SQL/PSM (SQL/Persistent Stored Modules) is an ISO standard mainly defining an extension of SQL with a procedural language for use in stored procedures. Initially published in 1996 as an extension of SQL-92 (ISO/IEC 9075-4:1996, a version sometimes called PSM-96 or even SQL-92/PSM), SQL/PSM was later incorporated into the multi-part SQL:1999 standard, and has been part 4 of that standard since then, most recently in SQL:2023. The SQL:1999 part 4 covered less than the original PSM-96 because the SQL statements for defining, managing, and invoking routines were actually incorporated into part 2 SQL/Foundation, leaving only the procedural language itself as SQL/PSM. The SQL/PSM facilities are still optional as far as the SQL standard is concerned; most of them are grouped in Features P001-P008. SQL/PSM standardizes syntax and semantics for control flow, exception handling (called "condition handling" in SQL/PSM), local variables, assignment of expressions to variables and parameters, and (procedural) use of cursors. It also defines an information schema (metadata) for stored procedures. SQL/PSM is one language in which methods for the SQL:1999 structured types can be defined. The other is Java, via SQL/JRT. SQL/PSM is derived, seemingly directly, from Oracle's PL/SQL. Oracle developed PL/SQL and released it in 1991, basing the language on the US Department of Defense's Ada programming language. However, Oracle has maintained a distance from the standard in its documentation. IBM's SQL PL (used in DB2) and Mimer SQL's PSM were the first two products officially implementing SQL/PSM. It is commonly thought that these two languages, and perhaps also MySQL/MariaDB's procedural language, are closest to the SQL/PSM standard. However, a PostgreSQL addon implements SQL/PSM (alongside its other procedural languages like the PL/SQL-derived plpgsql), although it is not part of the core product. RDF functionality in OpenLink Virtuoso was developed entirely through SQL/PSM, combined with custom datatypes (e.g., ANY for handling URI and Literal relation objects), sophisticated indexing, and flexible physical storage choices (column-wise or row-wise).
Empirical dynamic modeling
Empirical dynamic modeling (EDM) is a framework for analysis and prediction of nonlinear dynamical systems. Applications include population dynamics, ecosystem service, medicine, neuroscience, dynamical systems, geophysics, and human-computer interaction. EDM was originally developed by Robert May and George Sugihara. It can be considered a methodology for data modeling, predictive analytics, dynamical system analysis, machine learning and time series analysis. == Description == Mathematical models have tremendous power to describe observations of real-world systems. They are routinely used to test hypothesis, explain mechanisms and predict future outcomes. However, real-world systems are often nonlinear and multidimensional, in some instances rendering explicit equation-based modeling problematic. Empirical models, which infer patterns and associations from the data instead of using hypothesized equations, represent a natural and flexible framework for modeling complex dynamics. Donald DeAngelis and Simeon Yurek illustrated that canonical statistical models are ill-posed when applied to nonlinear dynamical systems. A hallmark of nonlinear dynamics is state-dependence: system states are related to previous states governing transition from one state to another. EDM operates in this space, the multidimensional state-space of system dynamics rather than on one-dimensional observational time series. EDM does not presume relationships among states, for example, a functional dependence, but projects future states from localised, neighboring states. EDM is thus a state-space, nearest-neighbors paradigm where system dynamics are inferred from states derived from observational time series. This provides a model-free representation of the system naturally encompassing nonlinear dynamics. A cornerstone of EDM is recognition that time series observed from a dynamical system can be transformed into higher-dimensional state-spaces by time-delay embedding with Takens's theorem. The state-space models are evaluated based on in-sample fidelity to observations, conventionally with Pearson correlation between predictions and observations. == Methods == Primary EDM algorithms include Simplex projection, Sequential locally weighted global linear maps (S-Map) projection, Multivariate embedding in Simplex or S-Map, Convergent cross mapping (CCM), and Multiview Embeding, described below. Nearest neighbors are found according to: NN ( y , X , k ) = ‖ X N i E − y ‖ ≤ ‖ X N j E − y ‖ if 1 ≤ i ≤ j ≤ k {\displaystyle {\text{NN}}(y,X,k)=\|X_{N_{i}}^{E}-y\|\leq \|X_{N_{j}}^{E}-y\|{\text{ if }}1\leq i\leq j\leq k} === Simplex === Simplex projection is a nearest neighbor projection. It locates the k {\displaystyle k} nearest neighbors to the location in the state-space from which a prediction is desired. To minimize the number of free parameters k {\displaystyle k} is typically set to E + 1 {\displaystyle E+1} defining an E + 1 {\displaystyle E+1} dimensional simplex in the state-space. The prediction is computed as the average of the weighted phase-space simplex projected T p {\displaystyle Tp} points ahead. Each neighbor is weighted proportional to their distance to the projection origin vector in the state-space. Find k {\displaystyle k} nearest neighbor: N k ← NN ( y , X , k ) {\displaystyle N_{k}\gets {\text{NN}}(y,X,k)} Define the distance scale: d ← ‖ X N 1 E − y ‖ {\displaystyle d\gets \|X_{N_{1}}^{E}-y\|} Compute weights: For{ i = 1 , … , k {\displaystyle i=1,\dots ,k} } : w i ← exp ( − ‖ X N i E − y ‖ / d ) {\displaystyle w_{i}\gets \exp(-\|X_{N_{i}}^{E}-y\|/d)} Average of state-space simplex: y ^ ← ∑ i = 1 k ( w i X N i + T p ) / ∑ i = 1 k w i {\displaystyle {\hat {y}}\gets \sum _{i=1}^{k}\left(w_{i}X_{N_{i}+T_{p}}\right)/\sum _{i=1}^{k}w_{i}} === S-Map === S-Map extends the state-space prediction in Simplex from an average of the E + 1 {\displaystyle E+1} nearest neighbors to a linear regression fit to all neighbors, but localised with an exponential decay kernel. The exponential localisation function is F ( θ ) = exp ( − θ d / D ) {\displaystyle F(\theta )={\text{exp}}(-\theta d/D)} , where d {\displaystyle d} is the neighbor distance and D {\displaystyle D} the mean distance. In this way, depending on the value of θ {\displaystyle \theta } , neighbors close to the prediction origin point have a higher weight than those further from it, such that a local linear approximation to the nonlinear system is reasonable. This localisation ability allows one to identify an optimal local scale, in-effect quantifying the degree of state dependence, and hence nonlinearity of the system. Another feature of S-Map is that for a properly fit model, the regression coefficients between variables have been shown to approximate the gradient (directional derivative) of variables along the manifold. These Jacobians represent the time-varying interaction strengths between system variables. Find k {\displaystyle k} nearest neighbor: N ← NN ( y , X , k ) {\displaystyle N\gets {\text{NN}}(y,X,k)} Sum of distances: D ← 1 k ∑ i = 1 k ‖ X N i E − y ‖ {\displaystyle D\gets {\frac {1}{k}}\sum _{i=1}^{k}\|X_{N_{i}}^{E}-y\|} Compute weights: For{ i = 1 , … , k {\displaystyle i=1,\dots ,k} } : w i ← exp ( − θ ‖ X N i E − y ‖ / D ) {\displaystyle w_{i}\gets \exp(-\theta \|X_{N_{i}}^{E}-y\|/D)} Reweighting matrix: W ← diag ( w i ) {\displaystyle W\gets {\text{diag}}(w_{i})} Design matrix: A ← [ 1 X N 1 X N 1 − 1 … X N 1 − E + 1 1 X N 2 X N 2 − 1 … X N 2 − E + 1 ⋮ ⋮ ⋮ ⋱ ⋮ 1 X N k X N k − 1 … X N k − E + 1 ] {\displaystyle A\gets {\begin{bmatrix}1&X_{N_{1}}&X_{N_{1}-1}&\dots &X_{N_{1}-E+1}\\1&X_{N_{2}}&X_{N_{2}-1}&\dots &X_{N_{2}-E+1}\\\vdots &\vdots &\vdots &\ddots &\vdots \\1&X_{N_{k}}&X_{N_{k}-1}&\dots &X_{N_{k}-E+1}\end{bmatrix}}} Weighted design matrix: A ← W A {\displaystyle A\gets WA} Response vector at T p {\displaystyle Tp} : b ← [ X N 1 + T p X N 2 + T p ⋮ X N k + T p ] {\displaystyle b\gets {\begin{bmatrix}X_{N_{1}+T_{p}}\\X_{N_{2}+T_{p}}\\\vdots \\X_{N_{k}+T_{p}}\end{bmatrix}}} Weighted response vector: b ← W b {\displaystyle b\gets Wb} Least squares solution (SVD): c ^ ← argmin c ‖ A c − b ‖ 2 2 {\displaystyle {\hat {c}}\gets {\text{argmin}}_{c}\|Ac-b\|_{2}^{2}} Local linear model c ^ {\displaystyle {\hat {c}}} is prediction: y ^ ← c ^ 0 + ∑ i = 1 E c ^ i y i {\displaystyle {\hat {y}}\gets {\hat {c}}_{0}+\sum _{i=1}^{E}{\hat {c}}_{i}y_{i}} === Multivariate Embedding === Multivariate Embedding recognizes that time-delay embeddings are not the only valid state-space construction. In Simplex and S-Map one can generate a state-space from observational vectors, or time-delay embeddings of a single observational time series, or both. === Convergent Cross Mapping === Convergent cross mapping (CCM) leverages a corollary to the Generalized Takens Theorem that it should be possible to cross predict or cross map between variables observed from the same system. Suppose that in some dynamical system involving variables X {\displaystyle X} and Y {\displaystyle Y} , X {\displaystyle X} causes Y {\displaystyle Y} . Since X {\displaystyle X} and Y {\displaystyle Y} belong to the same dynamical system, their reconstructions (via embeddings) M x {\displaystyle M_{x}} , and M y {\displaystyle M_{y}} , also map to the same system. The causal variable X {\displaystyle X} leaves a signature on the affected variable Y {\displaystyle Y} , and consequently, the reconstructed states based on Y {\displaystyle Y} can be used to cross predict values of X {\displaystyle X} . CCM leverages this property to infer causality by predicting X {\displaystyle X} using the M y {\displaystyle M_{y}} library of points (or vice versa for the other direction of causality), while assessing improvements in cross map predictability as larger and larger random samplings of M y {\displaystyle M_{y}} are used. If the prediction skill of X {\displaystyle X} increases and saturates as the entire M y {\displaystyle M_{y}} is used, this provides evidence that X {\displaystyle X} is casually influencing Y {\displaystyle Y} . === Multiview Embedding === Multiview Embedding is a Dimensionality reduction technique where a large number of state-space time series vectors are combitorially assessed towards maximal model predictability. == Extensions == Extensions to EDM techniques include: Generalized Theorems for Nonlinear State Space Reconstruction Extended Convergent Cross Mapping Dynamic stability S-Map regularization Visual analytics with EDM Convergent Cross Sorting Expert system with EDM hybrid Sliding windows based on the extended convergent cross-mapping Empirical Mode Modeling Accounting for missing data and variable step sizes Accounting for observation noise Hierarchical Bayesian EDM via Gaussian processes Intelligent and Adaptive Control Optimal control via Empirical dynamic programming Multiview distance regularised S-map
FreePBX Distro
The FreePBX Distro was a freeware unified communications software system that consisted of FreePBX, a graphical user interface (GUI) for configuring, controlling and managing Asterisk PBX software. The FreePBX Distro included packages that offer VoIP, PBX, Fax, IVR, voice-mail and email functions. The FreePBX Distro Linux distribution was based on CentOS, which maintains binary compatibility with Red Hat Enterprise Linux. FreePBX has contributed to the popularity of Asterisk. As a result of CentOS Linux being discontinued and the last version of CentOS 7 going out of support on June 30, 2024, FreePBX 17 has moved over to and is supported on Debian Linux. FreePBX will no longer be providing a pre-configured FreePBX Distro, but will provide a script to install FreePBX on a fresh install of Debian Linux. In-place migration will not be possible, but will be possible by restoring a backup on the new version from the previous version. As FreePBX 16 will be supported until the release of FreePBX 18, FreePBX on this distribution will still work and be supported, however, there will be no further support for the underlying operating system. == Installation == The Official FreePBX Distro is installed from a ISO image available by web download, that includes the system CentOS, Asterisk, FreePBX GUI and assorted dependencies. This can then either be burned to DVD or written to a USB stick for installation == Support for telephony hardware == The FreePBX Distro has built-in support for cards from multiple vendors, including Digium, OpenVox, Alto, Rhino Equipment, Xorcom and Sangoma. The FreePBX Distro supports a large number of phone models via open-source modules. Supported VoIP phone manufacturers include Algo, AND, AudioCodes, Cisco, Cyberdata, Digium, Grandstream, Mitel/Aastra, Nortel/Avaya, Panasonic, Polycom, Sangoma, Snom, Xorcom and Yealink. == Development == FreePBX made its debut in 2004 as the AMP project (Asterisk Management Portal). The FreePBX Distro was released in 2011 as an turnkey solution for building a PBX using Asterisk, CentOS and FreePBX. FreePBX has over 1 million active production PBXs and over 20,000 new systems added each month. The core telephony engine is Asterisk, as configured by the Open Source FreePBX GUI. The last stable release is FreePBX Distro Stable SNG7-PBX16-64bit-2302-1 based on these main components: FreePBX 16 CentOS 7.8 Asterisk 16, 18, 19 (20 supported by upgrade once installed)
Web API
A web API is an application programming interface (API) for either a web server or a web browser. As a web development concept, it can be related to a web application's client side (including any web frameworks being used). A server-side web API consists of one or more publicly exposed endpoints to a defined request–response message system, typically expressed in JSON or XML by means of an HTTP-based web server. A server API (SAPI) is not considered a server-side web API, unless it is publicly accessible by a remote web application. == Client side == A client-side web API is a programmatic interface to extend functionality within a web browser or other HTTP client. Originally these were most commonly in the form of native plug-in browser extensions however most newer ones target standardized JavaScript bindings. The Mozilla Foundation created their WebAPI specification which is designed to help replace native mobile applications with HTML5 applications. Google created their Native Client architecture which is designed to help replace insecure native plug-ins with secure native sandboxed extensions and applications. They have also made this portable by employing a modified LLVM AOT compiler. == Server side == A server-side web API consists of one or more publicly exposed endpoints to a defined request–response message system, typically expressed in JSON or XML. The web API is exposed most commonly by means of an HTTP-based web server. Mashups are web applications which combine the use of multiple server-side web APIs. Webhooks are server-side web APIs that take input as a Uniform Resource Identifier (URI) that is designed to be used like a remote named pipe or a type of callback such that the server acts as a client to dereference the provided URI and trigger an event on another server which handles this event thus providing a type of peer-to-peer IPC. === Endpoints === Endpoints are important aspects of interacting with server-side web APIs, as they specify where resources can be accessed by third-party software. Usually the access is via a URI to which HTTP requests are posted, and from which the response is thus expected. Web APIs may be public or private, the latter of which requires an access token. Endpoints need to be static, otherwise the correct functioning of software that interacts with them cannot be guaranteed. If the location of a resource changes (and with it the endpoint) then previously written software will break, as the required resource can no longer be found at the same place. As API providers still want to update their web APIs, many have introduced a versioning system in the URI that points to an endpoint. === Resources versus services === Web 2.0 Web APIs often use machine-based interactions such as REST and SOAP. RESTful web APIs use HTTP methods to access resources via URL-encoded parameters, and use JSON or XML to transmit data. By contrast, SOAP protocols are standardized by the W3C and mandate the use of XML as the payload format, typically over HTTP. Furthermore, SOAP-based Web APIs use XML validation to ensure structural message integrity, by leveraging the XML schemas provisioned with WSDL documents. A WSDL document accurately defines the XML messages and transport bindings of a Web service. === Documentation === Server-side web APIs are interfaces for the outside world to interact with the business logic. For many companies this internal business logic and the intellectual property associated with it are what distinguishes them from other companies, and potentially what gives them a competitive edge. They do not want this information to be exposed. However, in order to provide a web API of high quality, there needs to be a sufficient level of documentation. One API provider that not only provides documentation, but also links to it in its error messages is Twilio. However, there are now directories of popular documented server-side web APIs. === Growth and impact === The number of available web APIs has grown consistently over the past years, as businesses realize the growth opportunities associated with running an open platform, that any developer can interact with. ProgrammableWeb tracks over 24000 Web APIs that were available in 2022, up from 105 in 2005. Web APIs have become ubiquitous. There are few major software applications/services that do not offer some form of web API. One of the most common forms of interacting with these web APIs is via embedding external resources, such as tweets, Facebook comments, YouTube videos, etc. In fact there are very successful companies, such as Disqus, whose main service is to provide embeddable tools, such as a feature-rich comment system. Any website of the TOP 100 Alexa Internet ranked websites uses APIs and/or provides its own APIs, which is a very distinct indicator for the prodigious scale and impact of web APIs as a whole. As the number of available web APIs has grown, open source tools have been developed to provide more sophisticated search and discovery. APIs.json provides a machine-readable description of an API and its operations, and the related project APIs.io offers a searchable public listing of APIs based on the APIs.json metadata format. === Business === ==== Commercial ==== Many companies and organizations rely heavily on their Web API infrastructure to serve their core business clients. In 2014 Netflix received around 5 billion API requests, most of them within their private API. ==== Governmental ==== Many governments collect a lot of data, and some governments are now opening up access to this data. The interfaces through which this data is typically made accessible are web APIs. Web APIs allow for data, such as "budget, public works, crime, legal, and other agency data" to be accessed by any developer in a convenient manner. == Example == An example of a popular web API is the Astronomy Picture of the Day API operated by the American space agency NASA. It is a server-side API used to retrieve photographs of space or other images of interest to astronomers, and metadata about the images. According to the API documentation, the API has one endpoint: https://api.nasa.gov/planetary/apod The documentation states that this endpoint accepts GET requests. It requires one piece of information from the user, an API key, and accepts several other optional pieces of information. Such pieces of information are known as parameters. The parameters for this API are written in a format known as a query string, which is separated by a question mark character (?) from the endpoint. An ampersand (&) separates the parameters in the query string from each other. Together, the endpoint and the query string form a URL that determines how the API will respond. This URL is also known as a query or an API call. In the below example, two parameters are transmitted (or passed) to the API via the query string. The first is the required API key and the second is an optional parameter — the date of the photograph requested. https://api.nasa.gov/planetary/apod?api_key=DEMO_KEY&date=1996-12-03 Visiting the above URL in a web browser will initiate a GET request, calling the API and showing the user a result, known as a return value or as a return. This API returns JSON, a type of data format intended to be understood by computers, but which is somewhat easy for a human to read as well. In this case, the JSON contains information about a photograph of a white dwarf star: The above API return has been reformatted so that names of JSON data items, known as keys, appear at the start of each line. The last of these keys, named url, indicates a URL which points to a photograph: https://apod.nasa.gov/apod/image/9612/ngc2440_hst2.jpg Following the above URL, a web browser user would see this photo: Although this API can be called by an end user with a web browser (as in this example) it is intended to be called automatically by software or by computer programmers while writing software. JSON is intended to be parsed by a computer program, which would extract the URL of the photograph and the other metadata. The resulting photo could be embedded in a website, automatically sent via text message, or used for any other purpose envisioned by a software developer.
Interstellar communication
Interstellar communication is the transmission of signals between planetary systems. Sending interstellar messages is potentially much easier than interstellar travel, being possible with technologies and equipment which are currently available. However, the distances from Earth to other potentially inhabited systems introduce prohibitive delays, assuming the limitations of the speed of light. Even an immediate reply to radio communications sent to stars tens of thousands of light-years away would take many human generations to arrive. == Radio == The SETI project has for the past several decades been conducting a search for signals being transmitted by extraterrestrial life located outside the Solar System, primarily in the radio frequencies of the electromagnetic spectrum. Special attention has been given to the Water Hole, the frequency of one of neutral hydrogen's absorption lines, due to the low background noise at this frequency and its symbolic association with the basis for what is likely to be the most common system of biochemistry (but see alternative biochemistry). The regular radio pulses emitted by pulsars were briefly thought to be potential intelligent signals; the first pulsar to be discovered was originally designated "LGM-1", for "Little Green Men." They were quickly determined to be of natural origin, however. Several attempts have been made to transmit signals to other stars as well. (See "Realized projects" at Active SETI.) One of the earliest and most famous was the 1974 radio message sent from the largest radio telescope in the world, the Arecibo Observatory in Puerto Rico. An extremely simple message was aimed at a globular cluster of stars known as M13 in the Milky Way Galaxy and at a distance of 30,000 light years from the Solar System. These efforts have been more symbolic than anything else, however. Further, a possible answer needs double the travel time, i.e. tens of years (near stars) or 60,000 years (M13). == Other methods == It has also been proposed that higher frequency signals, such as lasers operating at visible light frequencies, may prove to be a fruitful method of interstellar communication; at a given frequency it takes surprisingly small energy output for a laser emitter to outshine its local star from the perspective of its target. Other more exotic methods of communication have been proposed, such as modulated neutrino or gravitational wave emissions. These would have the advantage of being essentially immune to interference by intervening matter. Sending physical mail packets between stars may prove to be optimal for many applications. While mail packets would likely be limited to speeds far below that of electromagnetic or other light-speed signals (resulting in very high latency), the amount of information that could be encoded in only a few tons of physical matter could more than make up for it in terms of average bandwidth. The possibility of using interstellar messenger probes for interstellar communication — known as Bracewell probes — was first suggested by Ronald N. Bracewell in 1960, and the technical feasibility of this approach was demonstrated by the British Interplanetary Society's starship study Project Daedalus in 1978. Starting in 1979, Robert Freitas advanced arguments for the proposition that physical space-probes provide a superior mode of interstellar communication to radio signals, then undertook telescopic searches for such probes in 1979 and 1982.
Oversampled binary image sensor
An oversampled binary image sensor is an image sensor with non-linear response capabilities reminiscent of traditional photographic film. Each pixel in the sensor has a binary response, giving only a one-bit quantized measurement of the local light intensity. The response function of the image sensor is non-linear and similar to a logarithmic function, which makes the sensor suitable for high dynamic range imaging. == Working principle == Before the advent of digital image sensors, photography, for the most part of its history, used film to record light information. At the heart of every photographic film are a large number of light-sensitive grains of silver-halide crystals. During exposure, each micron-sized grain has a binary fate: Either it is struck by some incident photons and becomes "exposed", or it is missed by the photon bombardment and remains "unexposed". In the subsequent film development process, exposed grains, due to their altered chemical properties, are converted to silver metal, contributing to opaque spots on the film; unexposed grains are washed away in a chemical bath, leaving behind the transparent regions on the film. Thus, in essence, photographic film is a binary imaging medium, using local densities of opaque silver grains to encode the original light intensity information. Thanks to the small size and large number of these grains, one hardly notices this quantized nature of film when viewing it at a distance, observing only a continuous gray tone. The oversampled binary image sensor is reminiscent of photographic film. Each pixel in the sensor has a binary response, giving only a one-bit quantized measurement of the local light intensity. At the start of the exposure period, all pixels are set to 0. A pixel is then set to 1 if the number of photons reaching it during the exposure is at least equal to a given threshold q. One way to build such binary sensors is to modify standard memory chip technology, where each memory bit cell is designed to be sensitive to visible light. With current CMOS technology, the level of integration of such systems can exceed 109~1010 (i.e., 1 giga to 10 giga) pixels per chip. In this case, the corresponding pixel sizes (around 50~nm ) are far below the diffraction limit of light, and thus the image sensor is oversampling the optical resolution of the light field. Intuitively, one can exploit this spatial redundancy to compensate for the information loss due to one-bit quantizations, as is classic in oversampling delta-sigma converters. Building a binary sensor that emulates the photographic film process was first envisioned by Fossum, who coined the name digital film sensor (now referred to as a quanta image sensor). The original motivation was mainly out of technical necessity. The miniaturization of camera systems calls for the continuous shrinking of pixel sizes. At a certain point, however, the limited full-well capacity (i.e., the maximum photon-electrons a pixel can hold) of small pixels becomes a bottleneck, yielding very low signal-to-noise ratios (SNRs) and poor dynamic ranges. In contrast, a binary sensor whose pixels need to detect only a few photon-electrons around a small threshold q has much less requirement for full-well capacities, allowing pixel sizes to shrink further. == Imaging model == === Lens === Consider a simplified camera model shown in Fig.1. The λ 0 ( x ) {\displaystyle \lambda _{0}(x)} is the incoming light intensity field. By assuming that light intensities remain constant within a short exposure period, the field can be modeled as only a function of the spatial variable x {\displaystyle x} . After passing through the optical system, the original light field λ 0 ( x ) {\displaystyle \lambda _{0}(x)} gets filtered by the lens, which acts like a linear system with a given impulse response. Due to imperfections (e.g., aberrations) in the lens, the impulse response, a.k.a. the point spread function (PSF) of the optical system, cannot be a Dirac delta, thus, imposing a limit on the resolution of the observable light field. However, a more fundamental physical limit is due to light diffraction. As a result, even if the lens is ideal, the PSF is still unavoidably a small blurry spot. In optics, such diffraction-limited spot is often called the Airy disk, whose radius R a {\displaystyle R_{a}} can be computed as R a = 1.22 w f , {\displaystyle R_{a}=1.22\,wf,} where w {\displaystyle w} is the wavelength of the light and f {\displaystyle f} is the F-number of the optical system. Due to the lowpass (smoothing) nature of the PSF, the resulting λ ( x ) {\displaystyle \lambda (x)} has a finite spatial-resolution, i.e., it has a finite number of degrees of freedom per unit space. === Sensor === Fig.2 illustrates the binary sensor model. The s m {\displaystyle s_{m}} denote the exposure values accumulated by the sensor pixels. Depending on the local values of s m {\displaystyle s_{m}} , each pixel (depicted as "buckets" in the figure) collects a different number of photons hitting on its surface. y m {\displaystyle y_{m}} is the number of photons impinging on the surface of the m {\displaystyle m} th pixel during an exposure period. The relation between s m {\displaystyle s_{m}} and the photon count y m {\displaystyle y_{m}} is stochastic. More specifically, y m {\displaystyle y_{m}} can be modeled as realizations of a Poisson random variable, whose intensity parameter is equal to s m {\displaystyle s_{m}} , As a photosensitive device, each pixel in the image sensor converts photons to electrical signals, whose amplitude is proportional to the number of photons impinging on that pixel. In a conventional sensor design, the analog electrical signals are then quantized by an A/D converter into 8 to 14 bits (usually the more bits the better). But in the binary sensor, the quantizer is 1 bit. In Fig.2, b m {\displaystyle b_{m}} is the quantized output of the m {\displaystyle m} th pixel. Since the photon counts y m {\displaystyle y_{m}} are drawn from random variables, so are the binary sensor output b m {\displaystyle b_{m}} . === Spatial and temporal oversampling === If it is allowed to have temporal oversampling, i.e., taking multiple consecutive and independent frames without changing the total exposure time τ {\displaystyle \tau } , the performance of the binary sensor is equivalent to the sensor with same number of spatial oversampling under certain condition. It means that people can make trade off between spatial oversampling and temporal oversampling. This is quite important, since technology usually gives limitation on the size of the pixels and the exposure time. == Advantages over traditional sensors == Due to the limited full-well capacity of conventional image pixel, the pixel will saturate when the light intensity is too strong. This is the reason that the dynamic range of the pixel is low. For the oversampled binary image sensor, the dynamic range is not defined for a single pixel, but a group of pixels, which makes the dynamic range high. == Reconstruction == One of the most important challenges with the use of an oversampled binary image sensor is the reconstruction of the light intensity λ ( x ) {\displaystyle \lambda (x)} from the binary measurement b m {\displaystyle b_{m}} . Maximum likelihood estimation can be used for solving this problem. Fig. 4 shows the results of reconstructing the light intensity from 4096 binary images taken by single photon avalanche diodes (SPADs) camera. A better reconstruction quality with fewer temporal measurements and faster, hardware friendly implementation, can be achieved by more sophisticated algorithms.
Media preservation
Preservation of documents, pictures, recordings, digital content, etc., is a major aspect of archival science. It is also an important consideration for people who are creating time capsules, family history, historical documents, scrapbooks and family trees. Common storage media are not permanent, and there are few reliable methods of preserving documents and pictures for the future. == Paper/prints (photos) == Color negatives and ordinary color prints may fade away to nothing in a relatively short period if not stored and handled properly. This happens even if the negatives and prints are kept in the dark, because ambient light is not the determining factor, but heat and humidity are. The color degradation is the result of the dyes used in the color processes. Because color processing results in a less stable image than traditional black-and-white processing, black-and-white pictures from the 1920s are more likely to survive long-term than color films and photographs from after the middle 20th century. Black-and-white photographic films using silver halide emulsions are the only film types that have proven to last for archival storage. The determining factors for longevity include the film base type, proper processing (develop, stop, fix and wash) and proper storage. Early films used a Cellulose nitrate base which was prone to decomposition and highly flammable. Nitrate film was replaced with acetate-base films. These Cellulose acetate films were later discovered to outgass acids (also referred to as vinegar syndrome). Acetate films were replaced in the early 1980s by polyester film base materials which have been determined to be more stable than film stocks with a nitrate or acetate base. Color prints made on most inkjet printers look very good at first but they have a very short lifespan, measured in months rather than in years. Even prints from commercial photo labs will start to fade in a matter of years if not processed properly and stored in cool, dry environments. == Documents/books == With documents for which the media are not so critical as what the documents contain, the information in documents can be copied by using photocopiers and image scanners. Books and manuscripts can also have their information saved without destruction by using a book scanner. Where the medium itself needs to be preserved, for example if a document is a crayon sketch by a famous artist on paper, a complex process of preservation may be used. Depending on the condition and importance of the item this can include gluing the media onto more stable media, or protective enclosing of the media. Polyester sleeves, acid-free folders, and pH buffered document boxes are common supportive protective enclosures whose selection must match the media's chemical and physical properties. Other considerations in preserving paper/books are: Damaging light, particularly UV light, which fades and destroys media over time by breaking down the molecules. Atmosphere contains small traces of sulfur dioxide and nitric acid which turn media yellow and break the fibers down. Humidity and moisture also aid in the breakdown of media. If there is too much, the document can be attacked by bacteria, and if too little, cellulose material breaks down. Temperature, particularly elevated ones, can destroy some media. Low temperatures can cause the water to form crystals which expands destroying the structure of paper-based documents. == Online photo albums == Although there are many websites that allow the upload of photographs and videos, digital preservation for the long-term is still considered an issue. There is a lack of confidence that such websites are capable of storing data for long periods of time (ex. 50 years) without data degradation or loss. == Optical media - CD, DVD, Blu-ray, M-Disc == Write-once optical media, such as CD-Rs and DVD-Rs, typically contain an organic dye that distinguishes data reading from data writing based on the dye's transparency along the disc. Conventional CDs and DVDs have finite shelf-life due to natural degradation of the dye; the newer M-DISC uses inorganic material technology to produce molded DVDs and Blu-Rays (up to 3-layer 100GB BDXL) with a claimed lifespan of 100-1000 years if stored correctly with most BD & BDXL rated read/writers enabling the higher power mode for the M-Disc format after 2011. The National Archives and Records Administration lists published life expectancies to be 10 or 25 years or more for normal CDs and DVDs and conservative life expectancies to be between 2 and 5 years. Storage environments, such as temperature and humidity, as well as handling conditions such as frequency of media use and compatibility between the recorder and media, affect media shelf-life. Improvements in media storage and migrations to new recording technologies can make certain formats obsolete within their respective lifespan. Technologists have pointed to internet streaming services, where services such as video-on-demand have contributed to the 33 percent decline in DVD sales the past 5 years, as a challenge for digital preservation. == Magnetic media - video cassettes, tapes, hard drives == Magnetic media such as audio and video tape and floppy disks also have limited life spans. Audio and video tapes require specific care and handling to ensure that the recorded information will be preserved. For information that must be preserved indefinitely, periodic transcription from old media to new ones is necessary, not only because the media are unstable but also because the recording technology may become obsolete. Magnetic media also deteriorates naturally with typical shelf lives between 10 and 20 years. Magnetic tape can degrade from binder hydrolysis or magnetic remanence decay. Binder hydrolysis, also known as sticky-shed syndrome, refers to the breakdown of binder, or glue, that holds the magnetic particles to the polyester base of the tape. Tapes which have been stored in hot, humid conditions are particularly vulnerable to this phenomenon and may suffer from accelerated degradation. Severe binder can cause the magnetic material to fall off or sheds from the base, leaving a pile of dust and clear backing. Archivists can bake the tape, which evaporates water molecules on the tape, to temporarily restore the binder before making a copy. Magnetic tape can also be destabilized by magnetic remanence decay, which refers to the weakening of the tape's magnetization over time. This weakens the affected tape's readability, leading to reduced sound clarity and volume or picture hue and contrast. Baking the tape will not restore magnetization. Media at risk include recorded media such as master audio recordings of symphonies and videotape recordings of the news gathered over the last 40 years. Threats to media that must be considered when archiving important record media include accidental erasure, physical loss due to disasters such as fires and floods, and media degradation. Along with the actual media being degraded over the years, the machines that are available to play back or reproduce the audio sources are becoming archaic themselves. Manufacturers and their support (parts, technical updates) for their machines have disappeared throughout the years. Even if the medium is vaulted and archived correctly, the mechanical properties of the machines have deteriorated to the point that they could do more harm than good to the tape being played. Many major film studios are now backing up their libraries by converting them to electronic media files, such as .AIFF or .WAV-based files via digital audio workstations. That way, even if the digital platform manufacturer goes out of business or no longer supports their product, the files can still be played on any common computer. There is a detailed process that must take place previous to the final archival product now that a digital solution is in place. Sample rates and their conversion and reference speed are both critical in this process. In floppy disks, the lubricants inside the plastic jackets of many older floppies promote the decay of the magnetic medium. Also, the alignment of the magnetic particles of the disk substrate may gradually degrade, leading to a loss of formatting and data. Early laser disk media were prone to degradation as the layers of the disk substrate were bonded with an adhesive that was vulnerable to decay and would crumble over time. This would lead the different layers of the disk to peel apart, damaging the pitted data surface and rendering the disk unreadable.