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Epaulette	Germany	Until World War I, officers of the Imperial German Army generally wore silver epaulettes as a distinguishing feature of their full-dress uniforms. For ranks up to and including captain these were "scale" epaulettes without fringes, for majors and colonels with fine fringes and for generals with a heavy fringe. The base of the epaulette was of regimental colors. For ordinary duty, dress "shoulder-cords" of silver braid intertwined with state colors, were worn.During the period 1919–1945, German Army uniforms were known for a four cord braided "figure-of-eight" decoration which acted as a shoulder board for senior and general officers. This was called a "shoulder knot" and was in silver with the specialty color piping (for field officers) and silver with red border (for generals). Although it was once seen on US Army uniforms, it remains only in the mess uniform. A similar form of shoulder knot was worn by officers of the British Army in full dress until 1914 and is retained by the Household Cavalry today. Epaulettes of this pattern are used by the Republic of Korea Army's general officers and were widely worn by officers of the armies of Venezuela, Chile, Colombia, Paraguay, Ecuador and Bolivia; all of which formerly wore uniforms closely following the Imperial German model. The Chilean Army still retains the German style of epaulette in the uniforms of its ceremonial units, the Military Academy and the NCO School while the 5th Cavalry Regiment "Aca Caraya" of the Paraguayan Army sports both epaulettes and shoulder knots in its dress uniforms (save for a platoon wearing Chaco War uniforms). Epaulettes of the German pattern (as well as shoulder knots) are used by officers of ceremonial units and schools of the Bolivian Army.
Epaulette	Haiti	Gold epaulettes in Haiti, were frequently worn throughout the 18th and 19th centuries in full dress. During the Haitian Revolution, Gen. Charles Leclerc of the French Army wrote a letter to Napoleon Bonaparte saying, "We must destroy half of those in the plains and must not leave a single colored person in the colony who has worn an epaulette.”
Epaulette	Ottoman Empire	During the Tanzimat period in the Ottoman Empire, western style uniforms and court dresses were adopted. Gold epaulettes were worn in full dress.
Epaulette	Russian Empire	Both the Imperial Russian Army and the Imperial Russian Navy sported different forms of epaulettes for its officers and senior NCOs. Today the current Kremlin Regiment continues the epaulette tradition. Types of epaulette of the Russian Empire 1. Infantry 1a. Subaltern-officer, here: poruchik of the 13th Life Grenadier Erivan His Imperial Majesty's regiment 1b. Staff-officer, here: polkovnik of the 46th Artillery brigade 1c. General, here: Field marshal of Russian Vyborg 85th infantry regiment of German Emperor Wilhelm II. 2. Guards 2a. Subaltern-officer, here: captain of the Mikhailovsky artillery school 2b. Staff-officer, here: polkovnik of Life Guards Lithuanian regiment. 2c. Flagofficer, here: Vice-Admiral 3. Cavalry 3a. Of the lower ranks, here: junior unteroffizier (junior non-commissioned officer) of the 3rd Smolensk lancers HIM Emperor Alexander III regiment 3b. Subaltern-officer, here: podyesaul of Russian Kizlyar-Grebensky 1st Cossack horse regiment. 3c. Staff-officer, here: lieutenant-colonel of the 2nd Life Dragoon Pskov Her Imperial Majesty Empress Maria Feodorovna regiment 3d. General, here: General of the cavalry. 4. Others 4a. Subaltern-officer, here: Titular councillor, veterinary physician. 4b. Staff-officer, here: flagship mechanical engineer, Fleet Engineer Mechanical Corps. 4c. General, here: Privy councillor, Professor of the Imperial Military medical Academy.
Epaulette	Sweden	Epaulettes first appeared on Swedish uniforms in the second half of the 18th century. The epaulette was officially incorporated into Swedish uniform regulations in 1792, although foreign recruited regiments had had them earlier. Senior officers were to wear golden crowns to distinguish their rank from lower ranking officers who wore golden stars. Epaulettes were discontinued on the field uniform in the mid-19th century, switching to rank insignia on the collar of the uniform jacket. Epaulettes were discontinued when they were removed from the general issue dress uniform in the 1930s. They are, however, still worn by the Royal Lifeguards and by military bands when in ceremonial full dress.
Epaulette	United Kingdom	Epaulettes first appeared on British uniforms in the second half of the 18th century. The epaulette was officially incorporated into Royal Navy uniform regulations in 1795, although some officers wore them before this date. Under this system, flag officers wore silver stars on their epaulettes to distinguish their ranks. A captain with at least three years seniority had two plain epaulettes, while a junior captain wore one on the right shoulder, and a commander one on the left.In 1855, army officers' large, gold-fringed epaulettes were abolished and replaced by a simplified equivalent officially known as twisted shoulder-cords. These were generally worn with full dress uniforms. Naval officers retained the historic fringed epaulettes for full dress during this period. These were officially worn until 1960 when they were replaced with shoulder boards. Today, only the officers of the Yeomen of the Guard, the Military Knights of Windsor, the Elder Brethren of Trinity House and the Lord Warden of the Cinque Ports retain fringed epaulettes.
Epaulette	United Kingdom	British cavalry on active service in the Sudan (1898) and during the Boer War (1899–1902) sometimes wore epaulettes made of chainmail to protect against sword blows landing on the shoulder. The blue "Number 1 dress" uniforms of some British cavalry regiments and yeomanry units still retain this feature in ornamental silvered form.With the introduction of khaki service dress in 1902, the British Army stopped wearing epaulettes in the field, switching to rank insignia embroidered on the cuffs of the uniform jacket. During World War I, this was found to make officers a target for snipers, so the insignia was frequently moved to the shoulder straps, where it was less conspicuous.The current multi-terrain pattern (MTP) and the older combat uniform (DPM) have the insignia formerly used on shoulder straps displayed on a single strap worn vertically in the centre of the chest. Earlier DPM uniforms had shoulder straps on the shoulders, though only officers wore rank on rank slides which attached to these straps, other ranks wore rank on the upper right sleeve at this time though later on regimental titles were worn on the rank slides. This practice continued into later patterns where rank was worn on the chest, rank was also added.
Epaulette	United Kingdom	In modern times, epaulettes are frequently worn by professionals within the ambulance service to signify clinical grade for easy identification. These are typically green in colour with gold writing and may contain one to three pips to signify higher managerial ranks.
Epaulette	United States	Epaulettes were authorized for the United States Navy in the first official uniform regulations, Uniform of the Navy of the United States, 1797. Captains wore an epaulette on each shoulder, lieutenants wore only one, on the right shoulder. By 1802, lieutenants wore their epaulette on the left shoulder, with lieutenants in command of a vessel wearing them on the right shoulder; after the creation of the rank of master commandants, they wore their epaulettes on the right shoulder similar to lieutenants in command. By 1842, captains wore epaulettes on each shoulder with a star on the straps, master commandant were renamed commander in 1838 and wore the same epaulettes as captains except the straps were plain, and lieutenants wore a single epaulette similar to those of the commander, on the left shoulder. After 1852, captains, commanders, lieutenants, pursers, surgeons, passed assistant and assistant surgeons, masters in the line of promotion and chief engineers wore epaulettes.Epaulettes were specified for all United States Army officers in 1832; infantry officers wore silver epaulettes, while those of the artillery and other branches wore gold epaulettes, following the French manner. The rank insignia was of a contrasting metal, silver on gold and vice versa.
Epaulette	United States	In 1851, the epaulettes became universally gold. Both majors and second lieutenants had no specific insignia. A major would have been recognizable as he would have worn a senior field officer's more elaborate epaulette fringes. The rank insignia was silver for senior officers and gold for the bars of captains and first lieutenants. The choice of silver eagles over gold ones is thought to be one of economy; there were more cavalry and artillery colonels than infantry, so replacing the numerically fewer gold ones was cheaper.
Epaulette	United States	Shoulder straps were adopted to replace epaulettes for field duty in 1836.
Epaulette	United States	Licensed officers of the U.S. Merchant Marine may wear shoulder marks and sleeve stripes appropriate to their rank and branch of service. Deck officers wear a foul anchor above the stripes on their shoulder marks, and engineering officers wear a three-bladed propeller. In the U.S. Merchant Marine, the correct wear of shoulder marks depicting the fouled anchor is with the un-fouled stock of the anchor forward on the wearer.
Epaulette	In popular culture	In literature, film and political satire, dictators, particularly of unstable Third World nations, are often depicted in military dress with oversized gold epaulettes.The eponymous character of Revolutionary Girl Utena along with the rest of the duelists have stylised epaulettes on their uniforms. The members of the Teikoku Kageki-dan from Sakura Wars have epaulettes on their uniforms. Grand Admiral Thrawn, a member on the Galactic Empire's Imperial Fleet on the Star Wars franchise including Star Wars Rebels wore gold epaulettes on his uniform. Clara Stahlbaum and Captain Philip Hoffman on the 2018 film The Nutcracker and the Four Realms wore epaulettes on their uniforms. The Genie wore gold epaulettes on some suits in the 1992 film Aladdin and the 1996 sequel Aladdin and the King of Thieves. Stephen Fry wore gold epaulettes when playing the Duke of Wellington on Blackadder the Third.
Artificial neural network	Artificial neural network	Artificial neural networks (ANNs, also shortened to neural networks (NNs) or neural nets) are a branch of machine learning models that are built using principles of neuronal organization discovered by connectionism in the biological neural networks constituting animal brains.An ANN is based on a collection of connected units or nodes called artificial neurons, which loosely model the neurons in a biological brain. Each connection, like the synapses in a biological brain, can transmit a signal to other neurons. An artificial neuron receives signals then processes them and can signal neurons connected to it. The "signal" at a connection is a real number, and the output of each neuron is computed by some non-linear function of the sum of its inputs. The connections are called edges. Neurons and edges typically have a weight that adjusts as learning proceeds. The weight increases or decreases the strength of the signal at a connection. Neurons may have a threshold such that a signal is sent only if the aggregate signal crosses that threshold.
Artificial neural network	Artificial neural network	Typically, neurons are aggregated into layers. Different layers may perform different transformations on their inputs. Signals travel from the first layer (the input layer), to the last layer (the output layer), possibly after traversing the layers multiple times.
Artificial neural network	Training	Neural networks learn (or are trained) by processing examples, each of which contains a known "input" and "result", forming probability-weighted associations between the two, which are stored within the data structure of the net itself. The training of a neural network from a given example is usually conducted by determining the difference between the processed output of the network (often a prediction) and a target output. This difference is the error. The network then adjusts its weighted associations according to a learning rule and using this error value. Successive adjustments will cause the neural network to produce output that is increasingly similar to the target output. After a sufficient number of these adjustments, the training can be terminated based on certain criteria. This is a form of supervised learning.
Artificial neural network	Training	Such systems "learn" to perform tasks by considering examples, generally without being programmed with task-specific rules. For example, in image recognition, they might learn to identify images that contain cats by analyzing example images that have been manually labeled as "cat" or "no cat" and using the results to identify cats in other images. They do this without any prior knowledge of cats, for example, that they have fur, tails, whiskers, and cat-like faces. Instead, they automatically generate identifying characteristics from the examples that they process.
Artificial neural network	History	The simplest kind of feedforward neural network (FNN) is a linear network, which consists of a single layer of output nodes; the inputs are fed directly to the outputs via a series of weights. The sum of the products of the weights and the inputs is calculated in each node. The mean squared errors between these calculated outputs and the given target values are minimized by creating an adjustment to the weights. This technique has been known for over two centuries as the method of least squares or linear regression. It was used as a means of finding a good rough linear fit to a set of points by Legendre (1805) and Gauss (1795) for the prediction of planetary movement.Wilhelm Lenz and Ernst Ising created and analyzed the Ising model (1925) which is essentially a non-learning artificial recurrent neural network (RNN) consisting of neuron-like threshold elements. In 1972, Shun'ichi Amari made this architecture adaptive. His learning RNN was popularised by John Hopfield in 1982.Warren McCulloch and Walter Pitts (1943) also considered a non-learning computational model for neural networks. In the late 1940s, D. O. Hebb created a learning hypothesis based on the mechanism of neural plasticity that became known as Hebbian learning. Farley and Wesley A. Clark (1954) first used computational machines, then called "calculators", to simulate a Hebbian network. In 1958, psychologist Frank Rosenblatt invented the perceptron, the first implemented artificial neural network, funded by the United States Office of Naval Research.Some say that research stagnated following Minsky and Papert (1969), who discovered that basic perceptrons were incapable of processing the exclusive-or circuit and that computers lacked sufficient power to process useful neural networks. However, by the time this book came out, methods for training multilayer perceptrons (MLPs) were already known.
Artificial neural network	History	The first deep learning MLP was published by Alexey Grigorevich Ivakhnenko and Valentin Lapa in 1965, as the Group Method of Data Handling. The first deep learning MLP trained by stochastic gradient descent was published in 1967 by Shun'ichi Amari.
Artificial neural network	History	In computer experiments conducted by Amari's student Saito, a five layer MLP with two modifiable layers learned useful internal representations to classify non-linearily separable pattern classes.Self-organizing maps (SOMs) were described by Teuvo Kohonen in 1982. SOMs are neurophysiologically inspired neural networks that learn low-dimensional representations of high-dimensional data while preserving the topological structure of the data. They are trained using competitive learning.The convolutional neural network (CNN) architecture with convolutional layers and downsampling layers was introduced by Kunihiko Fukushima in 1980. He called it the neocognitron. In 1969, he also introduced the ReLU (rectified linear unit) activation function. The rectifier has become the most popular activation function for CNNs and deep neural networks in general. CNNs have become an essential tool for computer vision.
Artificial neural network	History	The backpropagation algorithm is an efficient application of the Leibniz chain rule (1673) to networks of differentiable nodes. It is also known as the reverse mode of automatic differentiation or reverse accumulation, due to Seppo Linnainmaa (1970). The term "back-propagating errors" was introduced in 1962 by Frank Rosenblatt, but he did not have an implementation of this procedure, although Henry J. Kelley and Bryson had dynamic programming based continuous precursors of backpropagation already in 1960–61 in the context of control theory. In 1973, Dreyfus used backpropagation to adapt parameters of controllers in proportion to error gradients. In 1982, Paul Werbos applied backpropagation to MLPs in the way that has become standard. In 1986 Rumelhart, Hinton and Williams showed that backpropagation learned interesting internal representations of words as feature vectors when trained to predict the next word in a sequence.The time delay neural network (TDNN) of Alex Waibel (1987) combined convolutions and weight sharing and backpropagation. In 1988, Wei Zhang et al. applied backpropagation to a CNN (a simplified Neocognitron with convolutional interconnections between the image feature layers and the last fully connected layer) for alphabet recognition. In 1989, Yann LeCun et al. trained a CNN to recognize handwritten ZIP codes on mail. In 1992, max-pooling for CNNs was introduced by Juan Weng et al. to help with least-shift invariance and tolerance to deformation to aid 3D object recognition. LeNet-5 (1998), a 7-level CNN by Yann LeCun et al., that classifies digits, was applied by several banks to recognize hand-written numbers on checks digitized in 32x32 pixel images.
Artificial neural network	History	From 1988 onward, the use of neural networks transformed the field of protein structure prediction, in particular when the first cascading networks were trained on profiles (matrices) produced by multiple sequence alignments.In the 1980s, backpropagation did not work well for deep FNNs and RNNs. To overcome this problem, Juergen Schmidhuber (1992) proposed a hierarchy of RNNs pre-trained one level at a time by self-supervised learning. It uses predictive coding to learn internal representations at multiple self-organizing time scales. This can substantially facilitate downstream deep learning. The RNN hierarchy can be collapsed into a single RNN, by distilling a higher level chunker network into a lower level automatizer network. In 1993, a chunker solved a deep learning task whose depth exceeded 1000.In 1992, Juergen Schmidhuber also published an alternative to RNNs which is now called a linear Transformer or a Transformer with linearized self-attention (save for a normalization operator). It learns internal spotlights of attention: a slow feedforward neural network learns by gradient descent to control the fast weights of another neural network through outer products of self-generated activation patterns FROM and TO (which are now called key and value for self-attention). This fast weight attention mapping is applied to a query pattern.
Artificial neural network	History	The modern Transformer was introduced by Ashish Vaswani et al. in their 2017 paper "Attention Is All You Need." It combines this with a softmax operator and a projection matrix.
Artificial neural network	History	Transformers have increasingly become the model of choice for natural language processing. Many modern large language models such as ChatGPT, GPT-4, and BERT use it. Transformers are also increasingly being used in computer vision.In 1991, Juergen Schmidhuber also published adversarial neural networks that contest with each other in the form of a zero-sum game, where one network's gain is the other network's loss. The first network is a generative model that models a probability distribution over output patterns. The second network learns by gradient descent to predict the reactions of the environment to these patterns. This was called "artificial curiosity." In 2014, this principle was used in a generative adversarial network (GAN) by Ian Goodfellow et al. Here the environmental reaction is 1 or 0 depending on whether the first network's output is in a given set. This can be used to create realistic deepfakes.
Artificial neural network	History	Excellent image quality is achieved by Nvidia's StyleGAN (2018) based on the Progressive GAN by Tero Karras, Timo Aila, Samuli Laine, and Jaakko Lehtinen. Here the GAN generator is grown from small to large scale in a pyramidal fashion.
Artificial neural network	History	Sepp Hochreiter's diploma thesis (1991) was called "one of the most important documents in the history of machine learning" by his supervisor Juergen Schmidhuber. Hochreiter identified and analyzed the vanishing gradient problem and proposed recurrent residual connections to solve it. This led to the deep learning method called long short-term memory (LSTM), published in Neural Computation (1997). LSTM recurrent neural networks can learn "very deep learning" tasks with long credit assignment paths that require memories of events that happened thousands of discrete time steps before. The "vanilla LSTM" with forget gate was introduced in 1999 by Felix Gers, Schmidhuber and Fred Cummins. LSTM has become the most cited neural network of the 20th century.
Artificial neural network	History	In 2015, Rupesh Kumar Srivastava, Klaus Greff, and Schmidhuber used the LSTM principle to create the Highway network, a feedforward neural network with hundreds of layers, much deeper than previous networks. 7 months later, Kaiming He, Xiangyu Zhang; Shaoqing Ren, and Jian Sun won the ImageNet 2015 competition with an open-gated or gateless Highway network variant called Residual neural network. This has become the most cited neural network of the 21st century.The development of metal–oxide–semiconductor (MOS) very-large-scale integration (VLSI), in the form of complementary MOS (CMOS) technology, enabled increasing MOS transistor counts in digital electronics. This provided more processing power for the development of practical artificial neural networks in the 1980s.Neural networks' early successes included predicting the stock market and in 1995 a (mostly) self-driving car.Geoffrey Hinton et al. (2006) proposed learning a high-level representation using successive layers of binary or real-valued latent variables with a restricted Boltzmann machine to model each layer. In 2012, Ng and Dean created a network that learned to recognize higher-level concepts, such as cats, only from watching unlabeled images. Unsupervised pre-training and increased computing power from GPUs and distributed computing allowed the use of larger networks, particularly in image and visual recognition problems, which became known as "deep learning".Ciresan and colleagues (2010) showed that despite the vanishing gradient problem, GPUs make backpropagation feasible for many-layered feedforward neural networks. Between 2009 and 2012, ANNs began winning prizes in image recognition contests, approaching human level performance on various tasks, initially in pattern recognition and handwriting recognition. For example, the bi-directional and multi-dimensional long short-term memory (LSTM) of Graves et al. won three competitions in connected handwriting recognition in 2009 without any prior knowledge about the three languages to be learned.Ciresan and colleagues built the first pattern recognizers to achieve human-competitive/superhuman performance on benchmarks such as traffic sign recognition (IJCNN 2012).
Artificial neural network	Models	ANNs began as an attempt to exploit the architecture of the human brain to perform tasks that conventional algorithms had little success with. They soon reoriented towards improving empirical results, abandoning attempts to remain true to their biological precursors. ANNs have the ability to learn and model non-linearities and complex relationships. This is achieved by neurons being connected in various patterns, allowing the output of some neurons to become the input of others. The network forms a directed, weighted graph.An artificial neural network consists of simulated neurons. Each neuron is connected to other nodes via links like a biological axon-synapse-dendrite connection. All the nodes connected by links take in some data and use it to perform specific operations and tasks on the data. Each link has a weight, determining the strength of one node's influence on another, allowing weights to choose the signal between neurons.
Artificial neural network	Models	Artificial neurons ANNs are composed of artificial neurons which are conceptually derived from biological neurons. Each artificial neuron has inputs and produces a single output which can be sent to multiple other neurons. The inputs can be the feature values of a sample of external data, such as images or documents, or they can be the outputs of other neurons. The outputs of the final output neurons of the neural net accomplish the task, such as recognizing an object in an image.
Artificial neural network	Models	To find the output of the neuron we take the weighted sum of all the inputs, weighted by the weights of the connections from the inputs to the neuron. We add a bias term to this sum. This weighted sum is sometimes called the activation. This weighted sum is then passed through a (usually nonlinear) activation function to produce the output. The initial inputs are external data, such as images and documents. The ultimate outputs accomplish the task, such as recognizing an object in an image.
Artificial neural network	Models	Organization The neurons are typically organized into multiple layers, especially in deep learning. Neurons of one layer connect only to neurons of the immediately preceding and immediately following layers. The layer that receives external data is the input layer. The layer that produces the ultimate result is the output layer. In between them are zero or more hidden layers. Single layer and unlayered networks are also used. Between two layers, multiple connection patterns are possible. They can be 'fully connected', with every neuron in one layer connecting to every neuron in the next layer. They can be pooling, where a group of neurons in one layer connects to a single neuron in the next layer, thereby reducing the number of neurons in that layer. Neurons with only such connections form a directed acyclic graph and are known as feedforward networks. Alternatively, networks that allow connections between neurons in the same or previous layers are known as recurrent networks.
Artificial neural network	Models	Hyperparameter A hyperparameter is a constant parameter whose value is set before the learning process begins. The values of parameters are derived via learning. Examples of hyperparameters include learning rate, the number of hidden layers and batch size. The values of some hyperparameters can be dependent on those of other hyperparameters. For example, the size of some layers can depend on the overall number of layers.
Artificial neural network	Models	Learning Learning is the adaptation of the network to better handle a task by considering sample observations. Learning involves adjusting the weights (and optional thresholds) of the network to improve the accuracy of the result. This is done by minimizing the observed errors. Learning is complete when examining additional observations does not usefully reduce the error rate. Even after learning, the error rate typically does not reach 0. If after learning, the error rate is too high, the network typically must be redesigned. Practically this is done by defining a cost function that is evaluated periodically during learning. As long as its output continues to decline, learning continues. The cost is frequently defined as a statistic whose value can only be approximated. The outputs are actually numbers, so when the error is low, the difference between the output (almost certainly a cat) and the correct answer (cat) is small. Learning attempts to reduce the total of the differences across the observations. Most learning models can be viewed as a straightforward application of optimization theory and statistical estimation.
Artificial neural network	Models	Learning rate The learning rate defines the size of the corrective steps that the model takes to adjust for errors in each observation. A high learning rate shortens the training time, but with lower ultimate accuracy, while a lower learning rate takes longer, but with the potential for greater accuracy. Optimizations such as Quickprop are primarily aimed at speeding up error minimization, while other improvements mainly try to increase reliability. In order to avoid oscillation inside the network such as alternating connection weights, and to improve the rate of convergence, refinements use an adaptive learning rate that increases or decreases as appropriate. The concept of momentum allows the balance between the gradient and the previous change to be weighted such that the weight adjustment depends to some degree on the previous change. A momentum close to 0 emphasizes the gradient, while a value close to 1 emphasizes the last change.
Artificial neural network	Models	Cost function While it is possible to define a cost function ad hoc, frequently the choice is determined by the function's desirable properties (such as convexity) or because it arises from the model (e.g. in a probabilistic model the model's posterior probability can be used as an inverse cost).
Artificial neural network	Models	Backpropagation Backpropagation is a method used to adjust the connection weights to compensate for each error found during learning. The error amount is effectively divided among the connections. Technically, backprop calculates the gradient (the derivative) of the cost function associated with a given state with respect to the weights. The weight updates can be done via stochastic gradient descent or other methods, such as extreme learning machines, "no-prop" networks, training without backtracking, "weightless" networks, and non-connectionist neural networks.
Artificial neural network	Models	Learning paradigms Machine learning is commonly separated into three main learning paradigms, supervised learning, unsupervised learning and reinforcement learning. Each corresponds to a particular learning task.
Artificial neural network	Models	Supervised learning Supervised learning uses a set of paired inputs and desired outputs. The learning task is to produce the desired output for each input. In this case, the cost function is related to eliminating incorrect deductions. A commonly used cost is the mean-squared error, which tries to minimize the average squared error between the network's output and the desired output. Tasks suited for supervised learning are pattern recognition (also known as classification) and regression (also known as function approximation). Supervised learning is also applicable to sequential data (e.g., for handwriting, speech and gesture recognition). This can be thought of as learning with a "teacher", in the form of a function that provides continuous feedback on the quality of solutions obtained thus far.
Artificial neural network	Models	Unsupervised learning In unsupervised learning, input data is given along with the cost function, some function of the data x and the network's output. The cost function is dependent on the task (the model domain) and any a priori assumptions (the implicit properties of the model, its parameters and the observed variables). As a trivial example, consider the model f(x)=a where a is a constant and the cost C=E[(x−f(x))2] . Minimizing this cost produces a value of a that is equal to the mean of the data. The cost function can be much more complicated. Its form depends on the application: for example, in compression it could be related to the mutual information between x and f(x) , whereas in statistical modeling, it could be related to the posterior probability of the model given the data (note that in both of those examples, those quantities would be maximized rather than minimized). Tasks that fall within the paradigm of unsupervised learning are in general estimation problems; the applications include clustering, the estimation of statistical distributions, compression and filtering.
Artificial neural network	Models	Reinforcement learning In applications such as playing video games, an actor takes a string of actions, receiving a generally unpredictable response from the environment after each one. The goal is to win the game, i.e., generate the most positive (lowest cost) responses. In reinforcement learning, the aim is to weight the network (devise a policy) to perform actions that minimize long-term (expected cumulative) cost. At each point in time the agent performs an action and the environment generates an observation and an instantaneous cost, according to some (usually unknown) rules. The rules and the long-term cost usually only can be estimated. At any juncture, the agent decides whether to explore new actions to uncover their costs or to exploit prior learning to proceed more quickly.
Artificial neural network	Models	Formally the environment is modeled as a Markov decision process (MDP) with states s1,...,sn∈S and actions a1,...,am∈A . Because the state transitions are not known, probability distributions are used instead: the instantaneous cost distribution P(ct\|st) , the observation distribution P(xt\|st) and the transition distribution P(st+1\|st,at) , while a policy is defined as the conditional distribution over actions given the observations. Taken together, the two define a Markov chain (MC). The aim is to discover the lowest-cost MC.
Artificial neural network	Models	ANNs serve as the learning component in such applications. Dynamic programming coupled with ANNs (giving neurodynamic programming) has been applied to problems such as those involved in vehicle routing, video games, natural resource management and medicine because of ANNs ability to mitigate losses of accuracy even when reducing the discretization grid density for numerically approximating the solution of control problems. Tasks that fall within the paradigm of reinforcement learning are control problems, games and other sequential decision making tasks.
Artificial neural network	Models	Self-learning Self-learning in neural networks was introduced in 1982 along with a neural network capable of self-learning named crossbar adaptive array (CAA). It is a system with only one input, situation s, and only one output, action (or behavior) a. It has neither external advice input nor external reinforcement input from the environment. The CAA computes, in a crossbar fashion, both decisions about actions and emotions (feelings) about encountered situations. The system is driven by the interaction between cognition and emotion. Given the memory matrix, W =\|\|w(a,s)\|\|, the crossbar self-learning algorithm in each iteration performs the following computation: In situation s perform action a; Receive consequence situation s'; Compute emotion of being in consequence situation v(s'); Update crossbar memory w'(a,s) = w(a,s) + v(s').
Artificial neural network	Models	The backpropagated value (secondary reinforcement) is the emotion toward the consequence situation. The CAA exists in two environments, one is behavioral environment where it behaves, and the other is genetic environment, where from it initially and only once receives initial emotions about to be encountered situations in the behavioral environment. Having received the genome vector (species vector) from the genetic environment, the CAA will learn a goal-seeking behavior, in the behavioral environment that contains both desirable and undesirable situations.
Artificial neural network	Models	Neuroevolution Neuroevolution can create neural network topologies and weights using evolutionary computation. With modern enhancements, neuroevolution is competitive with sophisticated gradient descent approaches. One advantage of neuroevolution is that it may be less prone to get caught in "dead ends".
Artificial neural network	Models	Stochastic neural network Stochastic neural networks originating from Sherrington–Kirkpatrick models are a type of artificial neural network built by introducing random variations into the network, either by giving the network's artificial neurons stochastic transfer functions, or by giving them stochastic weights. This makes them useful tools for optimization problems, since the random fluctuations help the network escape from local minima. Stochastic neural networks trained using a Bayesian approach are known as Bayesian neural networks.
Artificial neural network	Models	Other In a Bayesian framework, a distribution over the set of allowed models is chosen to minimize the cost. Evolutionary methods, gene expression programming, simulated annealing, expectation-maximization, non-parametric methods and particle swarm optimization are other learning algorithms. Convergent recursion is a learning algorithm for cerebellar model articulation controller (CMAC) neural networks.
Artificial neural network	Models	Modes Two modes of learning are available: stochastic and batch. In stochastic learning, each input creates a weight adjustment. In batch learning weights are adjusted based on a batch of inputs, accumulating errors over the batch. Stochastic learning introduces "noise" into the process, using the local gradient calculated from one data point; this reduces the chance of the network getting stuck in local minima. However, batch learning typically yields a faster, more stable descent to a local minimum, since each update is performed in the direction of the batch's average error. A common compromise is to use "mini-batches", small batches with samples in each batch selected stochastically from the entire data set.
Artificial neural network	Types	ANNs have evolved into a broad family of techniques that have advanced the state of the art across multiple domains. The simplest types have one or more static components, including number of units, number of layers, unit weights and topology. Dynamic types allow one or more of these to evolve via learning. The latter is much more complicated but can shorten learning periods and produce better results. Some types allow/require learning to be "supervised" by the operator, while others operate independently. Some types operate purely in hardware, while others are purely software and run on general purpose computers.
Artificial neural network	Types	Some of the main breakthroughs include: convolutional neural networks that have proven particularly successful in processing visual and other two-dimensional data; long short-term memory avoid the vanishing gradient problem and can handle signals that have a mix of low and high frequency components aiding large-vocabulary speech recognition, text-to-speech synthesis, and photo-real talking heads; competitive networks such as generative adversarial networks in which multiple networks (of varying structure) compete with each other, on tasks such as winning a game or on deceiving the opponent about the authenticity of an input.
Artificial neural network	Network design	Neural architecture search (NAS) uses machine learning to automate ANN design. Various approaches to NAS have designed networks that compare well with hand-designed systems. The basic search algorithm is to propose a candidate model, evaluate it against a dataset, and use the results as feedback to teach the NAS network. Available systems include AutoML and AutoKeras. scikit-learn library provides functions to help with building a deep network from scratch. We can then implement a deep network with TensorFlow or Keras.
Artificial neural network	Network design	Design issues include deciding the number, type, and connectedness of network layers, as well as the size of each and the connection type (full, pooling, etc. ).
Artificial neural network	Network design	Hyperparameters must also be defined as part of the design (they are not learned), governing matters such as how many neurons are in each layer, learning rate, step, stride, depth, receptive field and padding (for CNNs), etc. The Python code snippet provides an overview of the training function, which uses the training dataset, number of hidden layer units, learning rate, and number of iterations as parameters:
Artificial neural network	Use	Using artificial neural networks requires an understanding of their characteristics. Choice of model: This depends on the data representation and the application. Overly complex models are slow learning. Learning algorithm: Numerous trade-offs exist between learning algorithms. Almost any algorithm will work well with the correct hyperparameters for training on a particular data set. However, selecting and tuning an algorithm for training on unseen data requires significant experimentation. Robustness: If the model, cost function and learning algorithm are selected appropriately, the resulting ANN can become robust.ANN capabilities fall within the following broad categories: Function approximation, or regression analysis, including time series prediction, fitness approximation and modeling. Classification, including pattern and sequence recognition, novelty detection and sequential decision making. Data processing, including filtering, clustering, blind source separation and compression. Robotics, including directing manipulators and prostheses.
Artificial neural network	Applications	Because of their ability to reproduce and model nonlinear processes, artificial neural networks have found applications in many disciplines. Application areas include system identification and control (vehicle control, trajectory prediction, process control, natural resource management), quantum chemistry, general game playing, pattern recognition (radar systems, face identification, signal classification, 3D reconstruction, object recognition and more), sensor data analysis, sequence recognition (gesture, speech, handwritten and printed text recognition), medical diagnosis, finance (e.g. ex-ante models for specific financial long-run forecasts and artificial financial markets), data mining, visualization, machine translation, social network filtering and e-mail spam filtering. ANNs have been used to diagnose several types of cancers and to distinguish highly invasive cancer cell lines from less invasive lines using only cell shape information.ANNs have been used to accelerate reliability analysis of infrastructures subject to natural disasters and to predict foundation settlements. It can also be useful to mitigate flood by the use of ANNs for modelling rainfall-runoff. ANNs have also been used for building black-box models in geoscience: hydrology, ocean modelling and coastal engineering, and geomorphology. ANNs have been employed in cybersecurity, with the objective to discriminate between legitimate activities and malicious ones. For example, machine learning has been used for classifying Android malware, for identifying domains belonging to threat actors and for detecting URLs posing a security risk. Research is underway on ANN systems designed for penetration testing, for detecting botnets, credit cards frauds and network intrusions.
Artificial neural network	Applications	ANNs have been proposed as a tool to solve partial differential equations in physics and simulate the properties of many-body open quantum systems. In brain research ANNs have studied short-term behavior of individual neurons, the dynamics of neural circuitry arise from interactions between individual neurons and how behavior can arise from abstract neural modules that represent complete subsystems. Studies considered long-and short-term plasticity of neural systems and their relation to learning and memory from the individual neuron to the system level.
Artificial neural network	Theoretical properties	Computational power The multilayer perceptron is a universal function approximator, as proven by the universal approximation theorem. However, the proof is not constructive regarding the number of neurons required, the network topology, the weights and the learning parameters. A specific recurrent architecture with rational-valued weights (as opposed to full precision real number-valued weights) has the power of a universal Turing machine, using a finite number of neurons and standard linear connections. Further, the use of irrational values for weights results in a machine with super-Turing power. Capacity A model's "capacity" property corresponds to its ability to model any given function. It is related to the amount of information that can be stored in the network and to the notion of complexity.
Artificial neural network	Theoretical properties	Two notions of capacity are known by the community. The information capacity and the VC Dimension. The information capacity of a perceptron is intensively discussed in Sir David MacKay's book which summarizes work by Thomas Cover. The capacity of a network of standard neurons (not convolutional) can be derived by four rules that derive from understanding a neuron as an electrical element. The information capacity captures the functions modelable by the network given any data as input. The second notion, is the VC dimension. VC Dimension uses the principles of measure theory and finds the maximum capacity under the best possible circumstances. This is, given input data in a specific form. As noted in, the VC Dimension for arbitrary inputs is half the information capacity of a Perceptron. The VC Dimension for arbitrary points is sometimes referred to as Memory Capacity.
Artificial neural network	Theoretical properties	Convergence Models may not consistently converge on a single solution, firstly because local minima may exist, depending on the cost function and the model. Secondly, the optimization method used might not guarantee to converge when it begins far from any local minimum. Thirdly, for sufficiently large data or parameters, some methods become impractical. Another issue worthy to mention is that training may cross some Saddle point which may lead the convergence to the wrong direction.
Artificial neural network	Theoretical properties	The convergence behavior of certain types of ANN architectures are more understood than others. When the width of network approaches to infinity, the ANN is well described by its first order Taylor expansion throughout training, and so inherits the convergence behavior of affine models. Another example is when parameters are small, it is observed that ANNs often fits target functions from low to high frequencies. This behavior is referred to as the spectral bias, or frequency principle, of neural networks. This phenomenon is the opposite to the behavior of some well studied iterative numerical schemes such as Jacobi method. Deeper neural networks have been observed to be more biased towards low frequency functions.
Artificial neural network	Theoretical properties	Generalization and statistics Applications whose goal is to create a system that generalizes well to unseen examples, face the possibility of over-training. This arises in convoluted or over-specified systems when the network capacity significantly exceeds the needed free parameters. Two approaches address over-training. The first is to use cross-validation and similar techniques to check for the presence of over-training and to select hyperparameters to minimize the generalization error.
Artificial neural network	Theoretical properties	The second is to use some form of regularization. This concept emerges in a probabilistic (Bayesian) framework, where regularization can be performed by selecting a larger prior probability over simpler models; but also in statistical learning theory, where the goal is to minimize over two quantities: the 'empirical risk' and the 'structural risk', which roughly corresponds to the error over the training set and the predicted error in unseen data due to overfitting.
Artificial neural network	Theoretical properties	Supervised neural networks that use a mean squared error (MSE) cost function can use formal statistical methods to determine the confidence of the trained model. The MSE on a validation set can be used as an estimate for variance. This value can then be used to calculate the confidence interval of network output, assuming a normal distribution. A confidence analysis made this way is statistically valid as long as the output probability distribution stays the same and the network is not modified.
Artificial neural network	Theoretical properties	By assigning a softmax activation function, a generalization of the logistic function, on the output layer of the neural network (or a softmax component in a component-based network) for categorical target variables, the outputs can be interpreted as posterior probabilities. This is useful in classification as it gives a certainty measure on classifications. The softmax activation function is: yi=exi∑j=1cexj
Artificial neural network	Criticism	Training A common criticism of neural networks, particularly in robotics, is that they require too much training for real-world operation. Potential solutions include randomly shuffling training examples, by using a numerical optimization algorithm that does not take too large steps when changing the network connections following an example, grouping examples in so-called mini-batches and/or introducing a recursive least squares algorithm for CMAC.
Artificial neural network	Criticism	Theory A central claim of ANNs is that they embody new and powerful general principles for processing information. These principles are ill-defined. It is often claimed that they are emergent from the network itself. This allows simple statistical association (the basic function of artificial neural networks) to be described as learning or recognition. In 1997, Alexander Dewdney commented that, as a result, artificial neural networks have a "something-for-nothing quality, one that imparts a peculiar aura of laziness and a distinct lack of curiosity about just how good these computing systems are. No human hand (or mind) intervenes; solutions are found as if by magic; and no one, it seems, has learned anything". One response to Dewdney is that neural networks handle many complex and diverse tasks, ranging from autonomously flying aircraft to detecting credit card fraud to mastering the game of Go.
Artificial neural network	Criticism	Technology writer Roger Bridgman commented: Neural networks, for instance, are in the dock not only because they have been hyped to high heaven, (what hasn't?) but also because you could create a successful net without understanding how it worked: the bunch of numbers that captures its behaviour would in all probability be "an opaque, unreadable table...valueless as a scientific resource".
Artificial neural network	Criticism	In spite of his emphatic declaration that science is not technology, Dewdney seems here to pillory neural nets as bad science when most of those devising them are just trying to be good engineers. An unreadable table that a useful machine could read would still be well worth having. Biological brains use both shallow and deep circuits as reported by brain anatomy, displaying a wide variety of invariance. Weng argued that the brain self-wires largely according to signal statistics and therefore, a serial cascade cannot catch all major statistical dependencies.
Artificial neural network	Criticism	Hardware Large and effective neural networks require considerable computing resources. While the brain has hardware tailored to the task of processing signals through a graph of neurons, simulating even a simplified neuron on von Neumann architecture may consume vast amounts of memory and storage. Furthermore, the designer often needs to transmit signals through many of these connections and their associated neurons – which require enormous CPU power and time.
Artificial neural network	Criticism	Schmidhuber noted that the resurgence of neural networks in the twenty-first century is largely attributable to advances in hardware: from 1991 to 2015, computing power, especially as delivered by GPGPUs (on GPUs), has increased around a million-fold, making the standard backpropagation algorithm feasible for training networks that are several layers deeper than before. The use of accelerators such as FPGAs and GPUs can reduce training times from months to days.Neuromorphic engineering or a physical neural network addresses the hardware difficulty directly, by constructing non-von-Neumann chips to directly implement neural networks in circuitry. Another type of chip optimized for neural network processing is called a Tensor Processing Unit, or TPU.
Artificial neural network	Criticism	Practical counterexamples Analyzing what has been learned by an ANN is much easier than analyzing what has been learned by a biological neural network. Furthermore, researchers involved in exploring learning algorithms for neural networks are gradually uncovering general principles that allow a learning machine to be successful. For example, local vs. non-local learning and shallow vs. deep architecture. Hybrid approaches Advocates of hybrid models (combining neural networks and symbolic approaches) say that such a mixture can better capture the mechanisms of the human mind.
Turbine engine failure	Turbine engine failure	A turbine engine failure occurs when a turbine engine unexpectedly stops producing power due to a malfunction other than fuel exhaustion. It often applies for aircraft, but other turbine engines can fail, like ground-based turbines used in power plants or combined diesel and gas vessels and vehicles.
Turbine engine failure	Reliability	Turbine engines in use on today's turbine-powered aircraft are very reliable. Engines operate efficiently with regularly scheduled inspections and maintenance. These units can have lives ranging in the tens of thousands of hours of operation. However, engine malfunctions or failures occasionally occur that require an engine to be shut down in flight. Since multi-engine airplanes are designed to fly with one engine inoperative and flight crews are trained to fly with one engine inoperative, the in-flight shutdown of an engine typically does not constitute a serious safety of flight issue.
Turbine engine failure	Reliability	The Federal Aviation Administration (FAA) was quoted as stating turbine engines have a failure rate of one per 375,000 flight hours, compared to of one every 3,200 flight hours for aircraft piston engines.
Turbine engine failure	Reliability	Due to "gross under-reporting" of general aviation piston engines in-flight shutdowns (IFSD), the FAA has no reliable data and assessed the rate "between 1 per 1,000 and 1 per 10,000 flight hours".Continental Motors reports the FAA states general aviation engines experience one failures or IFSD every 10,000 flight hours, and states its Centurion engines is one per 20,704 flight hours, lowering to one per 163,934 flight hours in 2013–2014.The General Electric GE90 has an in-flight shutdown rate (IFSD) of one per million engine flight-hours.
Turbine engine failure	Reliability	The Pratt & Whitney Canada PT6 is known for its reliability with an in-flight shutdown rate of one per 333,333 hours from 1963 to 2016, lowering to one per 651,126 hours over 12 months in 2016.
Turbine engine failure	Reliability	Emergency landing Following an engine shutdown, a precautionary landing is usually performed with airport fire and rescue equipment positioned near the runway. The prompt landing is a precaution against the risk that another engine will fail later in the flight or that the engine failure that has already occurred may have caused or been caused by other as-yet unknown damage or malfunction of aircraft systems (such as fire or damage to aircraft flight controls) that may pose a continuing risk to the flight. Once the airplane lands, fire department personnel assist with inspecting the airplane to ensure it is safe before it taxis to its parking position.
Turbine engine failure	Reliability	Rotorcraft Turboprop-powered aircraft and turboshaft-powered helicopters are also powered by turbine engines and are subject to engine failures for many similar reasons as jet-powered aircraft. In the case of an engine failure in a helicopter, it is often possible for the pilot to enter autorotation, using the unpowered rotor to slow the aircraft's descent and provide a measure of control, usually allowing for a safe emergency landing even without engine power.
Turbine engine failure	Shutdowns that are not engine failures	Most in-flight shutdowns are harmless and likely to go unnoticed by passengers. For example, it may be prudent for the flight crew to shut down an engine and perform a precautionary landing in the event of a low oil pressure or high oil temperature warning in the cockpit. However, passengers in a jet powered aircraft may become quite alarmed by other engine events such as a compressor surge — a malfunction that is typified by loud bangs and even flames from the engine's inlet and tailpipe. A compressor surge is a disruption of the airflow through a gas turbine jet engine that can be caused by engine deterioration, a crosswind over the engine's inlet, ice accumulation around the engine inlet, ingestion of foreign material, or an internal component failure such as a broken blade. While this situation can be alarming, the engine may recover with no damage.Other events that can happen with jet engines, such as a fuel control fault, can result in excess fuel in the engine's combustor. This additional fuel can result in flames extending from the engine's exhaust pipe. As alarming as this would appear, at no time is the engine itself actually on fire.Also, the failure of certain components in the engine may result in a release of oil into bleed air that can cause an odor or oily mist in the cabin. This is known as a fume event. The dangers of fume events are the subject of debate in both aviation and medicine.
Turbine engine failure	Possible causes	Engine failures can be caused by mechanical problems in the engine itself, such as damage to portions of the turbine or oil leaks, as well as damage outside the engine such as fuel pump problems or fuel contamination. A turbine engine failure can also be caused by entirely external factors, such as volcanic ash, bird strikes or weather conditions like precipitation or icing. Weather risks such as these can sometimes be countered through the usage of supplementary ignition or anti-icing systems.
Turbine engine failure	Failures during takeoff	A turbine-powered aircraft's takeoff procedure is designed around ensuring that an engine failure will not endanger the flight. This is done by planning the takeoff around three critical V speeds, V1, VR and V2. V1 is the critical engine failure recognition speed, the speed at which a takeoff can be continued with an engine failure, and the speed at which stopping distance is no longer guaranteed in the event of a rejected takeoff. VR is the speed at which the nose is lifted off the runway, a process known as rotation. V2 is the single-engine safety speed, the single engine climb speed. The use of these speeds ensure that either sufficient thrust to continue the takeoff, or sufficient stopping distance to reject it will be available at all times.
Turbine engine failure	Failure during extended operations	In order to allow twin-engined aircraft to fly longer routes that are over an hour from a suitable diversion airport, a set of rules known as ETOPS (Extended Twin-engine Operational Performance Standards) is used to ensure a twin turbine engine powered aircraft is able to safely arrive at a diversionary airport after an engine failure or shutdown, as well as to minimize the risk of a failure. ETOPS includes maintenance requirements, such as frequent and meticulously logged inspections and operation requirements such as flight crew training and ETOPS-specific procedures.
Turbine engine failure	Contained and uncontained failures	Engine failures may be classified as either as "contained" or "uncontained". A contained engine failure is one in which all internal rotating components remain within or embedded in the engine's case (including any containment wrapping that is part of the engine), or exit the engine through the tail pipe or air inlet.
Turbine engine failure	Contained and uncontained failures	An uncontained engine event occurs when an engine failure results in fragments of rotating engine parts penetrating and escaping through the engine case.The very specific technical distinction between a contained and uncontained engine failure derives from regulatory requirements for design, testing, and certification of aircraft engines under Part 33 of the U.S. Federal Aviation Regulations, which has always required turbine aircraft engines to be designed to contain damage resulting from rotor blade failure. Under Part 33, engine manufacturers are required to perform blade off tests to ensure containment of shrapnel if blade separation occurs. Blade fragments exiting the inlet or exhaust can still pose a hazard to the aircraft, and this should be considered by the aircraft designers. Note that a nominally contained engine failure can still result in engine parts departing the aircraft as long as the engine parts exit via the existing openings in the engine inlet or outlet, and do not create new openings in the engine case containment. Fan blade fragments departing via the inlet may also cause airframe parts such as the inlet duct and other parts of the engine nacelle to depart the aircraft due to deformation from the fan blade fragment's residual kinetic energy.
Turbine engine failure	Contained and uncontained failures	The containment of failed rotating parts is a complex process which involves high energy, high speed interactions of numerous locally and remotely located engine components (e.g., failed blade, other blades, containment structure, adjacent cases, bearings, bearing supports, shafts, vanes, and externally mounted components). Once the failure event starts, secondary events of a random nature may occur whose course and ultimate conclusion cannot be precisely predicted. Some of the structural interactions that have been observed to affect containment are the deformation and/or deflection of blades, cases, rotor, frame, inlet, casing rub strips, and the containment structure.Uncontained turbine engine disk failures within an aircraft engine present a direct hazard to an airplane and its crew and passengers because high-energy disk fragments can penetrate the cabin or fuel tanks, damage flight control surfaces, or sever flammable fluid or hydraulic lines. Engine cases are not designed to contain failed turbine disks. Instead, the risk of uncontained disk failure is mitigated by designating disks as safety-critical parts, defined as the parts of an engine whose failure is likely to present a direct hazard to the aircraft.
Turbine engine failure	Contained and uncontained failures	Notable uncontained engine failure accidents National Airlines Flight 27: a McDonnell Douglas DC-10 flying from Miami to San Francisco in 1973 had an overspeed failure of a General Electric CF6-6, resulting in one fatality.
Turbine engine failure	Contained and uncontained failures	Two LOT Polish Airlines flights, both Ilyushin Il-62s, suffered catastrophic uncontained engine failures in the 1980s. The first was in 1980 on LOT Polish Airlines Flight 7 where flight controls were destroyed, killing all 87 on board. In 1987, on LOT Polish Airlines Flight 5055, the aircraft's inner left (#2) engine, damaged the outer left (#1) engine, setting both on fire and causing loss of flight controls, leading to an eventual crash, which killed all 183 people on board. In both cases, the turbine shaft in engine #2 disintegrated due to production defects in the engines' bearings, which were missing rollers.
Turbine engine failure	Contained and uncontained failures	The Tu-154 crash near Krasnoyarsk was a major aircraft crash that occurred on Sunday, December 23, 1984, in the vicinity of Krasnoyarsk. The Tu-154B-2 airliner of the 1st Krasnoyarsk united aviation unit (Aeroflot) performed passenger flight SU-3519 on the Krasnoyarsk-Irkutsk route, but during the climb, engine No. 3 failed. The crew decided to return to the airport of departure, but during the landing approach a fire broke out, which destroyed the control systems and as a result, the plane crashed to the ground 3200 meters from the threshold of the runway of the Yemelyanovo airport and collapsed. Of the 111 people on board (104 passengers and 7 crew members), one survived. The cause of the catastrophe was the destruction of the disk of the first stage of the low pressure circuit of engine No. 3, which occurred due to the presence of fatigue cracks. The cracks were caused by a manufacturing defect – the inclusion of a titanium-nitrogen compound that has a higher microhardness than the original material. The methods used at that time for the manufacture and repair of disks, as well as the means of control, were found to be partially obsolete, which is why they did not ensure the effectiveness of control and detection of such a defect. The defect itself arose probably due to accidental ingestion of a titanium sponge or charge for smelting an ingot of a piece enriched with nitrogen.
Turbine engine failure	Contained and uncontained failures	Cameroon Airlines Flight 786: a Boeing 737 flying between Douala and Garoua, Cameroon in 1984 had a failure of a Pratt & Whitney JT8D-15 engine. Two people died.
Turbine engine failure	Contained and uncontained failures	British Airtours Flight 28M: a Boeing 737 flying from Manchester to Corfu in 1985 suffered an uncontained engine failure and fire on takeoff. The takeoff was aborted and the plane turned onto a taxiway and began evacuating. Fifty-five passengers and crew were unable to escape and died of smoke inhalation. The accident led to major changes to improve the survivability of aircraft evacuations.
Turbine engine failure	Contained and uncontained failures	United Airlines Flight 232: a McDonnell Douglas DC-10 flying from Denver to Chicago in 1989. The failure of the rear General Electric CF6-6 engine caused the loss of all hydraulics, forcing the pilots to attempt a landing using differential thrust. There were 111 fatalities. Prior to this crash, the probability of a simultaneous failure of all three hydraulic systems was considered as low as one in a billion. However, statistical models did not account for the position of the number-two engine, mounted at the tail close to hydraulic lines, nor the results of fragments released in many directions. Since then, aircraft engine designs have focused on keeping shrapnel from puncturing the cowling or ductwork, increasingly utilizing high-strength composite materials to achieve penetration resistance while keeping the weight low.
Turbine engine failure	Contained and uncontained failures	Baikal Airlines Flight 130: a starter of engine No. 2 on a Tu-154 heading from Irkutsk to Domodedovo, Moscow in 1994, failed to stop after engine startup and continued to operate at over 40,000 rpm with open bleed valves from engines, which caused an uncontained failure of the starter. A detached turbine disk damaged fuel and oil supply lines (which caused fire) and hydraulic lines. The fire-extinguishing system failed to stop the fire, and the plane diverted back to Irkutsk. However, due to loss of hydraulic pressure the crew lost control of the plane, which subsequently crashed into a dairy farm killing all 124 on board and one on the ground.
Turbine engine failure	Contained and uncontained failures	ValuJet 597: A DC-9-32 taking off from Hartsfield Jackson Atlanta International Airport on June 8, 1995, suffered an uncontained engine failure of the 7th stage high pressure compressor disk due to inadequate inspection of the corroded disk. The resulting rupture caused jet fuel to flow into the cabin and ignite, and the fire caused the jet to be a write-off.
Turbine engine failure	Contained and uncontained failures	Delta Air Lines Flight 1288: a McDonnell Douglas MD-88 flying from Pensacola, Florida to Atlanta in 1996 had a cracked compressor rotor hub failure on one of its Pratt & Whitney JT8D-219 engines. Two died.
Turbine engine failure	Contained and uncontained failures	TAM Flight 9755: a Fokker 100, departing Recife/Guararapes–Gilberto Freyre International Airport for São Paulo/Guarulhos International Airport on 15 September 2001, suffered an uncontained engine failure (Rolls-Royce RB.183 Tay) in which fragments of the engine shattered three cabin windows, causing decompression and pulling a passenger partly out of the plane. Another passenger held the passenger in until the aircraft landed, but the passenger blown out of the window died.
Turbine engine failure	Contained and uncontained failures	Qantas Flight 32: an Airbus A380 flying from London Heathrow to Sydney (via Singapore) in 2010 had an uncontained failure in a Rolls-Royce Trent 900 engine. The failure was found to have been caused by a misaligned counter bore within a stub oil pipe leading to a fatigue fracture. This in turn led to an oil leakage followed by an oil fire in the engine. The fire led to the release of the Intermediate Pressure Turbine (IPT) disc. The airplane, however, landed safely. This led to the grounding of the entire Qantas A380 fleet.
Turbine engine failure	Contained and uncontained failures	British Airways Flight 2276: a Boeing 777-200ER flying from Las Vegas to London in 2015 suffered an uncontained engine failure on its #1 GE90 engine during takeoff, resulting in a large fire on its port side. The aircraft successfully aborted takeoff and the plane was evacuated with no fatalities. American Airlines Flight 383: a Boeing 767-300ER flying from Chicago to Miami in 2016 suffered an uncontained engine failure on its #2 engine (General Electric CF6) during takeoff resulting in a large fire which destroyed the outer right wing. The aircraft aborted takeoff and was evacuated with 21 minor injuries, but no fatalities.
Turbine engine failure	Contained and uncontained failures	Air France Flight 66: an Airbus A380, registration F-HPJE performing flight from Paris, France, to Los Angeles, United States, was en route about 200 nautical miles (230 mi; 370 km) southeast of Nuuk, Greenland, when it suffered a catastrophic engine failure in 2017 (General Electric / Pratt & Whitney Engine Alliance GP7000). The crew descended the aircraft and diverted to Goose Bay, Canada, for a safe landing about two hours later.
Nuclear magnetic resonance	Nuclear magnetic resonance	Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are perturbed by a weak oscillating magnetic field (in the near field) and respond by producing an electromagnetic signal with a frequency characteristic of the magnetic field at the nucleus. This process occurs near resonance, when the oscillation frequency matches the intrinsic frequency of the nuclei, which depends on the strength of the static magnetic field, the chemical environment, and the magnetic properties of the isotope involved; in practical applications with static magnetic fields up to ca. 20 tesla, the frequency is similar to VHF and UHF television broadcasts (60–1000 MHz). NMR results from specific magnetic properties of certain atomic nuclei. Nuclear magnetic resonance spectroscopy is widely used to determine the structure of organic molecules in solution and study molecular physics and crystals as well as non-crystalline materials. NMR is also routinely used in advanced medical imaging techniques, such as in magnetic resonance imaging (MRI).
Nuclear magnetic resonance	Nuclear magnetic resonance	The most commonly used nuclei are 1H and 13C, although isotopes of many other elements, such as 19F, 31P, and33S, can be studied by high-field NMR spectroscopy as well. In order to interact with the magnetic field in the spectrometer, the nucleus must have an intrinsic nuclear magnetic moment and angular momentum. This occurs when an isotope has a nonzero nuclear spin, meaning an odd number of protons and/or neutrons (see Isotope). Nuclides with even numbers of both have a total spin of zero and are therefore NMR-inactive.

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