Kristian Kersting (born November 28, 1973, in Cuxhaven, Germany) is a German computer scientist. He is Professor of Artificial intelligence and Machine Learning at the Department of Computer Science at the Technische Universität Darmstadt, Head of the Artificial Intelligence and Machine Learning Lab (AIML) and Co-Director of hessian.AI, the Hessian Center for Artificial Intelligence. He is known for his research on statistical relational artificial intelligence, probabilistic programming, and deep probabilistic learning. == Life == Kersting studied computer science at the University of Freiburg, where he received his Ph.D. in 2006. At the university he attended a course on artificial intelligence given by Bernhard Nebel and became interested in the topic. He was a visiting postdoctoral researcher at the KU Leuven and a postdoctoral associate at the Massachusetts Institute of Technology (MIT). His advisor at MIT was Leslie Pack Kaelbling. From 2008 to 2012, he led a research group at the Fraunhofer Institute for Intelligent Analysis and Information Systems (IAIS). He then became a Juniorprofessor at the University of Bonn and associate Professor at the computer science department of the Technical University of Dortmund. From 2017 to 2019, he was professor of machine Learning and since 2019 professor of artificial intelligence and machine learning at the department of computer science of the Technische Universität Darmstadt. He is also a researcher at ATHENE, the largest research institute for IT security in Europe and leads a research department at the German Research Centre for Artificial Intelligence (DFKI). Kristian Kersting is the co-spokesperson of Cluster of Excellence "Reasonable Artificial Intelligence", RAI (2026-32). == Awards == In 2006, he received the AI Dissertation Award of the European Association for Artificial Intelligence. In 2008, he received the Fraunhofer Attract research grant with a budget of 2.5 million euros over five years. He was appointed Fellow of the European Association for Artificial Intelligence (EurAI) and Fellow of the European Laboratory for Learning and Intelligent Systems (ELLIS) in 2019. In 2019 he received the "Deutscher KI-Preis" ("German AI Award"), endowed with 100,000 euros, for his outstanding scientific achievements in the field of artificial intelligence. He was elected an AAAI Fellow in 2024. == Publications == De Raedt L., Kersting K. (2008) Probabilistic Inductive Logic Programming. In: De Raedt L., Frasconi P., Kersting K., Muggleton S. (eds) Probabilistic Inductive Logic Programming. Lecture Notes in Computer Science, vol 4911. Springer, Berlin, Heidelberg. ISBN 978-3-540-78651-1 Luc De Raedt, Kristian Kersting, Sriraam Natarajan and David Poole, "Statistical Relational Artificial Intelligence: Logic, Probability, and Computation", Synthesis Lectures on Artificial Intelligence and Machine Learning" Morgan & Claypool, March 2016 ISBN 9781627058414.
Advanced automation functions
In automation production technology the actions performed by an automated process are executed by a program of instructions which is run during a work cycle. To execute work cycle programs, an automated system should be available to execute these advanced functions. == Safety monitoring == If there is a need for workers in an automated system, a safety monitoring is required for the occupational safety and health of the workers. In a safety monitoring various steps can take place including a complete stop of the system, sounding an alarm or reducing the operating speed. Usually, limiting switches are sensors like temperature probes, heat and smoke detectors or pressure sensitive floor pads. == Maintenance and repair diagnostics == There are three modes of operations which are used in a cycle of maintenance and repair diagnostics: status monitoring, failure diagnostics and recommendation of the repair procedure. In the status monitoring mode, the current system status is displayed. The failure diagnostics mode takes place when a failure occurs. The system will then suggest an adequate repair procedure to a team of experts. == Error detection and recovery == The error detection mode is a step to determine if and when a failure occurs in automated system. The possible errors can be divided into three categories. random errors, systematic errors and aberrations. While in the error recovery mode, remedy actions take place for all detected errors.
Story (social media)
In social media, a story is a function in which the user tells a narrative or provides status messages and information in the form of short, time-limited clips in an automatically running sequence. == Definition == A story is a short sequence of images, videos, or other social media content, which can be accompanied by backgrounds, music, text, stickers, animations, filters or emojis. Social media platforms typically advance through the sequence automatically when presenting a story to a viewer. Although the sequential nature of stories can be used to tell a narrative, the pieces of a story can also be unrelated. Social media platforms that offer stories will typically have a primary story for each user which consists of everything the user posted to their story over a certain period of time, usually the most recent 24 hours. Most stories cannot be changed afterwards and are only available for a short time. Stories are almost exclusively created on a mobile device such as a smartphone or tablet computer and are usually displayed vertically. == History == In October 2013, Snapchat first introduced the story function as a series of Snaps that can together tell a narrative through a chronological order, with each Snap being viewable by all of the poster's friends and deleted after 24 hours. Stories soon surpassed private Snaps to become Snapchat's most-viewed type of post. After 2015, Snapchat introduced a feature allowing users to post private stories viewable by a chosen subset of their friends. Later other apps would copy this feature. In August 2016, Instagram introduced a stories function that deletes the content after 24 hours. Various commenters have accused the site of copying Snapchat. In February 2017, the instant messenger WhatsApp introduced the Now Status stories function in beta, which was later renamed Status. In March 2017, a story function was introduced in Facebook Messenger. In February 2018, Google launched AMP Stories, bringing a story-style format to certain Google search results on mobile devices. In August 2018, YouTube introduced a stories function that initially was limited to pictures, but was later expanded to support short video clips. The feature was shut down in June 2023. In August 2018, the GIF website Giphy introduced a story function. In March 2022, TikTok added a story feature which allowed users to create 15 second long videos that delete after 24 hours. In June 2023, Telegram CEO Pavel Durov announced stories for Telegram would be released in July 2023. In July 2023, the feature was released for premium users, and in August 2023 it was rolled out for all users. == User motivations == In 2022, a study performed by Jia-Dai (Evelyn) Lu and Jhih-Syuan (Elaine) Lin examined the various motivations for updating stories on Instagram. The researchers found a new configuration of motivations for using Instagram Stories: exploration, self-enhancement, perceived functionality, entertainment, social sharing, relationship building, novelty, and surveillance. The findings also highlighted that contribution and creation activities are likely to result in positive emotions, while creation alone predicts negative emotions while updating stories on Instagram. == Usage statistics == In 2019, around 1.5 billion people worldwide every day on average used the stories function in a social network or messenger. Younger people in particular use this function. More than 20% of people aged 18 to 24 use Instagram stories, while it is just under 2% of those over 55. In a Facebook survey of 18,000 participants from 12 countries, 68% said they used the stories function at least once a month. Stories in the areas of fashion and tourism are particularly popular. The website Fanpage Karma analyzed several Instagram accounts and determined the average reach of posts and stories per follower, concluding that posts have a higher reach than stories, which often have less than half the reach.
Social advertising (social relationships)
Social advertising is advertising that relies on social information or networks in generating, targeting, and delivering marketing communications. Many current examples of social advertising use a particular Internet service to collect social information, establish and maintain relationships with consumers, and for delivering communications. For example, the advertising platforms provided by Google, Twitter, and Facebook involve targeting and presenting ads based on relationships articulated on those same services. Social advertising can be part of a broader social media marketing strategy designed to connect with consumers. == Social targeting == Since a pair of consumers connected via a relationship are more likely to be similar than an unconnected pair, information about such relationships can be used to infer characteristics of consumers useful for targeting. For example, predictions of an individual's home location can be improved using geographic information about their peers. Existing advertising platforms can allow advertisers to explicitly target the peers (e.g., Facebook friends, Twitter followers) of consumers who have a known affiliation with their brand. Thus, one way social advertising is expected to be effective is because social networks encode information about unobserved characteristics of consumers, including their susceptibility to adopt a product and to influence their peers to adopt. Social advertisement targets audiences' demographics based on customers browsing histories. This helped companies understand users' interests and target a specific group of users. Whether it is location or personal interest, different categories of companies can make the consumers on social media rely heavily on their advertisements. This is one of the reasons why social advertising has grown over time. Targeting their audience to real life stakeholders generally increase the attention of the advertised deal which brings up more profits for companies. Subsequently, the psychological effects that social media gives off to its users play a huge role in advertisement companies keeping their customers online. One of the main reasons users rely on social media is because it's a source of entertainment that provides them with a feeling of inclusiveness. In making the customers feel the inclusiveness, social advertising targeting a specific group of users is presented as if these advertisements are customized for the users in their perspective making them feel the attention that they do not often feel in the real world. You can use Social signals checker tool to find more information about links. Social signals are metrics that measure how much people interact with your content on social media. From likes, to shares, to comments; each of these signals contributes to an overall number that tells search engines like Google how much people like your content. The more social signals your website gets, the more likely it is to rank higher in Google. The reason for this is two-fold. First, social media is used by millions of people every day, and if your content is being shared and interacted with on these sites, it shows that it’s worthy of being seen. And second, social media sites are highly trusted by Google. So if you can get your content seen and interacted with on these platforms, you’ll be off to a great start. == Social cues in advertisements == Social ads often include information about the affiliation of a peer with an advertised entity. For example, a social ad might indicate a friend has endorsed a product, highly rated a restaurant, or watched a particular film. In fact, some definitions make these personalized social signals a necessary condition for the advertising being social advertising. Inclusion of personalized social signals creates a channel for social influence. Experiments that remove peers' names or images from social advertisements provide evidence that their presence increases proximal outcomes (e.g., clicks on advertisements). This is technically how trends are started on social media. Since social media links a single profile to thousands of other accounts some being real-life friends or even acquaintances, the opinions and the bias a user has for other users who are also a customer of an advertisement on the feed can heavily affect whether to click on the advertisement or not. Once this pattern continues, the brand benefits from increased customers, profit, and attention. Social networking can spread rapidly because 71 percent of the world's population contributes and uses social media which means social advertising gives companies a better marketing technique than a physical poster advertisement. == Word of mouth == Advertisers often attempt to use word of mouth to affect consumers and their decisions to adopt products and services. Ads and other inducements targeted at a seed set of individuals can be designed to produce a larger cascade of adoption through influence. Businesses are also using social media to attempt to identify and persuade influential consumers to spread positive messages about their products or services. Consequently, not only on social platforms but also in physical settings, users start talking to each other. When individuals develop an intimate relationship with each other, it is quite heavily based on shared characteristics, interests, and personalities. If one social media user becomes a regular customer to a well-known company that advertises often, there is a higher chance that all the other people who have intimate relationships with that one customer will be exposed to the online advertisement more than another user who might be completely new to a brand that is being advertised on screen. In reality, this happens to not only one user but to most of the users which mean a single brand advertisement online can have to potential of being talked about between billions and trillions of people all around the globe. == Relationship marketing == To accurately conduct relationship marketing, businesses must develop and manage six marketplaces: internal, customer, referral, supplier, influencer and employee. To maintain relationship marketing, customers often see social media influencers getting free sponsorships or PR boxes just to advertise their products. At times, users who become customers through these social influencers will get a better deal than regular customers which stands as a very commonly used marketing technique. By doing this, users think they are receiving special treatment when in reality it very much benefits social influencers and brands. Especially for brands that are just starting, they use this marketing technique so that their names can be out there, and people will start talking, which is their initial goal.
Ultra (cryptography)
Ultra was the designation adopted by British military intelligence in June 1941 for wartime signals intelligence obtained by breaking high-level encrypted enemy radio and teleprinter communications at the Government Code and Cypher School (GC&CS) at Bletchley Park. Ultra eventually became the standard designation among the western Allies for all such intelligence. The name arose because the intelligence obtained was considered more important than that designated by the highest British security classification then used (Most Secret) and so was regarded as being Ultra Secret. Several other cryptonyms had been used for such intelligence. The code name "Boniface" was used as a cover name for Ultra. In order to ensure that the successful code-breaking did not become apparent to the Germans, British intelligence created a fictional MI6 master spy, Boniface, who controlled a fictional series of agents throughout Germany. Information obtained through code-breaking was often attributed to the human intelligence from the Boniface network. The U.S. used the codename Magic for its decrypts from Japanese sources, including the "Purple" cipher. Much of the German cipher traffic was encrypted on the Enigma machine. Used properly, the German military Enigma would have been virtually unbreakable; in practice, shortcomings in operation allowed it to be broken. The term "Ultra" has often been used almost synonymously with "Enigma decrypts". However, Ultra also encompassed decrypts of the German Lorenz SZ 40/42 machines that were used by the German High Command, and the Hagelin machine. Many observers, at the time and later, regarded Ultra as immensely valuable to the Allies. Winston Churchill was reported to have told King George VI, when presenting to him Stewart Menzies (head of the Secret Intelligence Service and the person who controlled distribution of Ultra decrypts to the government): "It is thanks to the secret weapon of General Menzies, put into use on all the fronts, that we won the war!" F. W. Winterbotham quoted the western Supreme Allied Commander, Dwight D. Eisenhower, at war's end describing Ultra as having been "decisive" to Allied victory. Sir Harry Hinsley, Bletchley Park veteran and official historian of British Intelligence in World War II, made a similar assessment of Ultra, saying that while the Allies would have won the war without it, "the war would have been something like two years longer, perhaps three years longer, possibly four years longer than it was." However, Hinsley and others have emphasized the difficulties of counterfactual history in attempting such conclusions, and some historians, such as John Keegan, have said the shortening might have been as little as the three months it took the United States to deploy the atomic bomb. == Sources of intelligence == Most Ultra intelligence was derived from reading radio messages that had been encrypted with cipher machines, complemented by material from radio communications using traffic analysis and direction finding. In the early phases of the war, particularly during the eight-month Phoney War, the Germans could transmit most of their messages using land lines and so had no need to use radio. This meant that those at Bletchley Park had some time to build up experience of collecting and starting to decrypt messages on the various radio networks. German Enigma messages were the main source, with those of the German air force (the Luftwaffe) predominating, as they used radio more and their operators were particularly ill-disciplined. === German === ==== Enigma ==== "Enigma" refers to a family of electro-mechanical rotor cipher machines. These produced a polyalphabetic substitution cipher and were widely thought to be unbreakable in the 1920s, when a variant of the commercial Model D was first used by the Reichswehr. The German Army (Heer), Navy, Air Force, Nazi party, Gestapo and German diplomats used Enigma machines in several variants. Abwehr (German military intelligence) used a four-rotor machine without a plugboard and Naval Enigma used different key management from that of the army or air force, making its traffic far more difficult to cryptanalyse; each variant required different cryptanalytic treatment. The commercial versions were not as secure and Dilly Knox of GC&CS is said to have broken one before the war. German military Enigma was first broken in December 1932 by Marian Rejewski and the Polish Cipher Bureau, using a combination of brilliant mathematics, the services of a spy in the German office responsible for administering encrypted communications, and good luck. The Poles read Enigma to the outbreak of World War II and beyond, in France. At the turn of 1939, the Germans made the systems ten times more complex, which required a tenfold increase in Polish decryption equipment, which they could not meet. On 25 July 1939, the Polish Cipher Bureau handed reconstructed Enigma machines and their techniques for decrypting ciphers to the French and British. Gordon Welchman wrote, Ultra would never have got off the ground if we had not learned from the Poles, in the nick of time, the details both of the German military Enigma machine, and of the operating procedures that were in use. At Bletchley Park, some of the key people responsible for success against Enigma included mathematicians Alan Turing and Hugh Alexander and, at the British Tabulating Machine Company, chief engineer Harold Keen. After the war, interrogation of German cryptographic personnel led to the conclusion that German cryptanalysts understood that cryptanalytic attacks against Enigma were possible but were thought to require impracticable amounts of effort and investment. The Poles' early start at breaking Enigma and the continuity of their success gave the Allies an advantage when World War II began. ==== Lorenz cipher ==== In June 1941, the Germans started to introduce on-line stream cipher teleprinter systems for strategic point-to-point radio links, to which the British gave the code-name Fish. Several systems were used, principally the Lorenz SZ 40/42 (codenamed "Tunny" by the British) and Geheimfernschreiber ("Sturgeon"). These cipher systems were cryptanalysed, particularly Tunny, which the British thoroughly penetrated. It was eventually attacked using Colossus machines, which were the first digital programme-controlled electronic computers. In many respects the Tunny work was more difficult than for the Enigma, since the British codebreakers had no knowledge of the machine producing it and no head-start such as that the Poles had given them against Enigma. Although the volume of intelligence derived from this system was much smaller than that from Enigma, its importance was often far higher because it produced primarily high-level, strategic intelligence that was sent between Wehrmacht high command (Oberkommando der Wehrmacht, OKW). The eventual bulk decryption of Lorenz-enciphered messages contributed significantly, and perhaps decisively, to the defeat of Nazi Germany. Nevertheless, the Tunny story has become much less well known among the public than the Enigma one. At Bletchley Park, some of the key people responsible for success in the Tunny effort included mathematicians W. T. "Bill" Tutte and Max Newman and electrical engineer Tommy Flowers. === Italian === In June 1940, the Italians were using book codes for most of their military messages, except for the Italian Navy, which in early 1941 had started using a version of the Hagelin rotor-based cipher machine C-38. This was broken from June 1941 onwards by the Italian subsection of GC&CS at Bletchley Park. === Japanese === In the Pacific theatre, a Japanese cipher machine, called "Purple" by the Americans, was used for highest-level Japanese diplomatic traffic. It produced a polyalphabetic substitution cipher, but unlike Enigma, was not a rotor machine, being built around electrical stepping switches. It was broken by the US Army Signal Intelligence Service and disseminated as Magic. Detailed reports by the Japanese ambassador to Germany were encrypted on the Purple machine. His reports included reviews of German assessments of the military situation, reviews of strategy and intentions, reports on direct inspections by the ambassador (in one case, of Normandy beach defences), and reports of long interviews with Hitler. The Japanese are said to have obtained an Enigma machine in 1937, although it is debated whether they were given it by the Germans or bought a commercial version, which, apart from the plugboard and internal wiring, was the German Heer/Luftwaffe machine. Having developed a similar machine, the Japanese did not use the Enigma machine for their most secret communications. The chief fleet communications code system used by the Imperial Japanese Navy was called JN-25 by the Americans, and by early 1942 the US Navy had made considerable progress in decrypting Japanese naval messages. The US Army also made progress on the
Kernel density estimation
In statistics, kernel density estimation (KDE) is the application of kernel smoothing for probability density estimation, i.e., a non-parametric method to estimate the probability density function of a random variable based on kernels as weights. KDE answers a fundamental data smoothing problem where inferences about the population are made based on a finite data sample. In some fields such as signal processing and econometrics it is also termed the Parzen–Rosenblatt window method, after Emanuel Parzen and Murray Rosenblatt, who are usually credited with independently creating it in its current form. One of the famous applications of kernel density estimation is in estimating the class-conditional marginal densities of data when using a naive Bayes classifier, which can improve its prediction accuracy. == Definition == Let x = ( x 1 , x 2 , x 3 , . . . ) {\displaystyle \mathbf {x} =\left(x_{1},x_{2},x_{3},...\right)} be independent and identically distributed samples drawn from some univariate distribution with an unknown density f at any given point x. We are interested in estimating the shape of this function f. Its kernel density estimator is f ^ h ( x ) = 1 n ∑ i = 1 n K h ( x − x i ) = 1 n h ∑ i = 1 n K ( x − x i h ) , {\displaystyle {\hat {f}}_{h}(x)={\frac {1}{n}}\sum _{i=1}^{n}K_{h}(x-x_{i})={\frac {1}{nh}}\sum _{i=1}^{n}K{\left({\frac {x-x_{i}}{h}}\right)},} where K is the kernel — a non-negative function — and h > 0 is a smoothing parameter called the bandwidth or simply width. A kernel with subscript h is called the scaled kernel and defined as Kh(x) = 1/h K(x/h). Intuitively one wants to choose h as small as the data will allow; however, there is always a trade-off between the bias of the estimator and its variance. The choice of bandwidth is discussed in more detail below. A range of kernel functions are commonly used: uniform, triangular, biweight, triweight, Epanechnikov (parabolic), normal, and others. The Epanechnikov kernel is optimal in a mean square error sense, though the loss of efficiency is small for the kernels listed previously. Due to its convenient mathematical properties, the normal kernel is often used, which means K(x) = ϕ(x), where ϕ is the standard normal density function. The kernel density estimator then becomes f ^ h ( x ) = 1 n ∑ i = 1 n 1 h 2 π exp ( − ( x − x i ) 2 2 h 2 ) , {\displaystyle {\hat {f}}_{h}(x)={\frac {1}{n}}\sum _{i=1}^{n}{\frac {1}{h{\sqrt {2\pi }}}}\exp \left({\frac {-(x-x_{i})^{2}}{2h^{2}}}\right),} where h {\displaystyle h} is the standard deviation of the sample x {\displaystyle \mathbf {x} } . The construction of a kernel density estimate finds interpretations in fields outside of density estimation. For example, in thermodynamics, this is equivalent to the amount of heat generated when heat kernels (the fundamental solution to the heat equation) are placed at each data point locations xi. Similar methods are used to construct discrete Laplace operators on point clouds for manifold learning (e.g. diffusion map). == Example == Kernel density estimates are closely related to histograms, but can be endowed with properties such as smoothness or continuity by using a suitable kernel. The diagram below based on these 6 data points illustrates this relationship: For the histogram, first, the horizontal axis is divided into sub-intervals or bins which cover the range of the data: In this case, six bins each of width 2. Whenever a data point falls inside this interval, a box of height 1/12 is placed there. If more than one data point falls inside the same bin, the boxes are stacked on top of each other. For the kernel density estimate, normal kernels with a standard deviation of 1.5 (indicated by the red dashed lines) are placed on each of the data points xi. The kernels are summed to make the kernel density estimate (solid blue curve). The smoothness of the kernel density estimate (compared to the discreteness of the histogram) illustrates how kernel density estimates converge faster to the true underlying density for continuous random variables. == Bandwidth selection == The bandwidth of the kernel is a free parameter which exhibits a strong influence on the resulting estimate. To illustrate its effect, we take a simulated random sample from the standard normal distribution (plotted at the blue spikes in the rug plot on the horizontal axis). The grey curve is the true density (a normal density with mean 0 and variance 1). In comparison, the red curve is undersmoothed since it contains too many spurious data artifacts arising from using a bandwidth h = 0.05, which is too small. The green curve is oversmoothed since using the bandwidth h = 2 obscures much of the underlying structure. The black curve with a bandwidth of h = 0.337 is considered to be optimally smoothed since its density estimate is close to the true density. An extreme situation is encountered in the limit h → 0 {\displaystyle h\to 0} (no smoothing), where the estimate is a sum of n delta functions centered at the coordinates of analyzed samples. In the other extreme limit h → ∞ {\displaystyle h\to \infty } the estimate retains the shape of the used kernel, centered on the mean of the samples (completely smooth). The most common optimality criterion used to select this parameter is the expected L2 risk function, also termed the mean integrated squared error: MISE ( h ) = E [ ∫ ( f ^ h ( x ) − f ( x ) ) 2 d x ] {\displaystyle \operatorname {MISE} (h)=\operatorname {E} \!\left[\int \!{\left({\hat {f}}\!_{h}(x)-f(x)\right)}^{2}dx\right]} Under weak assumptions on f and K, (f is the, generally unknown, real density function), MISE ( h ) = AMISE ( h ) + o ( ( n h ) − 1 + h 4 ) {\displaystyle \operatorname {MISE} (h)=\operatorname {AMISE} (h)+{\mathcal {o}}{\left((nh)^{-1}+h^{4}\right)}} where o is the little o notation, and n the sample size (as above). The AMISE is the asymptotic MISE, i. e. the two leading terms, AMISE ( h ) = R ( K ) n h + 1 4 m 2 ( K ) 2 h 4 R ( f ″ ) {\displaystyle \operatorname {AMISE} (h)={\frac {R(K)}{nh}}+{\frac {1}{4}}m_{2}(K)^{2}h^{4}R(f'')} where R ( g ) = ∫ g ( x ) 2 d x {\textstyle R(g)=\int g(x)^{2}\,dx} for a function g, m 2 ( K ) = ∫ x 2 K ( x ) d x {\textstyle m_{2}(K)=\int x^{2}K(x)\,dx} and f ″ {\displaystyle f''} is the second derivative of f {\displaystyle f} and K {\displaystyle K} is the kernel. The minimum of this AMISE is the solution to this differential equation ∂ ∂ h AMISE ( h ) = − R ( K ) n h 2 + m 2 ( K ) 2 h 3 R ( f ″ ) = 0 {\displaystyle {\frac {\partial }{\partial h}}\operatorname {AMISE} (h)=-{\frac {R(K)}{nh^{2}}}+m_{2}(K)^{2}h^{3}R(f'')=0} or h AMISE = R ( K ) 1 / 5 m 2 ( K ) 2 / 5 R ( f ″ ) 1 / 5 n − 1 / 5 = C n − 1 / 5 {\displaystyle h_{\operatorname {AMISE} }={\frac {R(K)^{1/5}}{m_{2}(K)^{2/5}R(f'')^{1/5}}}n^{-1/5}=Cn^{-1/5}} Neither the AMISE nor the hAMISE formulas can be used directly since they involve the unknown density function f {\displaystyle f} or its second derivative f ″ {\displaystyle f''} . To overcome that difficulty, a variety of automatic, data-based methods have been developed to select the bandwidth. Several review studies have been undertaken to compare their efficacies, with the general consensus that the plug-in selectors and cross validation selectors are the most useful over a wide range of data sets. Substituting any bandwidth h which has the same asymptotic order n−1/5 as hAMISE into the AMISE gives that AMISE(h) = O(n−4/5), where O is the big O notation. It can be shown that, under weak assumptions, there cannot exist a non-parametric estimator that converges at a faster rate than the kernel estimator. Note that the n−4/5 rate is slower than the typical n−1 convergence rate of parametric methods. If the bandwidth is not held fixed, but is varied depending upon the location of either the estimate (balloon estimator) or the samples (pointwise estimator), this produces a particularly powerful method termed adaptive or variable bandwidth kernel density estimation. Bandwidth selection for kernel density estimation of heavy-tailed distributions is relatively difficult. === A rule-of-thumb bandwidth estimator === If Gaussian basis functions are used to approximate univariate data, and the underlying density being estimated is Gaussian, the optimal choice for h (that is, the bandwidth that minimises the mean integrated squared error) is: h = ( 4 σ ^ 5 3 n ) 1 / 5 ≈ 1.06 σ ^ n − 1 / 5 , {\displaystyle h={\left({\frac {4{\hat {\sigma }}^{5}}{3n}}\right)}^{1/5}\approx 1.06\,{\hat {\sigma }}\,n^{-1/5},} An h {\displaystyle h} value is considered more robust when it improves the fit for long-tailed and skewed distributions or for bimodal mixture distributions. This is often done empirically by replacing the standard deviation σ ^ {\displaystyle {\hat {\sigma }}} by the parameter A {\displaystyle A} below: A = min ( σ ^ , I Q R 1.34 ) {\displaystyle A=\min \left({\hat {\sigma }},{\frac {\mathrm {IQR} }{1.34}}\right)} where IQR is the
Semi-Automatic Ground Environment
The Semi-Automated Ground Environment (SAGE) was a system of large computers and associated networking equipment that coordinated data from many radar sites and processed it to produce a single unified image of the airspace over a wide area. SAGE directed and controlled the NORAD response to a possible Soviet air attack, operating in this role from the late 1950s into the 1980s. The processing power behind SAGE was supplied by the largest discrete component-based computer ever built, the AN/FSQ-7, manufactured by IBM. Each SAGE Direction Center (DC) housed an FSQ-7 which occupied an entire floor, approximately 22,000 square feet (2,000 m2) not including supporting equipment. The FSQ-7 was actually two computers, "A" side and "B" side. Computer processing was switched from "A" side to "B" side on a regular basis, allowing maintenance on the unused side. Information was fed to the DCs from a network of radar stations as well as readiness information from various defense sites. The computers, based on the raw radar data, developed "tracks" for the reported targets, and automatically calculated which defenses were within range. Operators used light guns to select targets on-screen for further information, select one of the available defenses, and issue commands to attack. These commands would then be automatically sent to the defense site via teleprinter. Connecting the various sites was an enormous network of telephones, modems and teleprinters. Later additions to the system allowed SAGE's tracking data to be sent directly to CIM-10 Bomarc missiles and some of the US Air Force's interceptor aircraft in-flight, directly updating their autopilots to maintain an intercept course without operator intervention. Each DC also forwarded data to a Combat Center (CC) for "supervision of the several sectors within the division" ("each combat center [had] the capability to coordinate defense for the whole nation"). SAGE became operational in the late 1950s and early 1960s at an estimated total cost between 8 and 12 billion dollars, four times the cost of the Manhattan Project. Throughout its development, there were continual concerns about its real ability to deal with large attacks, and the Operation Sky Shield tests showed that only about one-fourth of enemy bombers would have been intercepted. Nevertheless, SAGE was the backbone of NORAD's air defense system into the 1980s, by which time the tube-based FSQ-7s were increasingly costly to maintain and completely outdated. Today the same command and control task is carried out by microcomputers, based on the same basic underlying data. == Background == === Earlier systems === Just prior to World War II, Royal Air Force (RAF) tests with the new Chain Home (CH) radars had demonstrated that relaying information to the fighter aircraft directly from the radar sites was not feasible. The radars determined the map coordinates of the enemy, but could generally not see the fighters at the same time. This meant the fighters had to be able to determine where to fly to perform an interception but were often unaware of their own exact location and unable to calculate an interception while also flying their aircraft. The solution was to send all of the radar information to a central control station where operators collated the reports into single tracks, and then reported these tracks to the airbases, or sectors. The sectors used additional systems to track their own aircraft, plotting both on a single large map. Operators viewing the map could then see what direction their fighters would have to fly to approach their targets and relay that simply by telling them to fly along a certain heading or vector. This Dowding system was the first ground-controlled interception (GCI) system of large scale, covering the entirety of the UK. It proved enormously successful during the Battle of Britain, and is credited as being a key part of the RAF's success. The system was slow, often providing information that was up to five minutes out of date. Against propeller driven bombers flying at perhaps 225 miles per hour (362 km/h) this was not a serious concern, but it was clear the system would be of little use against jet-powered bombers flying at perhaps 600 miles per hour (970 km/h). The system was extremely expensive in manpower terms, requiring hundreds of telephone operators, plotters and trackers in addition to the radar operators. This was a serious drain on manpower, making it difficult to expand the network. The idea of using a computer to handle the task of taking reports and developing tracks had been explored beginning late in the war. By 1944, analog computers had been installed at the CH stations to automatically convert radar readings into map locations, eliminating two people. Meanwhile, the Royal Navy began experimenting with the Comprehensive Display System (CDS), another analog computer that took X and Y locations from a map and automatically generated tracks from repeated inputs. Similar systems began development with the Royal Canadian Navy, DATAR, and the US Navy, the Naval Tactical Data System (NTDS). A similar system was also specified for the Nike SAM project, specifically referring to a US version of CDS, coordinating the defense over a battle area so that multiple batteries did not fire on a single target. All of these systems were relatively small in geographic scale, generally tracking within a city-sized area. === Valley Committee === When the Soviet Union tested its first atomic bomb in August 1949, the topic of air defense of the US became important for the first time. A study group, the "Air Defense Systems Engineering Committee", was set up under the direction of Dr. George Valley to consider the problem and is known to history as the "Valley Committee". Their December report noted a key problem in air defense using ground-based radars. A bomber approaching a radar station would detect the signals from the radar long before the reflection off the bomber was strong enough to be detected by the station. The committee suggested that when this occurred, the bomber would descend to low altitude, thereby greatly limiting the radar horizon, allowing the bomber to fly past the station undetected. Although flying at low altitude greatly increased fuel consumption, the team calculated that the bomber would only need to do this for about 10% of its flight, making the fuel penalty acceptable. The only solution to this problem was to build a huge number of stations with overlapping coverage. At that point the problem became one of managing the information. Manual plotting was ruled out as too slow, and a computerized solution was the only possibility. To handle this task, the computer would need to be fed information directly, eliminating any manual translation by phone operators, and it would have to be able to analyze that information and automatically develop tracks. A system tasked with defending cities against the predicted future Soviet bomber fleet would have to be dramatically more powerful than the models used in the NTDS or DATAR. The Committee then had to consider whether or not such a computer was possible. The Valley Committee was introduced to Jerome Wiesner, associate director of the Research Laboratory of Electronics at MIT. Wiesner noted that the Servomechanisms Laboratory had already begun development of a machine that might be fast enough. This was the Whirlwind I, originally developed for the Office of Naval Research as a general purpose flight simulator that could simulate any current or future aircraft by changing its software. Wiesner introduced the Valley Committee to Whirlwind's project lead, Jay Forrester, who convinced him that Whirlwind was sufficiently capable. In September 1950, an early microwave early-warning radar system at Hanscom Field was connected to Whirlwind using a custom interface developed by Forrester's team. An aircraft was flown past the site, and the system digitized the radar information and successfully sent it to Whirlwind. With this demonstration, the technical concept was proven. Forrester was invited to join the committee. === Project Charles === With this successful demonstration, Louis Ridenour, chief scientist of the Air Force, wrote a memo stating "It is now apparent that the experimental work necessary to develop, test, and evaluate the systems proposals made by ADSEC will require a substantial amount of laboratory and field effort." Ridenour approached MIT President James Killian with the aim of beginning a development lab similar to the war-era Radiation Laboratory that made enormous progress in radar technology. Killian was initially uninterested, desiring to return the school to its peacetime civilian charter. Ridenour eventually convinced Killian the idea was sound by describing the way the lab would lead to the development of a local electronics industry based on the needs of the lab and the students who would leave the lab to start their