Carrenza was a cloud-computing company based in London, United Kingdom. The company was acquired by Six Degrees Technology Group in 2016. == Operations == Carrenza was a UK-based IT company that provides Cloud computing technologies. It offered a range of public cloud, private cloud and hybrid cloud services, including Infrastructure as a Service (IaaS), Platform as a Service (PaaS), enterprise application integration and system integration. Carrenza partnered with several enterprise IT providers and was an accredited VMware Enterprise Service Partner and HP (Hewlett-Packard) Cloud Agile Partner. The company was based on Commercial Street, in the heart of the East London Tech City district, which is host to a large number of technology companies. == History == Carrenza was formed in 2001 as a consultancy by chief executive and founder Dan Sutherland. It began trading in 2004 and launched its first enterprise cloud computing platform in 2006, becoming one of the first companies in Europe to provide this type of hosting service. In 2009, it formed a partnership with Comic Relief and its affiliated campaigns Red Nose Day Sport Relief to provide IT infrastructure services to the charity, an arrangement that has won industry recognition. In 2013 it launched its first overseas services, with a mainland Europe cloud node based in Amsterdam. == Partnerships and customers == Carrenza had formed partnerships with a range of IT providers. It was one of the first companies in Europe to become a HP Cloud Agile partner., using HP blade servers and HP 3PAR SAN technology to power its cloud computing services. The company's products also use VMware vCloud IaaS tools and it is taking part in the VMware lighthouse initiative helping develop the next generation of VMware products and services. Other technology companies that Carrenza has worked closely with include Cisco, for enterprise security and loadblancing services, and Oracle. The company was the first to deploy Oracle Database 11g stretched RAC in production. It has also won two Oracle partner awards, including a Special Recognition award for its work with Comic Relief. The company has also been recognised by the UK IT Industry, receiving awards in 2009 for Community Project of the Year and in 2010 for best small business project for its Monopoly City Streets Work. Other companies that have partnered with Carrenza for their cloud-based IT services include Age UK, Haymarket Media Group, the World Wide Fund for Nature, Royal Bank of Scotland, eBay and Cineworld. == Accreditations == Carrenza's services are accredited for their compliance with several key international IT security and quality standards. These include: ISO27001:2005, Information Security Management System for all Carrenza services. UK Government G-Cloud, Carrenza has been awarded a place on the UK government's G-Cloud iii framework as an Infrastructure as a Service provider.
Firefox Lockwise
Firefox Lockwise (formerly Lockbox) is a deprecated password manager for the Firefox web browser, as well as the mobile operating systems iOS and Android. On desktop, Lockwise was simply part of Firefox, whereas on iOS and Android it was available as a standalone app. If Firefox Sync was activated (with a Firefox account), then Lockwise synced passwords between Firefox installations across devices. It also featured a built-in random password generator. The application and branding have since been "phased out." == History == Developed by Mozilla, it was originally named Firefox Lockbox in 2018. It was renamed "Lockwise" in May 2019. It was introduced for iOS on 10 July 2018 as part of the Test Pilot program. On 26 March 2019, it was released for Android. On desktop, Lockwise started out as a browser addon. Alphas were released between March and August 2019. Since Firefox version 70, Lockwise has been integrated into the browser (accessible at about:logins), having replaced a basic password manager presented in a popup window. Mozilla ended support for Firefox Lockwise on December 13, 2021. As of January 2026, Lockwise is still fully functional on Android to this day.
PenTile matrix family
PenTile matrix is a family of patented subpixel matrix schemes used in electronic device displays. PenTile is a trademark of Samsung. PenTile matrices are used in AMOLED and LCD displays. These subpixel layouts are specifically designed to operate with proprietary algorithms for subpixel rendering embedded in the display driver, allowing plug and play compatibility with conventional RGB (Red-Green-Blue) stripe panels. == Overview == "PenTile Matrix" (a neologism from penta-, meaning "five" in Greek and tile) describes the geometric layout of the prototypical subpixel arrangement developed in the early 1990s. The layout consists of a quincunx comprising two red subpixels, two green subpixels, and one central blue subpixel in each unit cell. It was inspired by biomimicry of the human retina, which has nearly equal numbers of L and M type cone cells, but significantly fewer S cones. As the S cones are primarily responsible for perceiving blue colors, which do not appreciably affect the perception of luminance, reducing the number of blue subpixels with respect to the red and green subpixels in a display does not reduce the image quality. However, the layout may cause color leakage image distortion, which can be reduced by filters. In some cases the layout causes reduced moiré and blockiness compared to conventional RGB layouts. The PenTile layout is specifically designed to work with and be dependent upon subpixel rendering that uses only one and a quarter subpixel per pixel, on average, to render an image. That is, that any given input pixel is mapped to either a red-centered logical pixel, or a green-centered logical pixel. === History === PenTile was invented by Candice H. Brown Elliott, for which she was awarded the Society for Information Display's Otto Schade Prize in 2014. The technology was licensed by the company Clairvoyante from 2000 until 2008, during which time several prototype PenTile displays were developed by a number of Asian liquid crystal display (LCD) manufacturers. In March 2008, Samsung Electronics acquired Clairvoyante's PenTile IP assets. Samsung then funded a new company, Nouvoyance, Inc. to continue development of the PenTile technology. == PenTile RGBG == PenTile RGBG layout used in AMOLED and plasma displays uses green pixels interleaved with alternating red and blue pixels. The human eye is most sensitive to green, especially for high resolution luminance information. The green subpixels are mapped to input pixels on a one-to-one basis. The red and blue subpixels are subsampled, reconstructing the chroma signal at a lower resolution. The luminance signal is processed using adaptive subpixel rendering filters to optimize reconstruction of high spatial frequencies from the input image, wherein the green subpixels provide the majority of the reconstruction. The red and blue subpixels are capable of reconstructing the horizontal and vertical spatial frequencies, but not the highest of the diagonal. Diagonal high spatial frequency information in the red and blue channels of the input image are transferred to the green subpixels for image reconstruction. Thus the RG-BG scheme creates a color display with one third fewer subpixels than a traditional RGB-RGB scheme but with the same measured luminance display resolution. This is similar to the Bayer filter commonly used in digital cameras. === Devices === As of 2021, "almost all" OLED screens in portable consumer devices use some form of Pentile subpixel layout. == PenTile RGBW == PenTile RGBW technology, used in LCD, adds an extra subpixel to the traditional red, green and blue subpixels that is a clear area without color filtering material and with the only purpose of letting backlight come through, hence W for white. This makes it possible to produce a brighter image compared to an RGB-matrix while using the same amount of power, or produce an equally bright image while using less power. The PenTile RGBW layout uses each red, green, blue and white subpixel to present high-resolution luminance information to the human eyes' red-sensing and green-sensing cone cells, while using the combined effect of all the color subpixels to present lower-resolution chroma (color) information to all three cone cell types. Combined, this optimizes the match of display technology to the biological mechanisms of human vision. The layout uses one third fewer subpixels for the same resolution as the RGB stripe (RGB-RGB) layout, in spite of having four color primaries instead of the conventional three, using subpixel rendering combined with metamer rendering. Metamer rendering optimizes the energy distribution between the white subpixel and the combined red, green, and blue subpixels: W <> RGB, to improve image sharpness. The display driver chip has an RGB to RGBW color vector space converter and gamut mapping algorithm, followed by metamer and subpixel rendering algorithms. In order to maintain saturated color quality, to avoid simultaneous contrast error between saturated colors and peak white brightness, while simultaneously reducing backlight power requirements, the display backlight brightness is under control of the PenTile driver engine. When the image is mostly desaturated colors, those near white or grey, the backlight brightness is significantly reduced, often to less than 50% peak, while the LCD levels are increased to compensate. When the image has very bright saturated colors, the backlight brightness is maintained at higher levels. The PenTile RGBW also has an optional high-brightness mode that doubles the brightness of the desaturated color image areas, such as black-and-white text, for improved outdoor viewability. === Devices === Motorola MC65 Motorola ES55 Motorola ES400 Motorola Atrix 4G Samsung Galaxy Note 10.1 2014 version Lenovo Yoga 2 Pro Lenovo Yoga 3 Pro HP ENVY TouchSmart 14-k022tx Sleekbook MSI GS60 Ghost Pro 4K Lenovo IdeaPad Y50 4K Asus ZenBook UX303LN 4K Asus ZenBook Pro UX501JW LG UH7500/6500/6100 LG ThinQ G7/G7+ Oculus Quest 1 == Controversy == An ongoing controversy regarding the definition or measurement of resolution of color subpixelated flat panel displays led many people to question the resolution claims of PenTile display products. Journalists have noted that in "just about every flat-panel TV in existence, each pixel is composed of one red, one green, and one blue subpixel (RGB), all of uniform size". In traditional flat-panel screens, the resolution is defined by the number of red, green, and blue subpixels, in groups of three, in an array in each axis. As a result, each pixel or group of subpixels can render any colour on the screen, regardless of neighbouring pixels. This is not the case with PenTile screens. The Video Electronics Standards Association (VESA) method of measuring and defining resolution in color displays is to measure the contrast of line pairs, requiring a minimum of 50% Michelson contrast for displays intended for rendering text. The developers of PenTile displays use this VESA criterion for contrast of line pairs to calculate the resolutions specified. In the RGBG layout the alternate red and blue subpixels are 'shared' or sub-sampled with neighboring pixels. Due to the one third lower subpixel density on PenTile displays the pixel structure may be more visible when compared to RGB stripe displays with the same pixel density. The loss of subpixels for a given resolution specification has led some journalists to describe the use of PenTile as "shady practice" and "sort of cheating". For a given size and resolution specification, the PenTile screen can appear grainy, pixelated, speckled, with blurred text on some saturated colors and backgrounds when compared to RGB stripe color. This effect is understood to be caused by the restriction of the number of subpixels that may participate in the image reconstruction when colors are highly saturated to primaries. In the RGBW case, this is caused as the W subpixel will not be available in order to maintain the saturated color. In the RGBG case, this effect will occur when the color boundary is primarily red or blue, as the fully populated (one green per pixel) sub-pixel cannot contribute. For all other cases, text and especially full color images are effectively reconstructed. == Advantages and disadvantages == The PenTile layout reduces the number of subpixels needed to create a specified resolution. Consequently it is possible to achieve an HD resolution on a PenTile AMOLED screen at lower cost than other technologies, and most reviewers note that "300 ppi" (as per VESA - not full pixels) resolution displays (such as Samsung Galaxy S III) make the PenTile effect less obvious than lower resolution PenTile displays (Droid Razr). The second advantage is lower power consumption: the HTC One S's use of a PenTile display makes it more energy efficient and thinner than equivalent LCD screens, giving it better battery life than the HTC One X's IPS LCD. A PenTile AMOLED screen is also
National Cyber Security Policy 2013
National Cyber Security Policy is a policy framework by Department of Electronics and Information Technology (DeitY) It aims at protecting the public and private infrastructure from cyber attacks. The policy also intends to safeguard "information, such as personal information (of web users), financial and banking information and sovereign data". This was particularly relevant in the wake of US National Security Agency (NSA) leaks that suggested the US government agencies are spying on Indian users, who have no legal or technical safeguards against it. Ministry of Communications and Information Technology (India) defines Cyberspace as a complex environment consisting of interactions between people, software services supported by worldwide distribution of information and communication technology. == Reason for Cyber Security policies == India had no Cyber security policy before 2013. In 2013, The Hindu newspaper, citing documents leaked by NSA whistle-blower Edward Snowden, has alleged that much of the NSA surveillance was focused on India's domestic politics and its strategic and commercial interests. This sparked a furore among people. Under pressure, the government unveiled a National Cyber Security Policy 2013 on 2 July 2013. == Vision == To build a secure and resilient cyberspace for citizens, business, and government and also to protect anyone from intervening in user's privacy.It mentioned a five year target of training five lakh cyber security personnel by 2018. == Mission == To protect information and information infrastructure in cyberspace, build capabilities to prevent and respond to cyber threat, reduce vulnerabilities and minimize damage from cyber incidents through a combination of institutional structures, people, processes, technology, and cooperation. == Objective == Ministry of Communications and Information Technology (India) define objectives as follows: To create a secure cyber ecosystem in the country, generate adequate trust and confidence in IT system and transactions in cyberspace and thereby enhance adoption of IT in all sectors of the economy. To create an assurance framework for the design of security policies and promotion and enabling actions for compliance to global security standards and best practices by way of conformity assessment (Product, process, technology & people). To strengthen the Regulatory Framework for ensuring a SECURE CYBERSPACE ECOSYSTEM. To enhance and create National and Sectoral level 24x7 mechanism for obtaining strategic information regarding threats to ICT infrastructure, creating scenarios for response, resolution and crisis management through effective predictive, preventive, protective response and recovery actions. -To improve visibility of integrity of ICT products and services by establishing infrastructure for testing & validation of security of such product. To create workforce for 500,000 professionals skilled in next 5 years through capacity building skill development and training. To provide fiscal benefit to businesses for adoption of standard security practices and processes. To enable Protection of information while in process, handling, storage & transit so as to safeguard privacy of citizen's data and reducing economic losses due to cyber crime or data theft. To enable effective prevention, investigation and prosecution of cybercrime and enhancement of law enforcement capabilities through appropriate legislative intervention. == Strategies == Creating a secured Ecosystem. Creating an assurance framework. Encouraging Open Standards. Strengthening The regulatory Framework. Creating a mechanism for Security Threats Early Warning, Vulnerability management, and response to security threats. Securing E-Governance services. Protection and resilience of Critical Information Infrastructure. Promotion of Research and Development in cyber security. Reducing supply chain risks Human Resource Development (fostering education and training programs both in formal and informal sectors to Support the Nation's cyber security needs and build capacity. Creating cyber security awareness. Developing effective Public-Private partnerships. To develop bilateral and multilateral relationships in the area of cyber security with another country. (Information sharing and cooperation) a Prioritized approach for implementation.
Medical data breach
Medical data, including patients' identity information, health status, disease diagnosis and treatment, and biogenetic information, not only involve patients' privacy but also have a special sensitivity and important value, which may bring physical and mental distress and property loss to patients and even negatively affect social stability and national security once leaked. However, the development and application of medical AI must rely on a large amount of medical data for algorithm training, and the larger and more diverse the amount of data, the more accurate the results of its analysis and prediction will be. However, the application of big data technologies such as data collection, analysis and processing, cloud storage, and information sharing has increased the risk of data leakage. In the United States, the rate of such breaches has increased over time, with 176 million records breached by the end of 2017. By 2024, the U.S. Department of Health and Human Services reported 725 large healthcare data breaches affecting approximately 275 million individual records in a single year, marking a significant escalation in both the frequency and scale of incidents. == Black market for health data == In February 2015 an NPR report claimed that organized crime networks had ways of selling health data in the black market. In 2015 a Beazley employee estimated that medical records could sell on the black market for US$40-50. == How data is lost == Theft, data loss, hacking, and unauthorized account access are ways in which medical data breaches happen. Among reported breaches of medical information in the United States networked information systems accounted for the largest number of records breached. There are many data breaches happening in the US health care system, among business associates of the health care providers that continuously gain access to patients' data. == List of data breaches == In February 2024, a ransomware attack on Change Healthcare, a subsidiary of UnitedHealth Group, compromised the protected health information of approximately 100 million individuals, making it the largest healthcare data breach in United States history. The attack disrupted claims processing for healthcare providers nationwide for several weeks. In May 2024, MediSecure suffered a cyberattack involving ransomware in Australia. In May 2021, the Health Service Executive in the Republic of Ireland was the victim of a cyberattack involving ransomware, in the Health Service Executive cyberattack, with admission records and test results present in a sample of the data reviewed by the Financial Times. In October 2018, the Centers for Medicare and Medicaid Services in the US reported that around 75,000 individual records had been affected by a data breach that took place through the ACA Agent and Broker Portal. In 2018, Social Indicators Research published the scientific evidence of 173,398,820 (over 173 million) individuals affected in USA from October 2008 (when the data were collected) to September 2017 (when the statistical analysis took place). In 2015, Anthem Inc. lost data for 37 million people in the Anthem medical data breach In 2014 4.5 million people using Complete Health Systems had their data stolen In 2013-14 1 million people using Montana Department of Public Health and Human Services had their data stolen In 2013 4 million people using Advocate Health and Hospitals Corporation had their data stolen In 2011 4.9 million users of Tricare services had their data stolen due to an employee error by Science Applications International Corporation In 2011 1.9 million people using Health Net had their data stolen In 2011 1 million people using Nemours Foundation had their data stolen In 2010 6800 people using New York-Presbyterian Hospital and Columbia University Medical Center had their data breached. In response, those organizations agreed to pay the United States Department of Health and Human Services a US$4.8 million dollar fine. In 2009 1 million people using BlueCross BlueShield of Tennessee had their data stolen == Regulation == In the United States, the Health Insurance Portability and Accountability Act and Health Information Technology for Economic and Clinical Health Act require companies to report data breaches to affected individuals and the federal government. Under the HIPAA Breach Notification Rule, covered entities must notify affected individuals without unreasonable delay and no later than 60 days after discovering a breach of unsecured protected health information. Breaches affecting 500 or more individuals must also be reported to the HHS Secretary and to prominent media outlets serving the affected state or jurisdiction within the same timeframe; HHS publicly lists these larger breaches on its breach portal, commonly known as the "wall of shame." Breaches affecting fewer than 500 individuals are reported to HHS annually, no later than 60 days after the end of the calendar year in which they were discovered. Health Information Privacy Health Insurance Portability and Accountability Act of 1996 (HIPAA). - 45 CFR Parts 160 and 164, Standards for Privacy of Individually Identifiable Health Information and Security Standards for the Protection of Electronic Protected Health Information. HIPAA includes provisions designed to save health care businesses money by encouraging electronic transactions, as well as regulations to protect the security and confidentiality of patient information. The Privacy Rule became effective April 14, 2001, and most covered entities (health plans, health care clearinghouses, and health care providers that conduct certain financial and administrative transactions electronically) had until April 2003 to comply. This security provision became effective April 21, 2003. The Health Insurance Portability and Accountability Act (HIPAA) is the baseline set of federal regulations governing medical information. It does three things: i. i. i.Establish a structure for how personal health information is disclosed and establish the rights of individuals with respect to health information; ii.Specify security standards for the retention and transmission of electronic patient information; iii.Need a common format and data structure for the electronic exchange of health information. California-Specific Laws California’s medical privacy laws, primarily the Confidentiality of Medical Information Act (CMIA), the data breach sections of the Civil Code, and sections of the Health and Safety Code, provide HIPAA-like protections, although the terminology is different. HIPAA establishes a federal "minimum standard" that applies where there are gaps in California law, and HIPAA also specifies that stricter state laws will override or supersede HIPAA. California's health care privacy laws apply to providers who provide personal health records (PHR), while HIPAA only applies when the provider providing the PHR is a business associate of a covered entity. Federal law does not grant individuals the right to file a lawsuit in the event of a data breach (only the Attorney General can file a lawsuit), but California law does. This means that California law sets a higher standard for medical privacy, and that individuals in California enjoy stronger legal protections and more ways to hold entities that violate their medical privacy accountable. In the UK, the legal framework for how patient data is cared for and processed is the Data Protection Act 2018 (DPA), which incorporates the EU General Data Protection Regulation (GDPR) into law, and the common law duty of confidentiality (CLDC). The data protection legislation requires that the collection and processing of personal data be fair, lawful and transparent. This means that the collection and processing of data as defined by data protection legislation must always have a valid lawful basis and must also meet the requirements of the CLDC. In the China, Article 18 of the "National Health Care Big Data Standards, Security and Services Management Measures (for Trial Implementation)" (National Health Planning and Development (2018) No. 23) promulgated by the National Health Care Commission in 2018 states, "The responsible unit shall adopt measures such as data classification, important data backup, and encryption authentication to guarantee the security of health care big data." However, the scope and definition of important data are not covered. Although the "Information Security Technology-Healthcare Data Security Guide" (the "Guide") issued by the National Standardization Committee also proposes that important data should be evaluated and approved in accordance with the regulations, there is likewise no definition of the connotation and definition of important data.
Intrinsic dimension
In mathematics, the intrinsic dimension of a subset can be thought of as the minimal number of variables needed to represent the subset. The concept has widespread applications in geometry, dynamical systems, signal processing, statistics, and other fields. Due to its widespread applications and vague conceptualization, there are many different ways to define it rigorously. Consequently, the same set might have different intrinsic dimensions according to different definitions. The intrinsic dimension can be used as a lower bound of what dimension it is possible to compress a data set into through dimension reduction, but it can also be used as a measure of the complexity of the data set or signal. For a data set or signal of N variables, its intrinsic dimension M satisfies 0 ≤ M ≤ N, although estimators may yield higher values. == Exact dimension == === Differential === In differential geometry, given a differentiable manifold N and a submanifold M, the intrinsic dimension of M is its dimension. Suppose N has n dimensions and M has m dimensions, then that means around any point in M, there exists a local coordinate system ( x 1 , … , x m , x m + 1 , … , x n ) {\displaystyle (x_{1},\dots ,x_{m},x_{m+1},\dots ,x_{n})} of N, such that the manifold M is simply the subset of N defined by x m + 1 = 0 , … , x n = 0 {\displaystyle x_{m+1}=0,\dots ,x_{n}=0} . === Metric === Given a mere metric space, we can still define its intrinsic dimension. The most general case is the Hausdorff dimension, though for metric spaces occurring in practice, the box-counting dimension and the packing dimension often are identical to the Hausdorff dimension. Let X , d {\textstyle X,d} be a metric space and A ⊂ X {\textstyle A\subset X} be totally bounded. Define the covering number N ( A , ε ) = min { k : A ⊂ ⋃ i = 1 k B ( x i , ε ) } . {\displaystyle N(A,\varepsilon )=\min \left\{k:A\subset \bigcup _{i=1}^{k}B\left(x_{i},\varepsilon \right)\right\}.} The metric entropy is H ( A , ε ) = log N ( A , ε ) {\textstyle H(A,\varepsilon )=\log N(A,\varepsilon )} (any log base). The upper and lower metric entropy dimensions are dim ¯ E A = lim sup ε ↓ 0 H ( A , ε ) log ( 1 / ε ) , dim _ E A = lim inf ε ↓ 0 H ( A , ε ) log ( 1 / ε ) . {\displaystyle {\overline {\dim }}_{E}A=\limsup _{\varepsilon \downarrow 0}{\frac {H(A,\varepsilon )}{\log(1/\varepsilon )}},\quad {\underline {\dim }}_{E}A=\liminf _{\varepsilon \downarrow 0}{\frac {H(A,\varepsilon )}{\log(1/\varepsilon )}}.} If they are equal, then dim E A {\textstyle \operatorname {dim} _{E}A} is that common value, called the metric entropy dimension. The entropy dimensions are usually used in information theory, and especially coding theory, since entropy is involved in its definition. === Topological === If X {\displaystyle X} is merely a topological space, then we can still define its intrinsic dimension, using the topological dimension or Lebesgue covering dimension. An open cover of a topological space X is a family of open sets Uα such that their union is the whole space, ∪ α {\displaystyle \cup _{\alpha }} Uα = X. The order or ply of an open cover A {\displaystyle {\mathfrak {A}}} = {Uα} is the smallest number m (if it exists) for which each point of the space belongs to at most m open sets in the cover: in other words Uα1 ∩ ⋅⋅⋅ ∩ Uαm+1 = ∅ {\displaystyle \emptyset } for α1, ..., αm+1 distinct. A refinement of an open cover A {\displaystyle {\mathfrak {A}}} = {Uα} is another open cover B {\displaystyle {\mathfrak {B}}} = {Vβ}, such that each Vβ is contained in some Uα. The covering dimension of a topological space X is defined to be the minimum value of n such that every finite open cover A {\displaystyle {\mathfrak {A}}} of X has an open refinement B {\displaystyle {\mathfrak {B}}} with order n + 1. The refinement B {\displaystyle {\mathfrak {B}}} can always be chosen to be finite. Thus, if n is finite, Vβ1 ∩ ⋅⋅⋅ ∩ Vβn+2 = ∅ {\displaystyle \emptyset } for β1, ..., βn+2 distinct. If no such minimal n exists, the space is said to have infinite covering dimension. == Introductory example == Let f ( x 1 , x 2 ) {\textstyle f(x_{1},x_{2})} be a two-variable function (or signal) which is of the form f ( x 1 , x 2 ) = g ( x 1 ) {\textstyle f(x_{1},x_{2})=g(x_{1})} for some one-variable function g which is not constant. This means that f varies, in accordance to g, with the first variable or along the first coordinate. On the other hand, f is constant with respect to the second variable or along the second coordinate. It is only necessary to know the value of one, namely the first, variable in order to determine the value of f. Hence, it is a two-variable function but its intrinsic dimension is one. A slightly more complicated example is f ( x 1 , x 2 ) = g ( x 1 + x 2 ) {\textstyle f(x_{1},x_{2})=g(x_{1}+x_{2})} . f is still intrinsic one-dimensional, which can be seen by making a variable transformation y 1 = x 1 + x 2 {\textstyle y_{1}=x_{1}+x_{2}} and y 2 = x 1 − x 2 {\textstyle y_{2}=x_{1}-x_{2}} which gives f ( y 1 + y 2 2 , y 1 − y 2 2 ) = g ( y 1 ) {\textstyle f\left({\frac {y_{1}+y_{2}}{2}},{\frac {y_{1}-y_{2}}{2}}\right)=g\left(y_{1}\right)} . Since the variation in f can be described by the single variable y1 its intrinsic dimension is one. For the case that f is constant, its intrinsic dimension is zero since no variable is needed to describe variation. For the general case, when the intrinsic dimension of the two-variable function f is neither zero or one, it is two. In the literature, functions which are of intrinsic dimension zero, one, or two are sometimes referred to as i0D, i1D or i2D, respectively. == Signal processing == In signal processing of multidimensional signals, the intrinsic dimension of the signal describes how many variables are needed to generate a good approximation of the signal. For an N-variable function f, the set of variables can be represented as an N-dimensional vector x: f = f ( x ) where x = ( x 1 , … , x N ) {\textstyle f=f\left(\mathbf {x} \right){\text{ where }}\mathbf {x} =\left(x_{1},\dots ,x_{N}\right)} . If for some M-variable function g and M × N matrix A it is the case that for all x; f ( x ) = g ( A x ) , {\textstyle f(\mathbf {x} )=g(\mathbf {Ax} ),} M is the smallest number for which the above relation between f and g can be found, then the intrinsic dimension of f is M. The intrinsic dimension is a characterization of f, it is not an unambiguous characterization of g nor of A. That is, if the above relation is satisfied for some f, g, and A, it must also be satisfied for the same f and g′ and A′ given by g ′ ( y ) = g ( B y ) {\textstyle g'\left(\mathbf {y} \right)=g\left(\mathbf {By} \right)} and A ′ = B − 1 A {\textstyle \mathbf {A'} =\mathbf {B} ^{-1}\mathbf {A} } where B is a non-singular M × M matrix, since f ( x ) = g ′ ( A ′ x ) = g ( B A ′ x ) = g ( A x ) {\textstyle f\left(\mathbf {x} \right)=g'\left(\mathbf {A'x} \right)=g\left(\mathbf {BA'x} \right)=g\left(\mathbf {Ax} \right)} . == The Fourier transform of signals of low intrinsic dimension == An N variable function which has intrinsic dimension M < N has a characteristic Fourier transform. Intuitively, since this type of function is constant along one or several dimensions its Fourier transform must appear like an impulse (the Fourier transform of a constant) along the same dimension in the frequency domain. === A simple example === Let f be a two-variable function which is i1D. This means that there exists a normalized vector n ∈ R 2 {\textstyle \mathbf {n} \in \mathbb {R} ^{2}} and a one-variable function g such that f ( x ) = g ( n T x ) {\textstyle f(\mathbf {x} )=g(\mathbf {n} ^{\operatorname {T} }\mathbf {x} )} for all x ∈ R 2 {\textstyle \mathbf {x} \in \mathbb {R} ^{2}} . If F is the Fourier transform of f (both are two-variable functions) it must be the case that F ( u ) = G ( n T u ) ⋅ δ ( m T u ) {\textstyle F\left(\mathbf {u} \right)=G\left(\mathbf {n} ^{\mathrm {T} }\mathbf {u} \right)\cdot \delta \left(\mathbf {m} ^{\mathrm {T} }\mathbf {u} \right)} . Here G is the Fourier transform of g (both are one-variable functions), δ is the Dirac impulse function and m is a normalized vector in R 2 {\textstyle \mathbb {R} ^{2}} perpendicular to n. This means that F vanishes everywhere except on a line which passes through the origin of the frequency domain and is parallel to m. Along this line F varies according to G. === The general case === Let f be an N-variable function which has intrinsic dimension M, that is, there exists an M-variable function g and M × N matrix A such that f ( x ) = g ( A x ) ∀ x {\textstyle f(\mathbf {x} )=g(\mathbf {Ax} )\quad \forall \mathbf {x} } . Its Fourier transform F can then be described as follows: F vanishes everywhere except for a subspace of dimension M The subspace M is spanned by the rows of the matrix A In the subspace, F varies according to G the Fourier transform of g == Generalizations == The type of intrinsic dimension described above assume
RFinder
RFinder ("repeater finder") is a subscription-based website and mobile app. RFinder's main service is the World Wide Repeater Directory (WWRD), which is a directory of amateur radio repeaters. RFinder is the official repeater directory of several amateur radio associations. RFinder has listings for several amateur radio modes, including FM, D-STAR, DMR, and ATV. == World Wide Repeater Directory == Repeaters are listed in the directory along with its call sign, Maidenhead Locator System and GPS coordinates, transmit/receive offset ("split"), CTCSS and DCS squelch settings, and VoIP settings (IRLP and Echolink nodes). The directory has over 50,000 repeater listings in over 170 countries. === Website === The RFinder website has several search options including for routes. === Forums === RFinder user forums is for help and support for the app and hardware. === Mobile app === RFinder has mobile apps for Android and iOS. When using the mobile app, RFinder can display the distance to repeaters, based on the mobile device's current location. === ARRL Repeater Directory === The ARRL publishes the ARRL Repeater Directory which contains over 31,000 repeater listings for the US and Canada with listings provided by RFinder. == Subscription == RFinder requires a subscription. A one-year subscription is US$12.99. == Radio programming software == Some radio programming software applications can query RFinder and download repeater listing to program radios. Compatible software includes: CHIRP RT Systems == Radio associations == RFinder is the official repeater directory of the following associations: Amateur Radio Society Italy American Radio Relay League Cayman Amateur Radio Society Deutscher Amateur Radio Club Federacion Mexicana de Radio Experimentadores L’association Réseau des Émetteurs Français Lietuvos Radijo Mėgėjų Draugija Liga de Amadores Brasilieros de Radio Emissão Radio Amateurs of Canada Radio Society of Great Britain Rede dos Emissores Portugueses Unión de Radioaficionados Españoles