The signal transfer function (SiTF) is a measure of the signal output versus the signal input of a system such as an infrared system or sensor. There are many general applications of the SiTF. Specifically, in the field of image analysis, it gives a measure of the noise of an imaging system, and thus yields one assessment of its performance. == SiTF evaluation == In evaluating the SiTF curve, the signal input and signal output are measured differentially; meaning, the differential of the input signal and differential of the output signal are calculated and plotted against each other. An operator, using computer software, defines an arbitrary area, with a given set of data points, within the signal and background regions of the output image of the infrared sensor, i.e. of the unit under test (UUT), (see "Half Moon" image below). The average signal and background are calculated by averaging the data of each arbitrarily defined region. A second order polynomial curve is fitted to the data of each line. Then, the polynomial is subtracted from the average signal and background data to yield the new signal and background. The difference of the new signal and background data is taken to yield the net signal. Finally, the net signal is plotted versus the signal input. The signal input of the UUT is within its own spectral response. (e.g. color-correlated temperature, pixel intensity, etc.). The slope of the linear portion of this curve is then found using the method of least squares. == SiTF curve == The net signal is calculated from the average signal and background, as in signal to noise ratio (imaging)#Calculations. The SiTF curve is then given by the signal output data, (net signal data), plotted against the signal input data (see graph of SiTF to the right). All the data points in the linear region of the SiTF curve can be used in the method of least squares to find a linear approximation. Given n {\displaystyle n\,} data points ( x i , y i ) {\displaystyle (x_{i}\,,y_{i}\,)} a best fit line parameterized as y = m x + b {\displaystyle y=mx+b\,} is given by: m = ∑ x i y i n − ∑ x i n ∑ y i n ∑ x i 2 n − ( ∑ x i n ) 2 b = ∑ y i n − m ∑ x i n {\displaystyle m={\frac {{\frac {\sum x_{i}y_{i}}{n}}-{\frac {\sum x_{i}}{n}}{\frac {\sum y_{i}}{n}}}{{\frac {\sum x_{i}^{2}}{n}}-({\frac {\sum x_{i}}{n}})^{2}}}\qquad \qquad b={\frac {\sum y_{i}}{n}}-m{\frac {\sum x_{i}}{n}}}
Cloud-to-cloud integration
Cloud-to-Cloud Integration ( C2I ) allows users to connect disparate cloud computing platforms. While Paas (Platform as a service) and Saas (Software as a service) continue to gain momentum, different vendors have different implementations for cloud computing, e.g. Database, REST, SOAP API. Another name for Cloud-to-Cloud Integration is Cloud-Surfing. See also Cloud-based integration
Bainu (website)
Bainu ("how are you?") is a Chinese social networking website written in the Mongolian language. As of 2020 it had about 400,000 users, concentrated in Inner Mongolia. == Core features and positioning == Language and Cultural Characteristics Bainu is based on Traditional Mongolian Script and supports social interactions in the Mongolian language, including various message formats such as text, voice, images, and video. This design aims to preserve and promote Mongolian language and culture, particularly appealing to users in Inner Mongolia and other Mongolian-populated areas. Social Features Instant Messaging: Supports one-on-one private chats and group chats. Users can create interest-based groups or join local communities. Life Sharing: Through the "Chomorlig" feature (similar to Moments or a dynamic feed), users can share daily highlights to enhance community interaction. Location-Based Socializing: Recommends nearby users based on location, making it easier to connect with Mongolian friends in the same city or neighboring regions. Multilingual Support The app interface is available in English, Mongolian, and Simplified Chinese. == Technical Features and User Experience == Cross-Platform Compatibility Supports iPhone, iPad, Mac (with M1 chip or above), and Apple Vision Pro devices, covering users across the Apple ecosystem. Pricing Model Free download and basic features are available. Premium services (e.g., ad-free experience, extended social functions) require a subscription, with pricing options including $0.99/month, $2.99/quarter, and $6.99/year. User Feedback Positive Reviews: Some users praise it as the "best Mongolian-language chat app," recognizing its cultural value and social convenience. Negative Feedback: Reports of app crashes and technical issues, with some users calling for improved stability (e.g., frequent crashes in the iOS version). == Privacy and Data Policy == Bainu collects user data such as location, contact information, and device identifiers, which are linked to user identities. Additionally, user behavior may be tracked through third-party services, raising some privacy concerns. == Current Development and Challenges == User Base As of 2020, Bainu had approximately 400,000 users, primarily concentrated in Inner Mongolia. Policy Impact It was reported by Voice of America (VOA) that the Chinese authorities blocked Bainu on 23 August 2020 in order to prohibit Mongolians from discussing the issue of the authorities’ implementation of "bilingual education" in elementary schools. But now, in 2025, this software is completely available for download and use. see:https://bainu.com/
Redshift (theory)
Redshift is a techno-economic theory suggesting hypersegmentation of information technology markets based on whether individual computing needs are over or under-served by Moore's law, which predicts the doubling of computing transistors (and therefore roughly computing power) every two years. The theory, proposed and named by New Enterprise Associates partner and former Sun Microsystems CTO Greg Papadopoulos, categorized a series of high growth markets (redshifting) while predicting slower GDP-driven growth in traditional computing markets (blueshifting). Papadopoulos predicted the result will be a fundamental redesign of components comprising computing systems. == Hypergrowth market segments (redshifting) == According to the Redshift theory, applications "redshift" when they grow dramatically faster than Moore's Law allows, growing quickly in their absolute number of systems. In these markets, customers are running out of datacenter real-estate, power and cooling infrastructure. According to Dell Senior Vice President Brad Anderson, “Businesses requiring hyperscale computing environments – where infrastructure deployments are measured by up to millions of servers, storage and networking equipment – are changing the way they approach IT.” While various Redshift proponents offer minor alterations on the original presentation, “Redshifting” generally includes: === ΣBW (Sum-of-Bandwidth) === These are companies that drive heavy Internet traffic. This includes popular web-portals like Google, Yahoo, AOL and MSN. It also includes telecoms, multimedia, television over IP, online games like World of Warcraft and others. This segment has been enabled by widespread availability of high-bandwidth Internet connections to consumers through a DSL or cable modem. A simple way to understand this market is that for every byte of content served to a PC, mobile phone or other device over a network, there must exist computing systems to send it over the network. === High performance computing (HPC) === These are companies that do complex simulations that involve (for example) weather, stock markets or drug-design simulations. This is a generally elastic market because businesses frequently spend every "available" dollar budgeted for IT. A common anecdote claims that cutting the cost of computing by half causes customers in this segment to buy at least twice as much, because each marginal IT dollar spent contributes to business advantage. === prise (or "Star-prise") === These are companies that aggregate traditional computing applications and offer them as services, typically in the form of Software as a Service (SaaS). For example, companies that deploy CRM are over-served by Moore's Law, but companies that aggregate CRM functions and offer them as a service, such as Salesforce.com, grow faster than Moore's Law. === The eBay crisis === A prime example of redshift was a crisis at eBay. In 1999 eBay suffered a database crisis when a single Oracle Database running on the fastest Sun machine available (these tracking Moore's law in this period) was not enough to cope with eBay's growth. The solution was to massively parallelise their system architecture. == Traditional computing markets (blueshifting) == Redshift theory suggests that traditional computing markets, such as those serving enterprise resource planning or customer relationship management applications, have reached relative saturation in industrialized nations. Thereafter, proponents argued further market growth will closely follow gross domestic product growth, which typically remains under 10% for most countries annually. Given that Moore's Law continues to predict accurately the rate of computing transistor growth, which roughly translates into computing power doubling every two years, the Redshift theory suggests that traditional computing markets will ultimately contract as a percentage of computing expenditures over time. Functionally, this means “Blueshifting” customers can satisfy computing requirement growth by swapping in faster processors without increasing the absolute number of computing systems. == Consequences and industry commentary == Papadopoulos argued that while traditional computing markets remain the dominant source of revenue through the late 2000s, a shift to hypergrowth markets will inevitably occur. When that shift occurs, he argued computing (but not computers) will become a utility, and differentiation in the IT market will be based upon a company's ability to deliver computing at massive scale, efficiently and with predictable service levels, much like electricity at that time. If computing is to be delivered as a utility, Nicholas Carr suggested Papadopoulos' vision compares with Microsoft researcher Jim Hamilton, who both agree that computing is most efficiently generated in shipping containers. Industry analysts are also beginning to quantify Redshifting and Blueshifting markets. According to International Data Corporation vice president Matthew Eastwood, "IDC believes that the IT market is in a period of hyper segmentation... This a class of customers that is Moore's law driven and as price performance gains continue, IDC believes that these organizations will accelerate their consumption of IT infrastructure.” == History and nomenclature == Key portions of Papadopoulos' theory were first presented by Sun Microsystems CEO Jonathan Schwartz in late 2006. Papadopoulos later gave a full presentation on Redshift to Sun's annual Analyst Summit in February 2007. The term Redshift refers to what happens when electromagnetic radiation, usually visible light, moves away from an observer. Papadopoulos chose this term to reflect growth markets because redshift helped cosmologists explain the expansion of the universe. Papadopoulos originally depicted traditional IT markets as green to represent their revenue base, but later changed them to “blueshift,” which occurs when a light source moves toward an observer, similar to what would happen during a contraction of the universe.
Friending and following
Friending is the act of adding someone to a list of "friends" on a social networking service. The notion does not necessarily involve the concept of friendship. It is also distinct from the idea of a "fan"—as employed on the WWW sites of businesses, bands, artists, and others—since it is more than a one-way relationship. A "fan" only receives things. A "friend" can communicate back to the person friending. The act of "friending" someone usually grants that person special privileges (on the service) with respect to oneself. On Facebook, for example, one's "friends" have the privilege of viewing and posting to one's "timeline". Following is a similar concept on other social network services, such as Twitter and Instagram, where a person (follower) chooses to add content from a person or page to their newsfeed. Unlike friending, following is not necessarily mutual, and a person can unfollow (stop following) or block another user at any time without affecting that user's following status. The first scholarly definition and examination of friending and defriending (the act of removing someone from one's friend list, also called unfriending) was David Fono and Kate Raynes-Goldie's "Hyperfriendship and beyond: Friends and Social Norms on LiveJournal" from 2005, which identified the use of the term as both a noun and a verb by users of early social network site and blogging platform LiveJournal, which was originally launched in 1999. == Friend/follower count, friend collecting, and multiple accounts == The addition of people to a friend list without regard to whether one actually is their friend is sometimes known as friend whoring. Matt Jones of Dopplr went so far as to coin the expression "friending considered harmful" to describe the problem of focusing upon the friending of more and more people at the expense of actually making any use of a social network. Friend collecting is the adding of hundreds or thousands of friends/followers, a not uncommon order of magnitude on some social sites. As a result, many teen users feel pressured to heavily curate their posts, posting only carefully posed and edited photographs with well-thought-out captions. Some Instagram users will create a second account, known as a Finsta (short for "Fake Instagram"). A Finsta is typically private, and the owner only allows close friends to follow it. Since the follower count is kept down, the posts can be more candid and silly in nature. Users may also create multiple accounts based on their interests. Someone with a personal social media account might be a photographer and maintain a separate account for that. There is risk associated with following large numbers of people: scholars say that social anxiety could be an effect of managing a large social media network, as users can feel jealous and have a "fear of missing out". == Unfriending and unfollowing == Unfriending is the act of removing someone from a friends list. On Facebook, this means the action is unilateral, meaning, the friendship is terminated on both sides. The act of unfriending is often used when one user was flirting and made the other uncomfortable. Unfollowing is a little different. When a user unfollows someone on Instagram or Twitter, it continues a one-sided relationship. Often, the unfollowed user doesn't realize they were unfollowed, so they continue the following. == Social network friending and friendship == There are distinct groups of "friends" that one can friend on a social networking service. The notion of a social network friend does not necessarily embody the concept of friendship. Although terminology has not yet evolved to distinguish the different types of social networking friends, they can be broken into the following three categories. friends who are actually known These are people that may be one's friends or family in real life, with whom one has regular interaction either on-line or off-line. organizational friends These are companies and other organizations who maintain a "friending" relationship as a contacts list. complete strangers These are social networking "friends" with whom one has no relationship at all. Within these categories "friends" can be made up of strong ties, weak existing ties, weak latent ties, and parasocial ties. Strong ties can be made up of close family members and friends where self-disclosure, intimacy and frequent content occur. Weak existing ties can be made up of acquaintances, co-workers and distance relatives with whom the user has inconsistent contact. Weak latent ties can be made up of people within a similar geographical location or profession that can be used as a potential future bridge to other connections. Parasocial ties can be made up of celebrities, public figures and media personas. Human nature is to reciprocate a friending, marking someone as a friend who has marked oneself as a friend. This is a social norm for social networking services. However, this leads to mixing up who is an actual friend, and who is a contact. Tagging someone as a "contact" who has marked one as a "friend" can be perceived as impolite. Other concerns about this issue are treated in Sherry Turkle's Alone Together which analyses many behavioral dynamics in social media friendships. Turkle defines herself as "cautiously optimistic", but expresses concern that distance communications may undermine genuine face-to-face spoken discourses, lessening people's expectations of one another. One social networking service, FriendFeed, allows one to friend someone as a "fake" friend. The person "fake" friended receives the usual notifications for friending, but that person's updates are not received. Gavin Bell, author of Building Social Web Applications, describes this mechanism as "ludicrous". Results from a 2007 survey the Center for the Digital Future stated that only 23% of internet users have at least one virtual friend whom they have only met online. Ideally the number of virtual friends is directly proportional to the use of the Internet, but the same survey showed 20% of heavy-users (more than 3 hours/day) who claimed an average of 8.7% online friends, reported at least one relationship that started virtually and migrated to in-person contact. This results and other concerning issues are included in the book Networked: The New Social Operating System co-written by Lee Rainie and Barry Wellman in 2012. == Ethical considerations == The act of "friending" someone on a social networking service has particular ethical implications for judges in the United States. Judicial codes of conducts in the various states generally incorporate some form of provision that judges should avoid even the appearance of impropriety. Whether this regulates and even prohibits judges "friending" attorneys that appear before them, and law enforcement personnel, has been the subject of some analysis by the judicial ethics panels of the various states. They haven't all agreed on the guidance that they have given to judges: The New York state Judicial Ethics committee in 2009 simply advised judges to employ caution, noting that the issue of "friending" someone on a social networking service is a publicly observable act that has little difference from other public behavior concerns judges already face. The Florida Judicial Ethics Advisory committee in 2009 noted that, judges being normal human beings, it was unavoidable for judges to form friendships without the responsibilities of their job. It prohibited judges from friending any attorneys that appeared before them, whilst allowing friending of those who do not, on the grounds that it may give the appearance to the general public (even if the substance is otherwise) that those attorneys who are friended hold special sway with the judge. A minority opinion of the committee asserted that there is a substantive difference between "friending" on a social networking service and actual friendship, and that the general public, being aware of the norms of social networking services, was capable of drawing this distinction and would not reasonably conclude either a special degree of influence or a violation of the code of judicial conduct. This minority opinion was outnumbered twice in 2009, both in the Judicial Ethics Advisory and in the Florida Supreme Court Judicial Ethics Advisory committee. The South Carolina judicial conduct committee in 2009 permitted judges to friend attorneys and law enforcement personnel, with the proviso that no judicial business should be conducted upon nor discussed via the social networking service. "... a judge should not become isolated from the community in which the judge lives.", the committee stated. The Kentucky Judicial Ethics committee in 2010 took the same position as the minority opinion in Florida. It urged judges to exercise caution, but recognized that the act of friending "does not, in and of itself, indicate the degree or intensity of a judge's relationship with the person who is the 'friend'
Speech segmentation
Speech segmentation is the process of identifying the boundaries between words, syllables, or phonemes in spoken natural languages. The term applies both to the mental processes used by humans, and to artificial processes of natural language processing. In the field of automatic pronunciation assessment, the process of segmenting an utterance against expected word(s) is called forced alignment. Speech segmentation is a subfield of general speech perception and an important subproblem of the technologically focused field of speech recognition, and cannot be adequately solved in isolation. As in most natural language processing problems, one must take into account context, grammar, and semantics, and even so the result is often a probabilistic division (statistically based on likelihood) rather than a categorical one. Though it seems that coarticulation—a phenomenon which may happen between adjacent words just as easily as within a single word—presents the main challenge in speech segmentation across languages, some other problems and strategies employed in solving those problems can be seen in the following sections. This problem overlaps to some extent with the problem of text segmentation that occurs in some languages which are traditionally written without inter-word spaces, like Chinese and Japanese, compared to writing systems which indicate speech segmentation between words by a word divider, such as the space. However, even for those languages, text segmentation is often much easier than speech segmentation, because the written language usually has little interference between adjacent words, and often contains additional clues not present in speech (such as the use of Chinese characters for word stems in Japanese). == Lexical recognition == In natural languages, the meaning of a complex spoken sentence can be understood by decomposing it into smaller lexical segments (roughly, the words of the language), associating a meaning to each segment, and combining those meanings according to the grammar rules of the language. Though lexical recognition is not thought to be used by infants in their first year, due to their highly limited vocabularies, it is one of the major processes involved in speech segmentation for adults. Three main models of lexical recognition exist in current research: first, whole-word access, which argues that words have a whole-word representation in the lexicon; second, decomposition, which argues that morphologically complex words are broken down into their morphemes (roots, stems, inflections, etc.) and then interpreted and; third, the view that whole-word and decomposition models are both used, but that the whole-word model provides some computational advantages and is therefore dominant in lexical recognition. To give an example, in a whole-word model, the word "cats" might be stored and searched for by letter, first "c", then "ca", "cat", and finally "cats". The same word, in a decompositional model, would likely be stored under the root word "cat" and could be searched for after removing the "s" suffix. "Falling", similarly, would be stored as "fall" and suffixed with the "ing" inflection. Though proponents of the decompositional model recognize that a morpheme-by-morpheme analysis may require significantly more computation, they argue that the unpacking of morphological information is necessary for other processes (such as syntactic structure) which may occur parallel to lexical searches. As a whole, research into systems of human lexical recognition is limited due to little experimental evidence that fully discriminates between the three main models. In any case, lexical recognition likely contributes significantly to speech segmentation through the contextual clues it provides, given that it is a heavily probabilistic system—based on the statistical likelihood of certain words or constituents occurring together. For example, one can imagine a situation where a person might say "I bought my dog at a ____ shop" and the missing word's vowel is pronounced as in "net", "sweat", or "pet". While the probability of "netshop" is extremely low, since "netshop" isn't currently a compound or phrase in English, and "sweatshop" also seems contextually improbable, "pet shop" is a good fit because it is a common phrase and is also related to the word "dog". Moreover, an utterance can have different meanings depending on how it is split into words. A popular example, often quoted in the field, is the phrase "How to wreck a nice beach", which sounds very similar to "How to recognize speech". As this example shows, proper lexical segmentation depends on context and semantics which draws on the whole of human knowledge and experience, and would thus require advanced pattern recognition and artificial intelligence technologies to be implemented on a computer. Lexical recognition is of particular value in the field of computer speech recognition, since the ability to build and search a network of semantically connected ideas would greatly increase the effectiveness of speech-recognition software. Statistical models can be used to segment and align recorded speech to words or phones. Applications include automatic lip-synch timing for cartoon animation, follow-the-bouncing-ball video sub-titling, and linguistic research. Automatic segmentation and alignment software is commercially available. == Phonotactic cues == For most spoken languages, the boundaries between lexical units are difficult to identify; phonotactics are one answer to this issue. One might expect that the inter-word spaces used by many written languages like English or Spanish would correspond to pauses in their spoken version, but that is true only in very slow speech, when the speaker deliberately inserts those pauses. In normal speech, one typically finds many consecutive words being said with no pauses between them, and often the final sounds of one word blend smoothly or fuse with the initial sounds of the next word. The notion that speech is produced like writing, as a sequence of distinct vowels and consonants, may be a relic of alphabetic heritage for some language communities. In fact, the way vowels are produced depends on the surrounding consonants just as consonants are affected by surrounding vowels; this is called coarticulation. For example, in the word "kit", the [k] is farther forward than when we say 'caught'. But also, the vowel in "kick" is phonetically different from the vowel in "kit", though we normally do not hear this. In addition, there are language-specific changes which occur in casual speech which makes it quite different from spelling. For example, in English, the phrase "hit you" could often be more appropriately spelled "hitcha". From a decompositional perspective, in many cases, phonotactics play a part in letting speakers know where to draw word boundaries. In English, the word "strawberry" is perceived by speakers as consisting (phonetically) of two parts: "straw" and "berry". Other interpretations such as "stra" and "wberry" are inhibited by English phonotactics, which does not allow the cluster "wb" word-initially. Other such examples are "day/dream" and "mile/stone" which are unlikely to be interpreted as "da/ydream" or "mil/estone" due to the phonotactic probability or improbability of certain clusters. The sentence "Five women left", which could be phonetically transcribed as [faɪvwɪmɘnlɛft], is marked since neither /vw/ in /faɪvwɪmɘn/ nor /nl/ in /wɪmɘnlɛft/ are allowed as syllable onsets or codas in English phonotactics. These phonotactic cues often allow speakers to easily distinguish the boundaries in words. Vowel harmony in languages like Finnish can also serve to provide phonotactic cues. While the system does not allow front vowels and back vowels to exist together within one morpheme, compounds allow two morphemes to maintain their own vowel harmony while coexisting in a word. Therefore, in compounds such as "selkä/ongelma" ('back problem') where vowel harmony is distinct between two constituents in a compound, the boundary will be wherever the switch in harmony takes place—between the "ä" and the "ö" in this case. Still, there are instances where phonotactics may not aid in segmentation. Words with unclear clusters or uncontrasted vowel harmony as in "opinto/uudistus" ('student reform') do not offer phonotactic clues as to how they are segmented. From the perspective of the whole-word model, however, these words are thought be stored as full words, so the constituent parts would not necessarily be relevant to lexical recognition. == In infants and non-natives == Infants are one major focus of research in speech segmentation. Since infants have not yet acquired a lexicon capable of providing extensive contextual clues or probability-based word searches within their first year, as mentioned above, they must often rely primarily upon phonotactic and rhythmic cues (with prosody being the dominant cue), all
Signal-to-interference-plus-noise ratio
In information theory and telecommunication engineering, the signal-to-interference-plus-noise ratio (SINR) (also known as the signal-to-noise-plus-interference ratio (SNIR)) is a quantity used to give theoretical upper bounds on channel capacity (or the rate of information transfer) in wireless communication systems such as networks. Analogous to the signal-to-noise ratio (SNR) used often in wired communications systems, the SINR is defined as the power of a certain signal of interest divided by the sum of the interference power (from all the other interfering signals) and the power of some background noise. If the power of noise term is zero, then the SINR reduces to the signal-to-interference ratio (SIR). Conversely, zero interference reduces the SINR to the SNR, which is used less often when developing mathematical models of wireless networks such as cellular networks. The complexity and randomness of certain types of wireless networks and signal propagation has motivated the use of stochastic geometry models in order to model the SINR, particularly for cellular or mobile phone networks. == Description == SINR is commonly used in wireless communication as a way to measure the quality of wireless connections. Typically, the energy of a signal fades with distance, which is referred to as a path loss in wireless networks. Conversely, in wired networks the existence of a wired path between the sender or transmitter and the receiver determines the correct reception of data. In a wireless network one has to take other factors into account (e.g. the background noise, interfering strength of other simultaneous transmission). The concept of SINR attempts to create a representation of this aspect. == Mathematical definition == The definition of SINR is usually defined for a particular receiver (or user). In particular, for a receiver located at some point x in space (usually, on the plane), then its corresponding SINR given by S I N R ( x ) = P I + N {\displaystyle \mathrm {SINR} (x){=}{\frac {P}{I+N}}} where P is the power of the incoming signal of interest, I is the interference power of the other (interfering) signals in the network, and N is some noise term, which may be a constant or random. Like other ratios in electronic engineering and related fields, the SINR is often expressed in decibels or dB. == Propagation model == To develop a mathematical model for estimating the SINR, a suitable mathematical model is needed to represent the propagation of the incoming signal and the interfering signals. A common model approach is to assume the propagation model consists of a random component and non-random (or deterministic) component. The deterministic component seeks to capture how a signal decays or attenuates as it travels a medium such as air, which is done by introducing a path-loss or attenuation function. A common choice for the path-loss function is a simple power-law. For example, if a signal travels from point x to point y, then it decays by a factor given by the path-loss function ℓ ( | x − y | ) = | x − y | α {\displaystyle \ell (|x-y|)=|x-y|^{\alpha }} , where the path-loss exponent α>2, and |x-y| denotes the distance between point y of the user and the signal source at point x. Although this model suffers from a singularity (when x=y), its simple nature results in it often being used due to the relatively tractable models it gives. Exponential functions are sometimes used to model fast decaying signals. The random component of the model entails representing multipath fading of the signal, which is caused by signals colliding with and reflecting off various obstacles such as buildings. This is incorporated into the model by introducing a random variable with some probability distribution. The probability distribution is chosen depending on the type of fading model and include Rayleigh, Rician, log-normal shadow (or shadowing), and Nakagami. == SINR model == The propagation model leads to a model for the SINR. Consider a collection of n {\displaystyle n} base stations located at points x 1 {\displaystyle x_{1}} to x n {\displaystyle x_{n}} in the plane or 3D space. Then for a user located at, say x = 0 {\displaystyle x=0} , then the SINR for a signal coming from base station, say, x i {\displaystyle x_{i}} , is given by S I N R ( x i ) = F i ℓ ( | x i | ) ∑ j ≠ i [ F j ℓ ( | x j | ) ] + N {\displaystyle \mathrm {SINR} (x_{i}){=}{\frac {\frac {F_{i}}{\ell (|x_{i}|)}}{\sum _{j\neq i}\left[{\frac {F_{j}}{\ell (|x_{j}|)}}\right]+N}}} , where F i {\displaystyle F_{i}} are fading random variables of some distribution. Under the simple power-law path-loss model becomes S I N R ( x i ) = F i | x i | α ∑ j ≠ i F j | x j | α + N {\displaystyle \mathrm {SINR} (x_{i}){=}{\frac {\frac {F_{i}}{|x_{i}|^{\alpha }}}{\sum _{j\neq i}{\frac {F_{j}}{|x_{j}|^{\alpha }}}+N}}} . == Stochastic geometry models == In wireless networks, the factors that contribute to the SINR are often random (or appear random) including the signal propagation and the positioning of network transmitters and receivers. Consequently, in recent years this has motivated research in developing tractable stochastic geometry models in order to estimate the SINR in wireless networks. The related field of continuum percolation theory has also been used to derive bounds on the SINR in wireless networks.