural person. Thus, it can either be data that has no personal information to begin with (such as weather data, stock prices, data from anonymous IoT sensors); or it is data that had personal data that was subsequently pseudoanonymized (for example, identifiable strings substituted with random strings) or anonymized (such as by irreversibly removing all personal data). NPD is part of the overall Data Governance Strategy of a region or country. While personal data are covered by Data Protection Legislation such as GDPR, other kinds of data would fall under the scope of NPD Regulation. == Importance of non-personal data == It has been pointed out that the future is data-driven. What this means is that much of the present innovation taking place in domains such as Machine Learning and Artificial Intelligence is fueled by data, which is needed for calibrating the complex models (comprising neural network-based as well as other kinds). The larger the volume, diversity and quality of the data, the higher is the quality of the model, leading to better predictions and explanations. However, there is a flip-side to data availability. The newly-emerging awareness of privacy and the consequent need for powerful Data Protection Regulations (such as GDPR) makes it increasingly difficult or impossible to obtain data in the quantities required. This is a contradiction, and the only way out would be to remove all personal data from data sets (either by Data anonymization or Pseudonymization coupled with noise injection, at which point it becomes NPD. Therefore, many innovation-friendly countries are coming out with regulatory regimes that would ensure that personal data is protected, while, at the same time, non-personal data can be extracted from personal data so that innovation is fostered. In other words, NPD 'unlocks' value that was locked away in data sets that have personally-identifiable information. It is expected that multiple NPD data sets will begin to be available on free or commercial basis from different providers once the regulations are in place. == Emerging regulatory frameworks == Non-Personal Data has significant uses that may be economic, social, political or security-related. Several countries and regions are in the process of regulating the use of NPD. In May 2019, the European Union operationalized its Regulation of the Free Flow of NPD. India announced a nine-member expert committee to make recommendations on the regulation of NPD in 2019, which published its first report in mid-2020. The report was opened for public comments, after which it was revised and published in December 2020. == Proposed NPD regulatory framework in India == The following were the objectives of the proposed Indian regulation as per the revised report: Sovereignty: India has rights over the data of India, its people and organisations. Benefit India: Benefits of data must accrue to India and its people. Benefits the world: Innovation, new models and algorithms for the world. Privacy: Misuse, reidentification and harms must be prevented. Simplicity: The regulations should be simple, digital and unambiguous. Innovation and entrepreneurship: The data should be freely available for innovation and entrepreneurship in India. == Concerns == The major concern in the use of NPD is if there are techniques (statistical or AI-based) by which multiple data sets can be used to extract personally-identifiable data.