A Feigenbaum test is a variation of the Turing test where a computer system attempts to replicate an expert in a given field such as chemistry or marketing. It is also known, as a subject matter expert Turing test and was proposed by Edward Feigenbaum in a 2003 paper. The concept is also described by Ray Kurzweil in his 2005 book The Singularity is Near. Kurzweil argues that machines who pass this test are an inevitable consequence of Moore's Law.
INDECT
INDECT is a research project in the area of intelligent security systems performed by several European universities since 2009 and funded by the European Union. The purpose of the project is to involve European scientists and researchers in the development of solutions to and tools for automatic threat detection through e.g. processing of CCTV camera data streams, standardization of video sequence quality for user applications, threat detection in computer networks as well as data and privacy protection. The area of research, applied methods, and techniques are described in the public deliverables which are available to the public on the project's website. Practically, all information related to the research is public. Only documents that comprise information related to financial data or information that could negatively influence the competitiveness and law enforcement capabilities of parties involved in the project are not published. This follows regulations and practices applied in EU research projects. == Application and target users == The main end-user of INDECT solutions are police forces and security services. The principle of operation of the project is detecting threats and identifying sources of threats, without monitoring and searching for particular citizens or groups of citizens. Then, the system operator (i.e. police officer) decides whether an intervention of services responsible for public security are required or not. Further investigation eventually leading to persons related to threats is performed, preserving the presumption of innocence, based on existing procedures already used by police services and prosecutors. As it can be found in the project deliverables, INDECT does not involve storage of personal data (such as names, addresses, identity document numbers, etc.). A similar, behavior-based surveillance program was SAMURAI (Suspicious and Abnormal behavior Monitoring Using a netwoRk of cAmeras & sensors for sItuation awareness enhancement). == Expected results == The main expected results of the INDECT project are: Trial of intelligent analysis of video and audio data for threat detection in urban environments Creation of tools and technology for privacy and data protection during storage and transmission of information using quantum cryptography and new methods of digital watermarking Performing computer-aided detection of threats and targeted crimes in Internet resources with privacy-protecting solutions Construction of a search engine for rapid semantic search based on watermarking of content related to child pornography and human organ trafficking Implementation of a distributed computer system that is capable of effective intelligent processing == Controversy == Some media and other sources accuse INDECT of privacy abuse, collecting personal data, and keeping information from the public. Consequently, these issues have been commented and discussed by some Members of the European Parliament. As seen in the project's documentation, INDECT does not involve mobile phone tracking or call interception. The rumors about testing INDECT during 2012 UEFA European Football Championship also turned out to be false. The mid-term review of the Seventh Framework Programme to the European Parliament strongly urges the European Commission to immediately make all documents available and to define a clear and strict mandate for the research goal, the application, and the end users of INDECT, and stresses a thorough investigation of the possible impact on fundamental rights. Nevertheless, according to Mr. Paweł Kowal, MEP, the project had the ethical review on 15 March 2011 in Brussels with the participation of ethics experts from Austria, France, Netherlands, Germany and Great Britain.
Automated dispensing cabinet
An automated dispensing cabinet (ADC), also called a unit-based cabinet (UBC), automated dispensing device (ADD), or automated dispensing machine (ADM)[1], is a computerized medicine cabinet for hospitals and healthcare settings. ADCs allow medications to be stored and dispensed near the point of care while controlling and tracking drug distribution. == Overview == Hospital pharmacies have provided medications for patients by filling patient-specific cassettes of unit-dose medications that were then delivered to the nursing unit and stored in medication cabinets or carts. ADCs, originally designed for hospital use, were introduced in hospitals in the 1980s and have facilitated the transition to alternative delivery models and more decentralized medication distribution systems.[2] Implementing automated dispensing cabinets as part of a decentralized or hybrid medication distribution system can improve patient safety and the accountability of the inventory, streamline certain billing processes. However, in the 2000s, the technology began to be deployed into other care settings where medication doses were stored onsite, and higher security methods were needed to control inventory, access, and dispensing of each patient dose. Settings that now deploy ADCs include long-term care facilities, hospice, critical access hospitals, surgery centers, group homes, residential care facilities, rehab and psych environments, animal health, dental clinics, and nursing education simulation. These diverse care settings share a common need to safely store, account for, and dispense individual doses of medications, especially narcotics and high-value medications, at the point of care.[3] ADCs track user access and dispensed medications, and their use can improve control over medication inventory. The real-time inventory reports generated by many cabinets can simplify the filling process and help the pharmacy track expired drugs. Furthermore, by restricting individual drugs – such as high-risk medications and controlled substances – to unique drawers within the cabinet, overall inventory management, patient safety, and medication security can be improved. Automated dispensing cabinets allow the pharmacy department to profile physician orders before they are dispensed.[4] ADCs can also enable providers to record medication charges upon dispensing, reducing the billing paperwork the pharmacy is responsible for. In addition, nurses can note returned medications using the cabinets' computers, enabling direct credits to patients' accounts. Since automated cabinets can be located on the nursing unit floor, nursing have speedier access to a patient's medications. Also, shorter waiting time ensures improved patient comfort and care.[5] == Role of automated dispensing in healthcare == Automated dispensing is a pharmacy practice in which a device dispenses medications and fills prescriptions. ADCs, which can handle many different medications, are available from a number of manufacturers such as BD, ARxIUM, and Omnicell. Though members of the pharmacy community have been utilizing automation technology since the 1980s, companies are constantly improving ADCs to meet changing needs and health standards in the industry. Several goals can be met by implementing an automated product in a healthcare facility. Patient safety can be ensured with the use of ADC technology such as barcoding. Anesthesia ADCs in operating rooms and perioperative areas may include label printing to prevent mix-ups such as errors between morphine and hydromorphone, two different opioid analgesics that frequently get confused. These systems also communicate with the pharmacy and its information management system to track medications removed and support inventory replenishment. == Key features == ADCs are like automated teller machines whose specific technologies such as barcode scanning and clinical decision support can improve medication safety. Some have metal locking drawers for added security and some have automated single-dose dispensing to prevent the need for a blind count each time a controlled substance is accessed. Over the years, ADCs have been adapted to facilitate compliance with emerging regulatory requirements such as pharmacy review of medication orders and safe practice recommendations. ADCs incorporate advanced software and electronic interfaces to synthesize high-risk steps in the medication use process. These unit-based medication repositories provide computer-controlled storage, dispensation, tracking, and documentation of medication distribution in the resident care unit. Since automated dispensing cabinets are not located in the pharmacy, they are considered "decentralized" medication distribution systems. Instead, they can be found at the point of care on the resident care unit. Tracking of the stocking and distribution process can occur by interfacing the unit with a central pharmacy computer. These cabinets can also be interfaced with other external databases such as resident profiles, the facility's admission/discharge/transfer system, and billing systems. Most ADC providers offer scalable systems since several important factors vary widely by facility such as budget, physical room size, patient population/demographics, type of healthcare facility, etc.
Aseprite
Aseprite ( ace-prite) is a proprietary, source-available image editor designed primarily for pixel art drawing and animation. It runs on Windows, macOS, and Linux, and features different tools for image and animation editing such as layers, frames, tilemap support, command-line interface, Lua scripting, among others. It is developed by Igara Studio S.A. and led by the developers David, Gaspar, and Martín Capello. Aseprite can be downloaded as freeware, (albeit it does not have the ability to save sprites) or purchased on Steam or Itch.io. Aseprite source code and binaries are distributed under EULA, educational, and Steam proprietary licenses. == History == Aseprite, formerly known as Allegro Sprite Editor, had its first release in 2001 as a free software project under the GPLv2 license. This license was kept until August 2016 with version v1.1.8, when the developers switched to a EULA, thus making the software proprietary. On the 1st of September 2016, the main developer, David Capello, wrote a post on the Aseprite Devblog explaining this change. The EULA permits others to download the Aseprite source code, compile it, and use it for personal purposes, but forbids its redistribution to third parties. After the license change, LibreSprite, a free and open source version of it, was created. Both before and after the license change, Aseprite was sold online, on Steam, itch.io, and the project's website. The project's code repository was hosted on Google Code until August 2014, when it was migrated to GitHub, where it remains hosted to date. As of October 2022, its repository has had 68 contributors and around 19 thousand stars. From 2014 to 2021, Aseprite had 66 different releases. Aseprite was used in the development of several notable games such as TowerFall (2013), Celeste (2018), Minit (2018), Wargroove (2019), Loop Hero (2021), Eastward (2021), Unpacking (2021), Haiku the Robot (2022) and Pizza Tower (2023). == Design and features == The main design purpose of Aseprite is to create animated 2D pixel-art sprites. Some of its features include: Layers and frames, with layer grouping and animation tagging Pixel-art specific transformations and tools (pixel-perfect modes, custom brushes, etc.) Animation real-time preview and onion skinning Tilemap and tileset modes Color palette managing, including 65 default palettes Color profiles and modes (RGBA, indexed and grayscale) Non-square pixels Command line interface (CLI) and Lua scripting Aseprite uses its own binary file type to store data, which is typically saved with .ase or .aseprite extensions. Different third-party projects were developed to support parsing of .ase files in programming languages including C#, Python and JavaScript, and in game engines such as Unity and Godot. Images and animations can be exported to different file formats including PNG, GIF, FLC, FLI, JPEG, PCX, TGA, ICO, SVG, and bitmap (BMP).
Ordered dithering
Ordered dithering is any image dithering algorithm which uses a pre-set threshold map tiled across an image. It is commonly used to display a continuous image on a display of smaller color depth. For example, Microsoft Windows uses it in 16-color graphics modes. With the most common "Bayer" threshold map, the algorithm is characterized by noticeable crosshatch patterns in the result. == Threshold map == The algorithm reduces the number of colors by applying a threshold map M to the pixels displayed, causing some pixels to change color, depending on the distance of the original color from the available color entries in the reduced palette. The first threshold maps were designed by hand to minimise the perceptual difference between a grayscale image and its two-bit quantisation for up to a 4x4 matrix. An optimal threshold matrix is one that for any possible quantisation of color has the minimum possible texture so that the greatest impression of the underlying feature comes from the image being quantised. It can be proven that for matrices whose side length is a power of two there is an optimal threshold matrix. The map may be rotated or mirrored without affecting the effectiveness of the algorithm. This threshold map (for sides with length as power of two) is also known as a Bayer matrix or, when unscaled, an index matrix. For threshold maps whose dimensions are a power of two, the map can be generated recursively via: M 2 n = 1 ( 2 n ) 2 [ 4 M n 4 M n + 2 J n 4 M n + 3 J n 4 M n + J n ] = J 2 ⊗ M n + 1 n 2 M 2 ⊗ J n , {\displaystyle \mathbf {M} _{2n}={\frac {1}{(2n)^{2}}}{\begin{bmatrix}4\mathbf {M} _{n}&4\mathbf {M} _{n}+2\mathbf {J} _{n}\\4\mathbf {M} _{n}+3\mathbf {J} _{n}&4\mathbf {M} _{n}+\mathbf {J} _{n}\end{bmatrix}}=\mathbf {J} _{2}\otimes \mathbf {M} _{n}+{\frac {1}{n^{2}}}\mathbf {M} _{2}\otimes \mathbf {J} _{n},} where J n {\displaystyle \mathbf {J} _{n}} are n × n {\displaystyle n\times n} matrices of ones and ⊗ {\displaystyle \otimes } is the Kronecker product. While the metric for texture that Bayer proposed could be used to find optimal matrices for sizes that are not a power of two, such matrices are uncommon as no simple formula for finding them exists, and relatively small matrix sizes frequently give excellent practical results (especially when combined with other modifications to the dithering algorithm). This function can also be expressed using only bit arithmetic: M(i, j) = bit_reverse(bit_interleave(bitwise_xor(i, j), i)) / n ^ 2 == Pre-calculated threshold maps == Rather than storing the threshold map as a matrix of n {\displaystyle n} × n {\displaystyle n} integers from 0 to n 2 {\displaystyle n^{2}} , depending on the exact hardware used to perform the dithering, it may be beneficial to pre-calculate the thresholds of the map into a floating point format, rather than the traditional integer matrix format shown above. For this, the following formula can be used: Mpre(i,j) = Mint(i,j) / n^2 This generates a standard threshold matrix. for the 2×2 map: this creates the pre-calculated map: Additionally, normalizing the values to average out their sum to 0 (as done in the dithering algorithm shown below) can be done during pre-processing as well by subtracting 1⁄2 of the largest value from every value: Mpre(i,j) = Mint(i,j) / n^2 – 0.5 maxValue creating the pre-calculated map: == Algorithm == The ordered dithering algorithm renders the image normally, but for each pixel, it offsets its color value with a corresponding value from the threshold map according to its location, causing the pixel's value to be quantized to a different color if it exceeds the threshold. For most dithering purposes, it is sufficient to simply add the threshold value to every pixel (without performing normalization by subtracting 1⁄2), or equivalently, to compare the pixel's value to the threshold: if the brightness value of a pixel is less than the number in the corresponding cell of the matrix, plot that pixel black, otherwise, plot it white. This lack of normalization slightly increases the average brightness of the image, and causes almost-white pixels to not be dithered. This is not a problem when using a gray scale palette (or any palette where the relative color distances are (nearly) constant), and it is often even desired, since the human eye perceives differences in darker colors more accurately than lighter ones, however, it produces incorrect results especially when using a small or arbitrary palette, so proper normalization should be preferred. In other words, the algorithm performs the following transformation on each color c of every pixel: c ′ = n e a r e s t _ p a l e t t e _ c o l o r ( c + r × ( M ( x mod n , y mod n ) − 1 / 2 ) ) {\displaystyle c'=\mathrm {nearest\_palette\_color} {\mathopen {}}\left(c+r\times \left(M(x{\bmod {n}},y{\bmod {n}})-1/2\right){\mathclose {}}\right)} where M(i, j) is the threshold map on the i-th row and j-th column, c′ is the transformed color, and r is the amount of spread in color space. Assuming an RGB palette with 23N evenly distanced colors where each color (a triple of red, green and blue values) is represented by an octet from 0 to 255, one would typically choose r ≈ 255 N {\textstyle r\approx {\frac {255}{N}}} . (1⁄2 is again the normalizing term.) Because the algorithm operates on single pixels and has no conditional statements, it is very fast and suitable for real-time transformations. Additionally, because the location of the dithering patterns always stays the same relative to the display frame, it is less prone to jitter than error-diffusion methods, making it suitable for animations. Because the patterns are more repetitive than error-diffusion method, an image with ordered dithering compresses better. Ordered dithering is more suitable for line-art graphics as it will result in straighter lines and fewer anomalies. The values read from the threshold map should preferably scale into the same range as the minimal difference between distinct colors in the target palette. Equivalently, the size of the map selected should be equal to or larger than the ratio of source colors to target colors. For example, when quantizing a 24 bpp image to 15 bpp (256 colors per channel to 32 colors per channel), the smallest map one would choose would be 4×2, for the ratio of 8 (256:32). This allows expressing each distinct tone of the input with different dithering patterns. === A variable palette: pattern dithering === == Non-Bayer approaches == The above thresholding matrix approach describes the Bayer family of ordered dithering algorithms. A number of other algorithms are also known; they generally involve changes in the threshold matrix, which changes the distribution of the "noise" introduced by all kinds of dithering (the difference between the original image and the dithered image). === Halftone === Halftone dithering performs a form of clustered dithering, creating a look similar to halftone patterns, using a specially crafted matrix. === Void and cluster === The Void and cluster algorithm uses a pre-generated blue noise as the matrix for the dithering process. The blue noise matrix keeps the Bayer's good high frequency content, but with a more uniform coverage of all the frequencies involved shows a much lower amount of patterning. The "voids-and-cluster" method gets its name from the matrix generation procedure, where a black image with randomly initialized white pixels is gaussian-blurred to find the brightest and darkest parts, corresponding to voids and clusters. After a few swaps have evenly distributed the bright and dark parts, the pixels are numbered by importance. It takes significant computational resources to generate the blue noise matrix: on a modern computer a 64×64 matrix requires a couple seconds using the original algorithm. This algorithm can be extended to make animated dither masks which also consider the axis of time. This is done by running the algorithm in three dimensions and using a kernel which is a product of a two-dimensional gaussian kernel on the XY plane, and a one-dimensional Gaussian kernel on the Z axis. === Simulated Annealing === Simulated annealing can generate dither masks by starting with a flat histogram and swapping values to optimize a loss function. The loss function controls the spectral properties of the mask, allowing it to make blue noise or noise patterns meant to be filtered by specific filters. The algorithm can also be extended over time for animated dither masks with chosen temporal properties.
Automatic acquisition of sense-tagged corpora
The knowledge acquisition bottleneck is perhaps the major impediment to solving the word-sense disambiguation (WSD) problem. Unsupervised learning methods rely on knowledge about word senses, which is barely formulated in dictionaries and lexical databases. Supervised learning methods depend heavily on the existence of manually annotated examples for every word sense, a requisite that can so far be met only for a handful of words for testing purposes, as it is done in the Senseval exercises. == Existing methods == Therefore, one of the most promising trends in WSD research is using the largest corpus ever accessible, the World Wide Web, to acquire lexical information automatically. WSD has been traditionally understood as an intermediate language engineering technology which could improve applications such as information retrieval (IR). In this case, however, the reverse is also true: Web search engines implement simple and robust IR techniques that can be successfully used when mining the Web for information to be employed in WSD. The most direct way of using the Web (and other corpora) to enhance WSD performance is the automatic acquisition of sense-tagged corpora, the fundamental resource to feed supervised WSD algorithms. Although this is far from being commonplace in the WSD literature, a number of different and effective strategies to achieve this goal have already been proposed. Some of these strategies are: acquisition by direct Web searching (searches for monosemous synonyms, hypernyms, hyponyms, parsed gloss' words, etc.), Yarowsky algorithm (bootstrapping), acquisition via Web directories, and acquisition via cross-language meaning evidences. == Summary == === Optimistic results === The automatic extraction of examples to train supervised learning algorithms reviewed has been, by far, the best explored approach to mine the web for word-sense disambiguation. Some results are certainly encouraging: In some experiments, the quality of the Web data for WSD equals that of human-tagged examples. This is the case of the monosemous relatives plus bootstrapping with Semcor seeds technique and the examples taken from the ODP Web directories. In the first case, however, Semcor-size example seeds are necessary (and only available for English), and it has only been tested with a very limited set of nouns; in the second case, the coverage is quite limited, and it is not yet clear whether it can be grown without compromising the quality of the examples retrieved. It has been shown that a mainstream supervised learning technique trained exclusively with web data can obtain better results than all unsupervised WSD systems which participated at Senseval-2. Web examples made a significant contribution to the best Senseval-2 English all-words system. === Difficulties === There are, however, several open research issues related to the use of Web examples in WSD: High precision in the retrieved examples (i.e., correct sense assignments for the examples) does not necessarily lead to good supervised WSD results (i.e., the examples are possibly not useful for training). The most complete evaluation of Web examples for supervised WSD indicates that learning with Web data improves over unsupervised techniques, but the results are nevertheless far from those obtained with hand-tagged data, and do not even beat the most-frequent-sense baseline. Results are not always reproducible; the same or similar techniques may lead to different results in different experiments. Compare, for instance, Mihalcea (2002) with Agirre and Martínez (2004), or Agirre and Martínez (2000) with Mihalcea and Moldovan (1999). Results with Web data seem to be very sensitive to small differences in the learning algorithm, to when the corpus was extracted (search engines change continuously), and on small heuristic issues (e.g., differences in filters to discard part of the retrieved examples). Results are strongly dependent on bias (i.e., on the relative frequencies of examples per word sense). It is unclear whether this is simply a problem of Web data, or an intrinsic problem of supervised learning techniques, or just a problem of how WSD systems are evaluated (indeed, testing with rather small Senseval data may overemphasize sense distributions compared to sense distributions obtained from the full Web as corpus). In any case, Web data has an intrinsic bias, because queries to search engines directly constrain the context of the examples retrieved. There are approaches that alleviate this problem, such as using several different seeds/queries per sense or assigning senses to Web directories and then scanning directories for examples; but this problem is nevertheless far from being solved. Once a Web corpus of examples is built, it is not entirely clear whether its distribution is safe from a legal perspective. === Future === Besides automatic acquisition of examples from the Web, there are some other WSD experiments that have profited from the Web: The Web as a social network has been successfully used for cooperative annotation of a corpus (OMWE, Open Mind Word Expert project), which has already been used in three Senseval-3 tasks (English, Romanian and Multilingual). The Web has been used to enrich WordNet senses with domain information: topic signatures and Web directories, which have in turn been successfully used for WSD. Also, some research benefited from the semantic information that the Wikipedia maintains on its disambiguation pages. It is clear, however, that most research opportunities remain largely unexplored. For instance, little is known about how to use lexical information extracted from the Web in knowledge-based WSD systems; and it is also hard to find systems that use Web-mined parallel corpora for WSD, even though there are already efficient algorithms that use parallel corpora in WSD.
Transfer function matrix
In control system theory, and various branches of engineering, a transfer function matrix, or just transfer matrix is a generalisation of the transfer functions of single-input single-output (SISO) systems to multiple-input and multiple-output (MIMO) systems. The matrix relates the outputs of the system to its inputs. It is a particularly useful construction for linear time-invariant (LTI) systems because it can be expressed in terms of the s-plane. In some systems, especially ones consisting entirely of passive components, it can be ambiguous which variables are inputs and which are outputs. In electrical engineering, a common scheme is to gather all the voltage variables on one side and all the current variables on the other regardless of which are inputs or outputs. This results in all the elements of the transfer matrix being in units of impedance. The concept of impedance (and hence impedance matrices) has been borrowed into other energy domains by analogy, especially mechanics and acoustics. Many control systems span several different energy domains. This requires transfer matrices with elements in mixed units. This is needed both to describe transducers that make connections between domains and to describe the system as a whole. If the matrix is to properly model energy flows in the system, compatible variables must be chosen to allow this. == General == A MIMO system with m outputs and n inputs is represented by a m × n matrix. Each entry in the matrix is in the form of a transfer function relating an output to an input. For example, for a three-input, two-output system, one might write, [ y 1 y 2 ] = [ g 11 g 12 g 13 g 21 g 22 g 23 ] [ u 1 u 2 u 3 ] {\displaystyle {\begin{bmatrix}y_{1}\\y_{2}\end{bmatrix}}={\begin{bmatrix}g_{11}&g_{12}&g_{13}\\g_{21}&g_{22}&g_{23}\end{bmatrix}}{\begin{bmatrix}u_{1}\\u_{2}\\u_{3}\end{bmatrix}}} where the un are the inputs, the ym are the outputs, and the gmn are the transfer functions. This may be written more succinctly in matrix operator notation as, Y = G U {\displaystyle \mathbf {Y} =\mathbf {G} \mathbf {U} } where Y is a column vector of the outputs, G is a matrix of the transfer functions, and U is a column vector of the inputs. In many cases, the system under consideration is a linear time-invariant (LTI) system. In such cases, it is convenient to express the transfer matrix in terms of the Laplace transform (in the case of continuous time variables) or the z-transform (in the case of discrete time variables) of the variables. This may be indicated by writing, for instance, Y ( s ) = G ( s ) U ( s ) {\displaystyle \mathbf {Y} (s)=\mathbf {G} (s)\mathbf {U} (s)} which indicates that the variables and matrix are in terms of s, the complex frequency variable of the s-plane arising from Laplace transforms, rather than time. The examples in this article are all assumed to be in this form, although that is not explicitly indicated for brevity. For discrete time systems s is replaced by z from the z-transform, but this makes no difference to subsequent analysis. The matrix is particularly useful when it is a proper rational matrix, that is, all its elements are proper rational functions. In this case, the state-space representation can be applied. In systems engineering, the overall system transfer matrix G (s) is decomposed into two parts: H (s) representing the system being controlled, and C(s) representing the control system. C (s) takes as its inputs the inputs of G (s) and the outputs of H (s). The outputs of C (s) form the inputs for H (s). == Electrical systems == In electrical systems, it is often the case that the distinction between input and output variables is ambiguous. They can be either, depending on circumstance and point of view. In such cases, the concept of port (a place where energy is transferred from one system to another) can be more useful than input and output. It is customary to define two variables for each port (p): the voltage across it (Vp) and the current entering it (Ip). For instance, the transfer matrix of a two-port network can be defined as follows, [ V 1 V 2 ] = [ z 11 z 12 z 21 z 22 ] [ I 1 I 2 ] {\displaystyle {\begin{bmatrix}V_{1}\\V_{2}\end{bmatrix}}={\begin{bmatrix}z_{11}&z_{12}\\z_{21}&z_{22}\\\end{bmatrix}}{\begin{bmatrix}I_{1}\\I_{2}\end{bmatrix}}} where the zmn are called the impedance parameters, or z-parameters. They are so-called because they are in units of impedance and relate port currents to a port voltage. The z-parameters are not the only way that transfer matrices are defined for two-port networks. Six basic matrices relate voltages and currents, each with advantages for particular system network topologies. However, only two of these can be extended beyond two ports to an arbitrary number of ports. These two are the z-parameters and their inverse, the admittance parameters or y-parameters. To understand the relationship between port voltages and currents and inputs and outputs, consider the simple voltage divider circuit. If we only wish to consider the output voltage (V2) resulting from applying the input voltage (V1) then the transfer function can be expressed as, [ V 2 ] = [ R 2 R 1 + R 2 ] [ V 1 ] {\displaystyle {\begin{bmatrix}V_{2}\end{bmatrix}}={\begin{bmatrix}{\dfrac {R_{2}}{R_{1}+R_{2}}}\end{bmatrix}}{\begin{bmatrix}V_{1}\end{bmatrix}}} which can be considered the trivial case of a 1×1 transfer matrix. The expression correctly predicts the output voltage if there is no current leaving port 2, but is increasingly inaccurate as the load increases. If, however, we attempt to use the circuit in reverse, driving it with a voltage at port 2 and calculate the resulting voltage at port 1 the expression gives completely the wrong result even with no load on port 1. It predicts a greater voltage at port 1 than was applied at port 2, an impossibility with a purely resistive circuit like this one. To correctly predict the behaviour of the circuit, the currents entering or leaving the ports must also be taken into account, which is what the transfer matrix does. The impedance matrix for the voltage divider circuit is, [ V 1 V 2 ] = [ R 1 + R 2 R 2 R 2 R 2 ] [ I 1 I 2 ] {\displaystyle {\begin{bmatrix}V_{1}\\V_{2}\end{bmatrix}}={\begin{bmatrix}R_{1}+R_{2}&R_{2}\\R_{2}&R_{2}\end{bmatrix}}{\begin{bmatrix}I_{1}\\I_{2}\end{bmatrix}}} which fully describes its behaviour under all input and output conditions. At microwave frequencies, none of the transfer matrices based on port voltages and currents are convenient to use in practice. Voltage is difficult to measure directly, current next to impossible, and the open circuits and short circuits required by the measurement technique cannot be achieved with any accuracy. For waveguide implementations, circuit voltage and current are entirely meaningless. Transfer matrices using different sorts of variables are used instead. These are the powers transmitted into, and reflected from a port, which are readily measured in the transmission line technology used in distributed-element circuits in the microwave band. The most well-known and widely used of these sorts of parameters is the scattering parameters, or s-parameters. == Mechanical and other systems == The concept of impedance can be extended into the mechanical and other domains through a mechanical-electrical analogy, hence the impedance parameters and other forms of 2-port network parameters can also be extended to the mechanical domain. To do this, an effort variable and a flow variable are made analogues of voltage and current, respectively. For mechanical systems under translation these variables are force and velocity respectively. Expressing the behaviour of a mechanical component as a two-port or multi-port with a transfer matrix is a useful thing to do because, like electrical circuits, the component can often be operated in reverse and its behaviour is dependent on the loads at the inputs and outputs. For instance, a gear train is often characterised simply by its gear ratio, a SISO transfer function. However, the gearbox output shaft can be driven around to turn the input shaft, requiring a MIMO analysis. In this example, the effort and flow variables are torque T and angular velocity ω, respectively. The transfer matrix in terms of z-parameters will look like, [ T 1 T 2 ] = [ z 11 z 12 z 21 z 22 ] [ ω 1 ω 2 ] {\displaystyle {\begin{bmatrix}T_{1}\\T_{2}\end{bmatrix}}={\begin{bmatrix}z_{11}&z_{12}\\z_{21}&z_{22}\end{bmatrix}}{\begin{bmatrix}\omega _{1}\\\omega _{2}\end{bmatrix}}} However, the z-parameters are not necessarily the most convenient for characterising gear trains. A gear train is the analogue of an electrical transformer and the h-parameters (hybrid parameters) better describe transformers because they directly include the turns ratios (the analogue of gear ratios). The gearbox transfer matrix in h-parameter format is, [ T 1 ω 2 ] = [ h 11 h 12 h 21 h 22 ] [ ω 1 T 2 ] {\displaystyle {\begin{bmatrix}T_{1}\\\omega _{2}\end{bm