Alexey Yakovlevich Chervonenkis (Russian: Алексей Яковлевич Червоненкис; 7 September 1938 – 22 September 2014) was a Soviet and Russian mathematician. Along with Vladimir Vapnik, he was one of the main developers of the Vapnik–Chervonenkis theory, also known as the "fundamental theory of learning", an important part of computational learning theory. Chervonenkis held joint appointments with the Russian Academy of Sciences and Royal Holloway, University of London. Alexey Chervonenkis got lost in Losiny Ostrov National Park on 22 September 2014, and later during a search operation was found dead near Mytishchi, a suburb of Moscow. He had died of hypothermia.
Cinema 4D
Cinema 4D is a 3D software suite developed by the German company Maxon. == Overview == As of R21, only a single version of Cinema 4D is available. It replaces all previous variants, including BodyPaint 3D, and includes all features of the past 'Studio' variant. With R21, all binaries were unified. There is no technical difference between commercial, educational, or demo versions. The difference is now only in licensing. 2014 saw the release of Cinema 4D Lite, which came packaged with Adobe After Effects Creative Cloud 2014. "Lite" acts as an introductory version, with many features withheld. This is part of a partnership between the two companies, where a Maxon-produced plug-in, called Cineware, allows any variant to create a seamless workflow with After Effects. The "Lite" variant is dependent on After Effects CC, needing the latter application running to launch, and is only sold as a package component included with After Effects CC through Adobe. Initially, Cinema 4D was developed for Amiga computers in the early 1990s, and the first three versions of the program were available exclusively for that platform. With v4, however, Maxon began to develop the application for Windows and Macintosh computers as well, citing the wish to reach a wider audience and the growing instability of the Amiga market following Commodore's bankruptcy. It was also released for BeOS. On Linux, Cinema 4D is available as a commandline rendering version. == Modules and older variants == From R12 to R20, Cinema 4D was available in four variants. A core Cinema 4D 'Prime' application, a 'Broadcast' version with additional motion-graphics features, 'Visualize,' which adds functions for architectural design and 'Studio,' which includes all modules. From Release 8 until Release 11.5, Cinema 4D had a modular approach to the application, with the ability to expand upon the core application with various modules. This ended with Release 12, though the functionality of these modules remains in the different flavors of Cinema 4D (Prime, Broadcast, Visualize, Studio) The old modules were: Advanced Render (global illumination/HDRI, caustics, ambient occlusion and sky simulation) BodyPaint 3D (direct painting on UVW meshes; now included in the core. In essence Cinema 4D Core/Prime and the BodyPaint 3D products are identical. The only difference between the two is the splash screen that is shown at startup and the default user interface.) Dynamics (for simulating soft body and rigid body dynamics) Hair (simulates hair, fur, grass, etc.) MOCCA (character animation and cloth simulation) MoGraph (Motion Graphics procedural modelling and animation toolset) NET Render (to render animations over a TCP/IP network in render farms) PyroCluster (simulation of smoke and fire effects) Prime (the core application) Broadcast (adds MoGraph2) Visualize (adds Virtual Walkthrough, Advanced Render, Sky, Sketch and Toon, data exchange, camera matching) Studio (the complete package) == Version history == == Use in industry == A number of films and related works have been modeled and rendered in Cinema 4D, including: == Cinebench == Cinebench is a cross-platform test suite which tests a computer's hardware capabilities. It can be used as a test for Cinema 4D's 3D modeling, animation, motion graphic and rendering performance on multiple CPU cores. The program "target[s] a certain niche and [is] better suited for high-end desktop and workstation platforms". Cinebench is commonly used to demonstrate hardware capabilities at tech shows to show a CPU performance, especially by tech YouTubers and review sites.
REEM
REEM is a prototype humanoid robot built by PAL Robotics in Spain. It is a 1.70 m high humanoid robot with 22 degrees of freedom, with a mobile base with wheels, allowing it to move at 4 km/hour. The upper part of the robot consists of a torso with a touch screen, two motorized arms, which give it a high degree of expression, and a head, which is also motorized. REEM-A and REEM-B are the first and second prototypes of humanoid robots created by PAL Robotics. REEM-B can recognize, grasp and lift objects and walk by itself, avoiding obstacles through simultaneous localization and mapping. The robot accepts voice commands and can recognize faces. == Specifications ==
SERVQUAL
SERVQUAL is a research tool that measures customer perception of service quality by comparing what customers expect from a service to their assessment of the service actually delivered. The instrument was developed in the United States in the mid-1980s by researchers A. Parasuraman, Valarie Zeithaml, and Leonard L. Berry, and is designed for use in after-service evaluation processes. It assesses service quality across five dimensions: reliability, assurance, tangibles, empathy, and responsiveness. SERVQUAL has been applied in sectors including healthcare, banking, education, and libraries. == Overview == The SERVQUAL questionnaire consists of matched pairs of items, 22 expectation items and 22 perception items, organized into five dimensions that correspond to the consumer's mental framework for evaluating service quality. Each item is part of a pair: one question asks what excellent organizations in a given industry should offer (expectation), and the other asks how the specific organization being evaluated performs (perception). == The model of service quality == The model of service quality, referred to as the gaps model, was developed by Parasuraman, Zeithaml, and Berry during a systematic research program conducted in the 1980s. The model identifies five gaps that may cause customers to experience poor service quality. In this framework, gap 5 is the service quality gap, which represents the difference between customer expectations and their perceptions of the service. This is the only gap that can be directly measured, and the SERVQUAL instrument was designed specifically to capture it. Gaps 1 through 4 have diagnostic value and point to probable causes of service failures. == Development of the instrument == Development of the model of service quality began in 1983 and, after iterative refinements, led to the publication of the SERVQUAL instrument in 1988. The research team conducted in-depth interviews and focus groups in four service sectors: retail banking, credit card services, securities brokerage, and product repair and maintenance. The questionnaire was tested across multiple samples to verify its reliability, validity, and factor structure. == Adaptations and variants == SERVQUAL has been adapted for specific industries and contexts. Well‑known derivatives include: LibQUAL+ – a library service quality survey developed by the Association of Research Libraries. EDUQUAL – an instrument tailored for the evaluation of service quality in educational institutions. HEALTHQUAL – adapted for measuring patient perceptions of healthcare service quality. ARTSQUAL – used to evaluate visitor perceptions of quality in museums and performing arts venues. == Criticisms == Researchers have raised several concerns about SERVQUAL. Critics argue that the instrument's definition of expectations is ambiguous and that it does not adequately account for the dynamic nature of customer expectations over time. Other scholars question whether the five‑dimension structure is universally applicable across all service contexts, and whether a generic instrument can capture the unique attributes of specific industries without modification.
Cerebellar model articulation controller
The cerebellar model arithmetic computer (CMAC) is a type of neural network based on a model of the mammalian cerebellum. It is also known as the cerebellar model articulation controller. It is a type of associative memory. The CMAC was first proposed as a function modeler for robotic controllers by James Albus in 1975 (hence the name), but has been extensively used in reinforcement learning and also as for automated classification in the machine learning community. The CMAC is an extension of the perceptron model. It computes a function for n {\displaystyle n} input dimensions. The input space is divided up into hyper-rectangles, each of which is associated with a memory cell. The contents of the memory cells are the weights, which are adjusted during training. Usually, more than one quantisation of input space is used, so that any point in input space is associated with a number of hyper-rectangles, and therefore with a number of memory cells. The output of a CMAC is the algebraic sum of the weights in all the memory cells activated by the input point. A change of value of the input point results in a change in the set of activated hyper-rectangles, and therefore a change in the set of memory cells participating in the CMAC output. The CMAC output is therefore stored in a distributed fashion, such that the output corresponding to any point in input space is derived from the value stored in a number of memory cells (hence the name associative memory). This provides generalisation. == Building blocks == In the adjacent image, there are two inputs to the CMAC, represented as a 2D space. Two quantising functions have been used to divide this space with two overlapping grids (one shown in heavier lines). A single input is shown near the middle, and this has activated two memory cells, corresponding to the shaded area. If another point occurs close to the one shown, it will share some of the same memory cells, providing generalisation. The CMAC is trained by presenting pairs of input points and output values, and adjusting the weights in the activated cells by a proportion of the error observed at the output. This simple training algorithm has a proof of convergence. It is normal to add a kernel function to the hyper-rectangle, so that points falling towards the edge of a hyper-rectangle have a smaller activation than those falling near the centre. One of the major problems cited in practical use of CMAC is the memory size required, which is directly related to the number of cells used. This is usually ameliorated by using a hash function, and only providing memory storage for the actual cells that are activated by inputs. == One-step convergent algorithm == Initially least mean square (LMS) method is employed to update the weights of CMAC. The convergence of using LMS for training CMAC is sensitive to the learning rate and could lead to divergence. In 2004, a recursive least squares (RLS) algorithm was introduced to train CMAC online. It does not need to tune a learning rate. Its convergence has been proved theoretically and can be guaranteed to converge in one step. The computational complexity of this RLS algorithm is O(N3). == Hardware implementation infrastructure == Based on QR decomposition, an algorithm (QRLS) has been further simplified to have an O(N) complexity. Consequently, this reduces memory usage and time cost significantly. A parallel pipeline array structure on implementing this algorithm has been introduced. Overall by utilizing QRLS algorithm, the CMAC neural network convergence can be guaranteed, and the weights of the nodes can be updated using one step of training. Its parallel pipeline array structure offers its great potential to be implemented in hardware for large-scale industry usage. == Continuous CMAC == Since the rectangular shape of CMAC receptive field functions produce discontinuous staircase function approximation, by integrating CMAC with B-splines functions, continuous CMAC offers the capability of obtaining any order of derivatives of the approximate functions. == Deep CMAC == In recent years, numerous studies have confirmed that by stacking several shallow structures into a single deep structure, the overall system could achieve better data representation, and, thus, more effectively deal with nonlinear and high complexity tasks. In 2018, a deep CMAC (DCMAC) framework was proposed and a backpropagation algorithm was derived to estimate the DCMAC parameters. Experimental results of an adaptive noise cancellation task showed that the proposed DCMAC can achieve better noise cancellation performance when compared with that from the conventional single-layer CMAC. == Summary ==
Deep learning
In machine learning, deep learning (DL) focuses on utilizing multilayered neural networks to perform tasks such as classification, regression, and representation learning. The field takes inspiration from biological neuroscience and revolves around stacking artificial neurons into layers and "training" them to process data. The adjective "deep" refers to the use of multiple layers (ranging from three to several hundred or thousands) in the network. Methods used can be supervised, semi-supervised or unsupervised. Some common deep learning network architectures include fully connected networks, deep belief networks, recurrent neural networks, convolutional neural networks, generative adversarial networks, transformers, and neural radiance fields. These architectures have been applied to fields including computer vision, speech recognition, natural language processing, machine translation, bioinformatics, drug design, medical image analysis, climate science, material inspection and board game programs, where they have produced results comparable to and in some cases surpassing human expert performance. Early forms of neural networks were inspired by information processing and distributed communication nodes in biological systems, particularly the human brain. However, current neural networks do not intend to model the brain function of organisms, and are generally seen as low-quality models for that purpose. == Overview == Most modern deep learning models are based on multi-layered neural networks such as convolutional neural networks and transformers, although they can also include propositional formulas or latent variables organized layer-wise in deep generative models such as the nodes in deep belief networks and deep Boltzmann machines. Fundamentally, deep learning refers to a class of machine learning algorithms in which a hierarchy of layers is used to transform input data into a progressively more abstract and composite representation. For example, in an image recognition model, the raw input may be an image (represented as a tensor of pixels). The first representational layer may attempt to identify basic shapes such as lines and circles, the second layer may compose and encode arrangements of edges, the third layer may encode a nose and eyes, and the fourth layer may recognize that the image contains a face. Importantly, a deep learning process can learn which features to optimally place at which level on its own. Prior to deep learning, machine learning techniques often involved hand-crafted feature engineering to transform the data into a more suitable representation for a classification algorithm to operate on. In the deep learning approach, features are not hand-crafted and the model discovers useful feature representations from the data automatically. This does not eliminate the need for hand-tuning; for example, varying numbers of layers and layer sizes can provide different degrees of abstraction. The word "deep" in "deep learning" refers to the number of layers through which the data is transformed. More precisely, deep learning systems have a substantial credit assignment path (CAP) depth. The CAP is the chain of transformations from input to output. CAPs describe potentially causal connections between input and output. For a feedforward neural network, the depth of the CAPs is that of the network and is the number of hidden layers plus one (as the output layer is also parameterized). For recurrent neural networks, in which a signal may propagate through a layer more than once, the CAP depth is potentially unlimited. No universally agreed-upon threshold of depth divides shallow learning from deep learning, but most researchers agree that deep learning involves CAP depth higher than two. CAP of depth two has been shown to be a universal approximator in the sense that it can emulate any function. Beyond that, more layers do not add to the function approximator ability of the network. Deep models (CAP > two) are able to extract better features than shallow models and hence, extra layers help in learning the features effectively. Deep learning architectures can be constructed with a greedy layer-by-layer method. Deep learning helps to disentangle these abstractions and pick out which features improve performance. Deep learning algorithms can be applied to unsupervised learning tasks. This is an important benefit because unlabeled data is more abundant than labeled data. Examples of deep structures that can be trained in an unsupervised manner are deep belief networks. The term deep learning was introduced to the machine learning community by Rina Dechter in 1986, and to artificial neural networks by Igor Aizenberg and colleagues in 2000, in the context of Boolean threshold neurons. The etymology of the term is more complicated. == Interpretations == Deep neural networks are generally interpreted in terms of the universal approximation theorem or probabilistic inference. The classic universal approximation theorem concerns the capacity of feedforward neural networks with a single hidden layer of finite size to approximate continuous functions. In 1989, the first proof was published by George Cybenko for sigmoid activation functions and was generalised to feed-forward multi-layer architectures in 1991 by Kurt Hornik. Recent work also showed that universal approximation also holds for non-bounded activation functions such as Kunihiko Fukushima's rectified linear unit. The universal approximation theorem for deep neural networks concerns the capacity of networks with bounded width but the depth is allowed to grow. Lu et al. proved that if the width of a deep neural network with ReLU activation is strictly larger than the input dimension, then the network can approximate any Lebesgue integrable function; if the width is smaller or equal to the input dimension, then a deep neural network is not a universal approximator. The probabilistic interpretation derives from the field of machine learning. It features inference, as well as the optimization concepts of training and testing, related to fitting and generalization, respectively. More specifically, the probabilistic interpretation considers the activation nonlinearity as a cumulative distribution function. The probabilistic interpretation led to the introduction of dropout as regularizer in neural networks. The probabilistic interpretation was introduced by researchers including Hopfield, Widrow and Narendra and popularized in surveys such as the one by Bishop. == History == === Before 1980 === There are two types of artificial neural network (ANN): feedforward neural network (FNN) or multilayer perceptron (MLP) and recurrent neural networks (RNN). RNNs have cycles in their connectivity structure, whereas FNNs do not. In the 1920s, Wilhelm Lenz and Ernst Ising created the Ising model which is essentially a non-learning RNN architecture consisting of neuron-like threshold elements. In 1972, Shun'ichi Amari made this architecture adaptive. His learning RNN was republished by John Hopfield in 1982. Other early recurrent neural networks were published by Kaoru Nakano in 1971. Already in 1948, Alan Turing produced work on "Intelligent Machinery" that was not published in his lifetime, containing "ideas related to artificial evolution and learning RNNs". Frank Rosenblatt (1958) proposed the perceptron, an MLP with 3 layers: an input layer, a hidden layer with randomized weights that did not learn, and an output layer. He later published a 1962 book that also introduced variants and computer experiments, including a version with four-layer perceptrons "with adaptive preterminal networks" where the last two layers have learned weights (here he credits H. D. Block and B. W. Knight). The book cites an earlier network by R. D. Joseph (1960) "functionally equivalent to a variation of" this four-layer system (the book mentions Joseph over 30 times). Should Joseph therefore be considered the originator of proper adaptive multilayer perceptrons with learning hidden units? Unfortunately, the learning algorithm was not a functional one, and fell into oblivion. The first working deep learning algorithm was the Group method of data handling, a method to train arbitrarily deep neural networks, published by Alexey Ivakhnenko and Lapa in 1965. They regarded it as a form of polynomial regression, or a generalization of Rosenblatt's perceptron to handle more complex, nonlinear, and hierarchical relationships. A 1971 paper described a deep network with eight layers trained by this method, which is based on layer by layer training through regression analysis. Superfluous hidden units are pruned using a separate validation set. Since the activation functions of the nodes are Kolmogorov-Gabor polynomials, these were also the first deep networks with multiplicative units or "gates". The first deep learning multilayer perceptron trained by stochastic gradient descent was published in 1967 by Shun'ichi
Mathematical model
A mathematical model is an abstract description of a concrete system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in many fields, including applied mathematics, natural sciences, social sciences and engineering. In particular, the field of operations research studies the use of mathematical modelling and related tools to solve problems in business or military operations. A model may help to characterize a system by studying the effects of different components, which may be used to make predictions about behavior or solve specific problems. == Elements of a mathematical model == Mathematical models can take many forms, including dynamical systems, statistical models, differential equations, or game theoretic models. These and other types of models can overlap, with a given model involving a variety of abstract structures. In many cases, the quality of a scientific field depends on how well the mathematical models developed on the theoretical side agree with results of repeatable experiments. Lack of agreement between theoretical mathematical models and experimental measurements often leads to important advances as better theories are developed. In the physical sciences, a traditional mathematical model contains most of the following elements: Governing equations Supplementary sub-models Defining equations Constitutive equations Assumptions and constraints Initial and boundary conditions Classical constraints and kinematic equations == Classifications == Mathematical models are of different types: === Linear vs. nonlinear === If all the operators in a mathematical model exhibit linearity, the resulting mathematical model is defined as linear. All other models are considered nonlinear. The definition of linearity and nonlinearity is dependent on context, and linear models may have nonlinear expressions in them. For example, in a statistical linear model, it is assumed that a relationship is linear in the parameters, but it may be nonlinear in the predictor variables. Similarly, a differential equation is said to be linear if it can be written with linear differential operators, but it can still have nonlinear expressions in it. In a mathematical programming model, if the objective functions and constraints are represented entirely by linear equations, then the model is regarded as a linear model. If one or more of the objective functions or constraints are represented with a nonlinear equation, then the model is known as a nonlinear model. Linear structure implies that a problem can be decomposed into simpler parts that can be treated independently or analyzed at a different scale, and therefore that the results will remain valid if the initial is recomposed or rescaled. Nonlinearity, even in fairly simple systems, is often associated with phenomena such as chaos and irreversibility. Although there are exceptions, nonlinear systems and models tend to be more difficult to study than linear ones. A common approach to nonlinear problems is linearization, but this can be problematic if one is trying to study aspects such as irreversibility, which are strongly tied to nonlinearity. === Static vs. dynamic === A dynamic model accounts for time-dependent changes in the state of the system, while a static (or steady-state) model calculates the system in equilibrium, and thus is time-invariant. Dynamic models are typically represented by differential equations or difference equations. === Explicit vs. implicit === If all of the input parameters of the overall model are known, and the output parameters can be calculated by a finite series of computations, the model is said to be explicit. But sometimes it is the output parameters which are known, and the corresponding inputs must be solved for by an iterative procedure, such as Newton's method or Broyden's method. In such a case the model is said to be implicit. For example, a jet engine's physical properties such as turbine and nozzle throat areas can be explicitly calculated given a design thermodynamic cycle (air and fuel flow rates, pressures, and temperatures) at a specific flight condition and power setting, but the engine's operating cycles at other flight conditions and power settings cannot be explicitly calculated from the constant physical properties. === Discrete vs. continuous === A discrete model treats objects as discrete, such as the particles in a molecular model or the states in a statistical model; while a continuous model represents the objects in a continuous manner, such as the velocity field of fluid in pipe flows, temperatures and stresses in a solid, and electric field that applies continuously over the entire model due to a point charge. === Deterministic vs. probabilistic (stochastic) === A deterministic model is one in which every set of variable states is uniquely determined by parameters in the model and by sets of previous states of these variables; therefore, a deterministic model always performs the same way for a given set of initial conditions. Conversely, in a stochastic model—usually called a "statistical model"—randomness is present, and variable states are not described by unique values, but rather by probability distributions. === Deductive, inductive, or floating === A deductive model is a logical structure based on a theory. An inductive model arises from empirical findings and generalization from them. If a model rests on neither theory nor observation, it may be described as a 'floating' model. Application of mathematics in social sciences outside of economics has been criticized for unfounded models. Application of catastrophe theory in science has been characterized as a floating model. === Strategic vs. non-strategic === Models used in game theory are distinct in the sense that they model agents with incompatible incentives, such as competing species or bidders in an auction. Strategic models assume that players are autonomous decision makers who rationally choose actions that maximize their objective function. A key challenge of using strategic models is defining and computing solution concepts such as the Nash equilibrium. An interesting property of strategic models is that they separate reasoning about rules of the game from reasoning about behavior of the players. == Construction == In business and engineering, mathematical models may be used to maximize a certain output. The system under consideration will require certain inputs. The system relating inputs to outputs depends on other variables too: decision variables, state variables, exogenous variables, and random variables. Decision variables are sometimes known as independent variables. Exogenous variables are sometimes known as parameters or constants. The variables are not independent of each other as the state variables are dependent on the decision, input, random, and exogenous variables. Furthermore, the output variables are dependent on the state of the system (represented by the state variables). Objectives and constraints of the system and its users can be represented as functions of the output variables or state variables. The objective functions will depend on the perspective of the model's user. Depending on the context, an objective function is also known as an index of performance, as it is some measure of interest to the user. Although there is no limit to the number of objective functions and constraints a model can have, using or optimizing the model becomes more involved (computationally) as the number increases. For example, economists often apply linear algebra when using input–output models. Complicated mathematical models that have many variables may be consolidated by use of vectors where one symbol represents several variables. === A priori information === Mathematical modeling problems are often classified into black box or white box models, according to how much a priori information on the system is available. A black-box model is a system of which there is no a priori information available. A white-box model (also called glass box or clear box) is a system where all necessary information is available. Practically all systems are somewhere between the black-box and white-box models, so this concept is useful only as an intuitive guide for deciding which approach to take. Usually, it is preferable to use as much a priori information as possible to make the model more accurate. Therefore, the white-box models are usually considered easier, because if you have used the information correctly, then the model will behave correctly. Often the a priori information comes in forms of knowing the type of functions relating different variables. For example, if we make a model of how a medicine works in a human system, we know that usually the amount of medicine in the blood is an exponentially decaying function, but we are still left with several unknown parameters; how