The artificial intelligence industry in Italy is growing and supports industrial development. In 2024 it reached a new record, reaching 1.2 billion euros with a growth of +58% compared to 2023. While in 2025, the growth of artificial intelligence in the industrial application was even greater than in 2024 both in terms of value and application to industrial sectors. == History == The roots of AI research in Italy extend back to the 1970s, when Italian scholars began exploring automated reasoning, programming language semantics, and pattern recognition. Researchers such as those involved in early projects at the National Research Council and various universities laid the groundwork for subsequent academic and industrial developments in the field. During this period, the focus was predominantly on developing algorithms for automated theorem proving and building systems to reason about complex mathematical problems. This era witnessed the birth of methodologies that would later influence numerous AI subfields, from natural language processing (NLP) to robotics. === Institutional milestones and academic contributions === A turning point in the Italian AI landscape was the formation of the Italian Association for Artificial Intelligence (AIxIA) in 1988. Founded by academics, including Luigia Carlucci Aiello, the association established a platform for collaboration between universities, research centers, and industry. Led by Aiello, AIIA played a role in promoting research, organizing national conferences, and fostering international partnerships that connected Italy's AI community to global networks. At the same time, professors such as Roberto Navigli and numerous practitioners contributed to the advancement of AI in Italy. Navigli has worked in multilingual NLP, including the creation of BabelNet, and led the Minerva project. === Industrial AI === Over recent decades, numerous national and European initiatives supported by funding from programs such as the National Recovery and Resilience Plan (PNRR) have spurred the transition from theoretical research to practical applications. Industrial sectors including manufacturing, banking, and healthcare increasingly embraced AI-driven automation, while research institutions collaborated with industrial partners to deploy cutting-edge solutions. In recent years, Italy has also seen the establishment of specialized research centers and institutes aimed at bridging the gap between academic innovation and industrial application. These initiatives indicate a broader national commitment to integrating AI into the fabric of Italian industry. == Recent developments == === Emergence of generative AI === A landmark in Italy's modern AI evolution is the development of Minerva AI. Developed by the Sapienza NLP research group at Sapienza University of Rome and led by Professor Roberto Navigli, Minerva represents the first family of large language models (LLMs) trained from scratch with a primary focus on the Italian language. ==== Minerva 7B ==== The latest iteration, Minerva 7B, has 7 billion parameters and has been trained on an extensive corpus of over 1.5 trillion words. By using advanced instruction tuning techniques, Minerva 7B is able to produce highly accurate, coherent, and contextually sensitive responses addressing common issues such as hallucinations and inappropriate content generation. This breakthrough sets a benchmark for transparent, open-source AI development in the country. Minerva's development, carried out within the FAIR (Future Artificial Intelligence Research) project in collaboration with CINECA and supported by supercomputing resources like the Leonardo (supercomputer), aligns closely with Italy's cultural and linguistic heritage. === Establishment of AI4I === The recent establishment of the Istituto Italiano per l’Intelligenza Artificiale (AI4I) is part of Italy's strategy to improve its industrial competitiveness in AI. This dedicated institute aims to bridge the gap between research institutions and industrial enterprises; promote training and R&D support to nurture the next generation of Italian AI experts; and enhance national competitiveness. This initiative is expected to serve as a hub for applied AI research, driving innovations that are tailored to the specific needs of Italian industry and public administration. === Benefits of InvestAI === Italy's AI industry stands to benefit from the European InvestAI initiative, a plan unveiled at the recent AI Action Summit in Paris. InvestAI is an effort by the European Commission to mobilize €200 billion for AI investments, with a dedicated €20 billion fund earmarked for building AI gigafactories. These gigafactories are planned as large-scale hubs for training advanced, complex AI models using approximately 100,000 last-generation AI chips. For Italy, this investment presents several major opportunities: Access to State-of-the-Art Infrastructure: Italian companies, research institutions, and start-ups can leverage the gigafactories’ immense computational resources, enabling them to train highly sophisticated language models and other AI systems. Enhanced Competitiveness and Collaboration: With InvestAI's layered funding model where EU funds help de-risk private investments Italian firms can access capital more readily. This will bolster public–private partnerships and create a more dynamic AI ecosystem that spans from academic research to industrial applications. Alignment with National and Regional Initiatives: The Istituto Italiano per l’Intelligenza Artificiale (AI4I), based in Turin, is already recognized as a strategic asset by both Italy and the European Union. As the main recipient of InvestAI funds in Italy, AI4I will play a pivotal role in implementing these investments locally, fostering innovation in sectors like manufacturing, healthcare and aerospace. Commission President Ursula von der Leyen emphasized that InvestAI is designed to democratize AI innovation throughout Europe by ensuring that even smaller companies have access to high-performance computing power. For Italy, this means not only keeping pace with global leaders but also harnessing European-scale investments to transform its AI industry and drive economic growth.
Contextual image classification
Contextual image classification, a topic of pattern recognition in computer vision, is an approach of classification based on contextual information in images. "Contextual" means this approach is focusing on the relationship of the nearby pixels, which is also called neighbourhood. The goal of this approach is to classify the images by using the contextual information. == Introduction == Similar as processing language, a single word may have multiple meanings unless the context is provided, and the patterns within the sentences are the only informative segments we care about. For images, the principle is same. Find out the patterns and associate proper meanings to them. As the image illustrated below, if only a small portion of the image is shown, it is very difficult to tell what the image is about. Even try another portion of the image, it is still difficult to classify the image. However, if we increase the contextual of the image, then it makes more sense to recognize. As the full images shows below, almost everyone can classify it easily. During the procedure of segmentation, the methods which do not use the contextual information are sensitive to noise and variations, thus the result of segmentation will contain a great deal of misclassified regions, and often these regions are small (e.g., one pixel). Compared to other techniques, this approach is robust to noise and substantial variations for it takes the continuity of the segments into account. Several methods of this approach will be described below. == Applications == === Functioning as a post-processing filter to a labelled image === This approach is very effective against small regions caused by noise. And these small regions are usually formed by few pixels or one pixel. The most probable label is assigned to these regions. However, there is a drawback of this method. The small regions also can be formed by correct regions rather than noise, and in this case the method is actually making the classification worse. This approach is widely used in remote sensing applications. === Improving the post-processing classification === This is a two-stage classification process: For each pixel, label the pixel and form a new feature vector for it. Use the new feature vector and combine the contextual information to assign the final label to the === Merging the pixels in earlier stages === Instead of using single pixels, the neighbour pixels can be merged into homogeneous regions benefiting from contextual information. And provide these regions to classifier. === Acquiring pixel feature from neighbourhood === The original spectral data can be enriched by adding the contextual information carried by the neighbour pixels, or even replaced in some occasions. This kind of pre-processing methods are widely used in textured image recognition. The typical approaches include mean values, variances, texture description, etc. === Combining spectral and spatial information === The classifier uses the grey level and pixel neighbourhood (contextual information) to assign labels to pixels. In such case the information is a combination of spectral and spatial information. === Powered by the Bayes minimum error classifier === Contextual classification of image data is based on the Bayes minimum error classifier (also known as a naive Bayes classifier). Present the pixel: A pixel is denoted as x 0 {\displaystyle x_{0}} . The neighbourhood of each pixel x 0 {\displaystyle x_{0}} is a vector and denoted as N ( x 0 ) {\displaystyle N(x_{0})} . The values in the neighbourhood vector is denoted as f ( x i ) {\displaystyle f(x_{i})} . Each pixel is presented by the vector ξ = ( f ( x 0 ) , f ( x 1 ) , … , f ( x k ) ) {\displaystyle \xi =\left(f(x_{0}),f(x_{1}),\ldots ,f(x_{k})\right)} x i ∈ N ( x 0 ) ; i = 1 , … , k {\displaystyle x_{i}\in N(x_{0});\quad i=1,\ldots ,k} The labels (classification) of pixels in the neighbourhood N ( x 0 ) {\displaystyle N(x_{0})} are presented as a vector η = ( θ 0 , θ 1 , … , θ k ) {\displaystyle \eta =\left(\theta _{0},\theta _{1},\ldots ,\theta _{k}\right)} θ i ∈ { ω 0 , ω 1 , … , ω k } {\displaystyle \theta _{i}\in \left\{\omega _{0},\omega _{1},\ldots ,\omega _{k}\right\}} ω s {\displaystyle \omega _{s}} here denotes the assigned class. A vector presents the labels in the neighbourhood N ( x 0 ) {\displaystyle N(x_{0})} without the pixel x 0 {\displaystyle x_{0}} η ^ = ( θ 1 , θ 2 , … , θ k ) {\displaystyle {\hat {\eta }}=\left(\theta _{1},\theta _{2},\ldots ,\theta _{k}\right)} The neighbourhood: Size of the neighbourhood. There is no limitation of the size, but it is considered to be relatively small for each pixel x 0 {\displaystyle x_{0}} . A reasonable size of neighbourhood would be 3 × 3 {\displaystyle 3\times 3} of 4-connectivity or 8-connectivity ( x 0 {\displaystyle x_{0}} is marked as red and placed in the centre). The calculation: Apply the minimum error classification on a pixel x 0 {\displaystyle x_{0}} , if the probability of a class ω r {\displaystyle \omega _{r}} being presenting the pixel x 0 {\displaystyle x_{0}} is the highest among all, then assign ω r {\displaystyle \omega _{r}} as its class. θ 0 = ω r if P ( ω r ∣ f ( x 0 ) ) = max s = 1 , 2 , … , R P ( ω s ∣ f ( x 0 ) ) {\displaystyle \theta _{0}=\omega _{r}\quad {\text{ if }}\quad P(\omega _{r}\mid f(x_{0}))=\max _{s=1,2,\ldots ,R}P(\omega _{s}\mid f(x_{0}))} The contextual classification rule is described as below, it uses the feature vector x 1 {\displaystyle x_{1}} rather than x 0 {\displaystyle x_{0}} . θ 0 = ω r if P ( ω r ∣ ξ ) = max s = 1 , 2 , … , R P ( ω s ∣ ξ ) {\displaystyle \theta _{0}=\omega _{r}\quad {\text{ if }}\quad P(\omega _{r}\mid \xi )=\max _{s=1,2,\ldots ,R}P(\omega _{s}\mid \xi )} Use the Bayes formula to calculate the posteriori probability P ( ω s ∣ ξ ) {\displaystyle P(\omega _{s}\mid \xi )} P ( ω s ∣ ξ ) = p ( ξ ∣ ω s ) P ( ω s ) p ( ξ ) {\displaystyle P(\omega _{s}\mid \xi )={\frac {p(\xi \mid \omega _{s})P(\omega _{s})}{p\left(\xi \right)}}} The number of vectors is the same as the number of pixels in the image. For the classifier uses a vector corresponding to each pixel x i {\displaystyle x_{i}} , and the vector is generated from the pixel's neighbourhood. The basic steps of contextual image classification: Calculate the feature vector ξ {\displaystyle \xi } for each pixel. Calculate the parameters of probability distribution p ( ξ ∣ ω s ) {\displaystyle p(\xi \mid \omega _{s})} and P ( ω s ) {\displaystyle P(\omega _{s})} Calculate the posterior probabilities P ( ω r ∣ ξ ) {\displaystyle P(\omega _{r}\mid \xi )} and all labels θ 0 {\displaystyle \theta _{0}} . Get the image classification result. == Algorithms == === Template matching === The template matching is a "brute force" implementation of this approach. The concept is first create a set of templates, and then look for small parts in the image match with a template. This method is computationally high and inefficient. It keeps an entire templates list during the whole process and the number of combinations is extremely high. For a m × n {\displaystyle m\times n} pixel image, there could be a maximum of 2 m × n {\displaystyle 2^{m\times n}} combinations, which leads to high computation. This method is a top down method and often called table look-up or dictionary look-up. === Lower-order Markov chain === The Markov chain also can be applied in pattern recognition. The pixels in an image can be recognised as a set of random variables, then use the lower order Markov chain to find the relationship among the pixels. The image is treated as a virtual line, and the method uses conditional probability. === Hilbert space-filling curves === The Hilbert curve runs in a unique pattern through the whole image, it traverses every pixel without visiting any of them twice and keeps a continuous curve. It is fast and efficient. === Markov meshes === The lower-order Markov chain and Hilbert space-filling curves mentioned above are treating the image as a line structure. The Markov meshes however will take the two dimensional information into account. === Dependency tree === The dependency tree is a method using tree dependency to approximate probability distributions.
Margin classifier
In machine learning (ML), a margin classifier is a type of classification model which is able to give an associated distance from the decision boundary for each data sample. For instance, if a linear classifier is used, the distance (typically Euclidean, though others may be used) of a sample from the separating hyperplane is the margin of that sample. The notion of margins is important in several ML classification algorithms, as it can be used to bound the generalization error of these classifiers. These bounds are frequently shown using the VC dimension. The generalization error bound in boosting algorithms and support vector machines is particularly prominent. == Margin for boosting algorithms == The margin for an iterative boosting algorithm given a dataset with two classes can be defined as follows: the classifier is given a sample pair ( x , y ) {\displaystyle (x,y)} , where x ∈ X {\displaystyle x\in X} is a domain space and y ∈ Y = { − 1 , + 1 } {\displaystyle y\in Y=\{-1,+1\}} is the sample's label. The algorithm then selects a classifier h j ∈ C {\displaystyle h_{j}\in C} at each iteration j {\displaystyle j} where C {\displaystyle C} is a space of possible classifiers that predict real values. This hypothesis is then weighted by α j ∈ R {\displaystyle \alpha _{j}\in R} as selected by the boosting algorithm. At iteration t {\displaystyle t} , the margin of a sample x {\displaystyle x} can thus be defined as y ∑ j t α j h j ( x ) ∑ | α j | . {\displaystyle {\frac {y\sum _{j}^{t}\alpha _{j}h_{j}(x)}{\sum |\alpha _{j}|}}.} By this definition, the margin is positive if the sample is labeled correctly, or negative if the sample is labeled incorrectly. This definition may be modified and is not the only way to define the margin for boosting algorithms. However, there are reasons why this definition may be appealing. == Examples of margin-based algorithms == Many classifiers can give an associated margin for each sample. However, only some classifiers utilize information of the margin while learning from a dataset. Many boosting algorithms rely on the notion of a margin to assign weight to samples. If a convex loss is utilized (as in AdaBoost or LogitBoost, for instance) then a sample with a higher margin will receive less (or equal) weight than a sample with a lower margin. This leads the boosting algorithm to focus weight on low-margin samples. In non-convex algorithms (e.g., BrownBoost), the margin still dictates the weighting of a sample, though the weighting is non-monotone with respect to the margin. == Generalization error bounds == One theoretical motivation behind margin classifiers is that their generalization error may be bound by the algorithm parameters and a margin term. An example of such a bound is for the AdaBoost algorithm. Let S {\displaystyle S} be a set of m {\displaystyle m} data points, sampled independently at random from a distribution D {\displaystyle D} . Assume the VC-dimension of the underlying base classifier is d {\displaystyle d} and m ≥ d ≥ 1 {\displaystyle m\geq d\geq 1} . Then, with probability 1 − δ {\displaystyle 1-\delta } , we have the bound: P D ( y ∑ j t α j h j ( x ) ∑ | α j | ≤ 0 ) ≤ P S ( y ∑ j t α j h j ( x ) ∑ | α j | ≤ θ ) + O ( 1 m d log 2 ( m / d ) / θ 2 + log ( 1 / δ ) ) {\displaystyle P_{D}\left({\frac {y\sum _{j}^{t}\alpha _{j}h_{j}(x)}{\sum |\alpha _{j}|}}\leq 0\right)\leq P_{S}\left({\frac {y\sum _{j}^{t}\alpha _{j}h_{j}(x)}{\sum |\alpha _{j}|}}\leq \theta \right)+O\left({\frac {1}{\sqrt {m}}}{\sqrt {d\log ^{2}(m/d)/\theta ^{2}+\log(1/\delta )}}\right)} for all θ > 0 {\displaystyle \theta >0} .
Automated Pain Recognition
Automated Pain Recognition (APR) is a method for objectively measuring pain and at the same time represents an interdisciplinary research area that comprises elements of medicine, psychology, psychobiology, and computer science. The focus is on computer-aided objective recognition of pain, implemented on the basis of machine learning. Automated pain recognition allows for the valid, reliable detection and monitoring of pain in people who are unable to communicate verbally. The underlying machine learning processes are trained and validated in advance by means of unimodal or multimodal body signals. Signals used to detect pain may include facial expressions or gestures and may also be of a (psycho-)physiological or paralinguistic nature. To date, the focus has been on identifying pain intensity, but visionary efforts are also being made to recognize the quality, site, and temporal course of pain. However, the clinical implementation of this approach is a controversial topic in the field of pain research. Critics of automated pain recognition argue that pain diagnosis can only be performed subjectively by humans. == Background == Pain diagnosis under conditions where verbal reporting is restricted - such as in verbally and/or cognitively impaired people or in patients who are sedated or mechanically ventilated - is based on behavioral observations by trained professionals. However, all known observation procedures (e.g., Zurich Observation Pain Assessment (ZOPA)); Pain Assessment in Advanced Dementia Scale (PAINAD) require a great deal of specialist expertise. These procedures can be made more difficult by perception- and interpretation-related misjudgments on the part of the observer. With regard to the differences in design, methodology, evaluation sample, and conceptualization of the phenomenon of pain, it is difficult to compare the quality criteria of the various tools. Even if trained personnel could theoretically record pain intensity several times a day using observation instruments, it would not be possible to measure it every minute or second. In this respect, the goal of automated pain recognition is to use valid, robust pain response patterns that can be recorded multimodally for a temporally dynamic, high-resolution, automated pain intensity recognition system. == Procedure == For automated pain recognition, pain-relevant parameters are usually recorded using non-invasive sensor technology, which captures data on the (physical) responses of the person in pain. This can be achieved with camera technology that captures facial expressions, gestures, or posture, while audio sensors record paralinguistic features. (Psycho-)physiological information such as muscle tone and heart rate can be collected via biopotential sensors (electrodes). Pain recognition requires the extraction of meaningful characteristics or patterns from the data collected. This is achieved using machine learning techniques that are able to provide an assessment of the pain after training (learning), e.g., "no pain," "mild pain," or "severe pain." == Parameters == Although the phenomenon of pain comprises different components (sensory discriminative, affective (emotional), cognitive, vegetative, and (psycho-)motor), automated pain recognition currently relies on the measurable parameters of pain responses. These can be divided roughly into the two main categories of "physiological responses" and "behavioral responses". === Physiological responses === In humans, pain almost always initiates autonomic nervous processes that are reflected measurably in various physiological signals. ==== Physiological signals ==== Measurements can include electrodermal activity (EDA, also skin conductance), electromyography (EMG), electrocardiogram (ECG), blood volume pulse (BVP), electroencephalogram (EEG), respiration, and body temperature, which are regulatory mechanisms of the sympathetic and parasympathetic systems. Physiological signals are mainly recorded using special non-invasive surface electrodes (for EDA, EMG, ECG, and EEG), a blood volume pulse sensor (BVP), a respiratory belt (respiration), and a thermal sensor (body temperature). Endocrinological and immunological parameters can also be recorded, but this requires measures that are somewhat invasive (e.g., blood sampling). === Behavioral responses === Behavioral responses to pain fulfil two functions: protection of the body (e.g., through protective reflexes) and external communication of the pain (e.g., as a cry for help). The responses are particularly evident in facial expressions, gestures, and paralinguistic features. ==== Facial expressions ==== Behavioral signals captured comprise facial expression patterns (expressive behavior), which are measured with the aid of video signals. Facial expression recognition is based on the everyday clinical observation that pain often manifests itself in the patient's facial expressions but that this is not necessarily always the case, since facial expressions can be inhibited through self-control. Despite the possibility that facial expressions may be influenced consciously, facial expression behavior represents an essential source of information for pain diagnosis and is thus also a source of information for automatic pain recognition. One advantage of video-based facial expression recognition is the contact-free measurement of the face, provided that it can be captured on video, which is not possible in every position (e.g., lying face down) or may be limited by bandages covering the face. Facial expression analysis relies on rapid, spontaneous, and temporary changes in neuromuscular activity that lead to visually detectable changes in the face. ==== Gestures ==== Gestures are also captured predominantly using non-contact camera technology. Motor pain responses vary and are strongly dependent on the type and cause of the pain. They range from abrupt protective reflexes (e.g., spontaneous retraction of extremities or doubling up) to agitation (pathological restlessness) and avoidance behavior (hesitant, cautious movements). ==== Paralinguistic features of language ==== Among other things, pain leads to nonverbal linguistic behavior that manifests itself in sounds such as sighing, gasping, moaning, whining, etc. Paralinguistic features are usually recorded using highly sensitive microphones. == Algorithms == After the recording, pre-processing (e.g., filtering), and extraction of relevant features, an optional information fusion can be performed. During this process, modalities from different signal sources are merged to generate new or more precise knowledge. The pain is classified using machine learning processes. The method chosen has a significant influence on the recognition rate and depends greatly on the quality and granularity of the underlying data. Similar to the field of affective computing, the following classifiers are currently being used: Support Vector Machine (SVM): The goal of an SVM is to find a clearly defined optimal hyperplane with the greatest minimal distance to two (or more) classes to be separated. The hyperplane acts as a decision function for classifying an unknown pattern. Random Forest (RF): RF is based on the composition of random, uncorrelated decision trees. An unknown pattern is judged individually by each tree and assigned to a class. The final classification of the patterns by the RF is then based on a majority decision. k-Nearest Neighbors (k-NN): The k-NN algorithm classifies an unknown object using the class label that most commonly classifies the k neighbors closest to it. Its neighbors are determined using a selected similarity measure (e.g., Euclidean distance, Jaccard coefficient, etc.). Artificial neural networks (ANNs): ANNs are inspired by biological neural networks and model their organizational principles and processes in a very simplified manner. Class patterns are learned by adjusting the weights of the individual neuronal connections. == Databases == In order to classify pain in a valid manner, it is necessary to create representative, reliable, and valid pain databases that are available to the machine learner for training. An ideal database would be sufficiently large and would consist of natural (not experimental), high-quality pain responses. However, natural responses are difficult to record and can only be obtained to a limited extent; in most cases they are characterized by suboptimal quality. The databases currently available therefore contain experimental or quasi-experimental pain responses, and each database is based on a different pain model. The following list shows a selection of the most relevant pain databases (last updated: April 2020): UNBC-McMaster Shoulder Pain BioVid Heat Pain EmoPain SenseEmotion X-ITE Pain
Mutation (evolutionary algorithm)
Mutation is a genetic operator used to maintain genetic diversity of the chromosomes of a population of an evolutionary algorithm (EA), including genetic algorithms in particular. It is analogous to biological mutation. The classic example of a mutation operator of a binary coded genetic algorithm (GA) involves a probability that an arbitrary bit in a genetic sequence will be flipped from its original state. A common method of implementing the mutation operator involves generating a random variable for each bit in a sequence. This random variable tells whether or not a particular bit will be flipped. This mutation procedure, based on the biological point mutation, is called single point mutation. Other types of mutation operators are commonly used for representations other than binary, such as floating-point encodings or representations for combinatorial problems. The purpose of mutation in EAs is to introduce diversity into the sampled population. Mutation operators are used in an attempt to avoid local minima by preventing the population of chromosomes from becoming too similar to each other, thus slowing or even stopping convergence to the global optimum. This reasoning also leads most EAs to avoid only taking the fittest of the population in generating the next generation, but rather selecting a random (or semi-random) set with a weighting toward those that are fitter. The following requirements apply to all mutation operators used in an EA: every point in the search space must be reachable by one or more mutations. there must be no preference for parts or directions in the search space (no drift). small mutations should be more probable than large ones. For different genome types, different mutation types are suitable. Some mutations are Gaussian, Uniform, Zigzag, Scramble, Insertion, Inversion, Swap, and so on. An overview and more operators than those presented below can be found in the introductory book by Eiben and Smith or in. == Bit string mutation == The mutation of bit strings ensue through bit flips at random positions. Example: The probability of a mutation of a bit is 1 l {\displaystyle {\frac {1}{l}}} , where l {\displaystyle l} is the length of the binary vector. Thus, a mutation rate of 1 {\displaystyle 1} per mutation and individual selected for mutation is reached. == Mutation of real numbers == Many EAs, such as the evolution strategy or the real-coded genetic algorithms, work with real numbers instead of bit strings. This is due to the good experiences that have been made with this type of coding. The value of a real-valued gene can either be changed or redetermined. A mutation that implements the latter should only ever be used in conjunction with the value-changing mutations and then only with comparatively low probability, as it can lead to large changes. In practical applications, the respective value range of the decision variables to be changed of the optimisation problem to be solved is usually limited. Accordingly, the values of the associated genes are each restricted to an interval [ x min , x max ] {\displaystyle [x_{\min },x_{\max }]} . Mutations may or may not take these restrictions into account. In the latter case, suitable post-treatment is then required as described below. === Mutation without consideration of restrictions === A real number x {\displaystyle x} can be mutated using normal distribution N ( 0 , σ ) {\displaystyle {\mathcal {N}}(0,\sigma )} by adding the generated random value to the old value of the gene, resulting in the mutated value x ′ {\displaystyle x'} : x ′ = x + N ( 0 , σ ) {\displaystyle x'=x+{\mathcal {N}}(0,\sigma )} In the case of genes with a restricted range of values, it is a good idea to choose the step size of the mutation σ {\displaystyle \sigma } so that it reasonably fits the range [ x min , x max ] {\displaystyle [x_{\min },x_{\max }]} of the gene to be changed, e.g.: σ = x max − x min 6 {\displaystyle \sigma ={\frac {x_{\text{max}}-x_{\text{min}}}{6}}} The step size can also be adjusted to the smaller permissible change range depending on the current value. In any case, however, it is likely that the new value x ′ {\displaystyle x'} of the gene will be outside the permissible range of values. Such a case must be considered a lethal mutation, since the obvious repair by using the respective violated limit as the new value of the gene would lead to a drift. This is because the limit value would then be selected with the entire probability of the values beyond the limit of the value range. The evolution strategy works with real numbers and mutation based on normal distribution. The step sizes are part of the chromosome and are subject to evolution together with the actual decision variables. === Mutation with consideration of restrictions === One possible form of changing the value of a gene while taking its value range [ x min , x max ] {\displaystyle [x_{\min },x_{\max }]} into account is the mutation relative parameter change of the evolutionary algorithm GLEAM (General Learning Evolutionary Algorithm and Method), in which, as with the mutation presented earlier, small changes are more likely than large ones. First, an equally distributed decision is made as to whether the current value x {\displaystyle x} should be increased or decreased and then the corresponding total change interval is determined. Without loss of generality, an increase is assumed for the explanation and the total change interval is then [ x , x max ] {\displaystyle [x,x_{\max }]} . It is divided into k {\displaystyle k} sub-areas of equal size with the width δ {\displaystyle \delta } , from which k {\displaystyle k} sub-change intervals of different size are formed: i {\displaystyle i} -th sub-change interval: [ x , x + δ ⋅ i ] {\displaystyle [x,x+\delta \cdot i]} with δ = ( x max − x ) k {\displaystyle \delta ={\frac {(x_{\text{max}}-x)}{k}}} and i = 1 , … , k {\displaystyle i=1,\dots ,k} Subsequently, one of the k {\displaystyle k} sub-change intervals is selected in equal distribution and a random number, also equally distributed, is drawn from it as the new value x ′ {\displaystyle x'} of the gene. The resulting summed probabilities of the sub-change intervals result in the probability distribution of the k {\displaystyle k} sub-areas shown in the adjacent figure for the exemplary case of k = 10 {\displaystyle k=10} . This is not a normal distribution as before, but this distribution also clearly favours small changes over larger ones. This mutation for larger values of k {\displaystyle k} , such as 10, is less well suited for tasks where the optimum lies on one of the value range boundaries. This can be remedied by significantly reducing k {\displaystyle k} when a gene value approaches its limits very closely. === Common properties === For both mutation operators for real-valued numbers, the probability of an increase and decrease is independent of the current value and is 50% in each case. In addition, small changes are considerably more likely than large ones. For mixed-integer optimization problems, rounding is usually used. == Mutation of permutations == Mutations of permutations are specially designed for genomes that are themselves permutations of a set. These are often used to solve combinatorial tasks. In the two mutations presented, parts of the genome are rotated or inverted. === Rotation to the right === The presentation of the procedure is illustrated by an example on the right: === Inversion === The presentation of the procedure is illustrated by an example on the right: === Variants with preference for smaller changes === The requirement raised at the beginning for mutations, according to which small changes should be more probable than large ones, is only inadequately fulfilled by the two permutation mutations presented, since the lengths of the partial lists and the number of shift positions are determined in an equally distributed manner. However, the longer the partial list and the shift, the greater the change in gene order. This can be remedied by the following modifications. The end index j {\displaystyle j} of the partial lists is determined as the distance d {\displaystyle d} to the start index i {\displaystyle i} : j = ( i + d ) mod | P 0 | {\displaystyle j=(i+d){\bmod {\left|P_{0}\right|}}} where d {\displaystyle d} is determined randomly according to one of the two procedures for the mutation of real numbers from the interval [ 0 , | P 0 | − 1 ] {\displaystyle \left[0,\left|P_{0}\right|-1\right]} and rounded. For the rotation, k {\displaystyle k} is determined similarly to the distance d {\displaystyle d} , but the value 0 {\displaystyle 0} is forbidden. For the inversion, note that i ≠ j {\displaystyle i\neq j} must hold, so for d {\displaystyle d} the value 0 {\displaystyle 0} must be excluded.
Materialized view
In computing, a materialized view is a database object that contains the results of a query. For example, it may be a local copy of data located remotely, or may be a subset of the rows and/or columns of a table or join result, or may be a summary using an aggregate function. The process of setting up a materialized view is sometimes called materialization. This is a form of caching the results of a query, similar to memoization of the value of a function in functional languages, and it is sometimes described as a form of precomputation. As with other forms of precomputation, database users typically use materialized views for performance reasons, i.e. as a form of optimization. Materialized views that store data based on remote tables were also known as snapshots (deprecated Oracle terminology). In any database management system following the relational model, a view is a virtual table representing the result of a database query. Whenever a query or an update addresses an ordinary view's virtual table, the DBMS converts these into queries or updates against the underlying base tables. A materialized view takes a different approach: the query result is cached as a concrete ("materialized") table (rather than a view as such) that may be updated from the original base tables from time to time. This enables much more efficient access, at the cost of extra storage and of some data being potentially out-of-date. Materialized views find use especially in data warehousing scenarios, where frequent queries of the actual base tables can be expensive. In a materialized view, indexes can be built on any column. In contrast, in a normal view, it's typically only possible to exploit indexes on columns that come directly from (or have a mapping to) indexed columns in the base tables; often this functionality is not offered at all. == Implementations == === Oracle === Materialized views were implemented first by the Oracle Database: the Query rewrite feature was added from version 8i. Example syntax to create a materialized view in Oracle: === PostgreSQL === In PostgreSQL, version 9.3 and newer natively support materialized views. In version 9.3, a materialized view is not auto-refreshed, and is populated only at time of creation (unless WITH NO DATA is used). It may be refreshed later manually using REFRESH MATERIALIZED VIEW. In version 9.4, the refresh may be concurrent with selects on the materialized view if CONCURRENTLY is used. Example syntax to create a materialized view in PostgreSQL: === SQL Server === Microsoft SQL Server differs from other RDBMS by the way of implementing materialized view via a concept known as "Indexed Views". The main difference is that such views do not require a refresh because they are in fact always synchronized to the original data of the tables that compound the view. To achieve this, it is necessary that the lines of origin and destination are "deterministic" in their mapping, which limits the types of possible queries to do this. This mechanism has been realised since the 2000 version of SQL Server. Example syntax to create a materialized view in SQL Server: === Stream processing frameworks === Apache Kafka (since v0.10.2), Apache Spark (since v2.0), Apache Flink, Kinetica DB, Materialize, RisingWave, and Epsio all support materialized views on streams of data. === Others === Materialized views are also supported in Sybase SQL Anywhere. In IBM Db2, they are called "materialized query tables". ClickHouse supports materialized views that automatically refresh on merges. MySQL doesn't support materialized views natively, but workarounds can be implemented by using triggers or stored procedures or by using the open-source application Flexviews. Materialized views can be implemented in Amazon DynamoDB using data modification events captured by DynamoDB Streams. Google announced in 8 April 2020 the availability of materialized views for BigQuery as a beta release.
Variable-order Bayesian network
Variable-order Bayesian network (VOBN) models provide an important extension of both the Bayesian network models and the variable-order Markov models. VOBN models are used in machine learning in general and have shown great potential in bioinformatics applications. These models extend the widely used position weight matrix (PWM) models, Markov models, and Bayesian network (BN) models. In contrast to the BN models, where each random variable depends on a fixed subset of random variables, in VOBN models these subsets may vary based on the specific realization of observed variables. The observed realizations are often called the context and, hence, VOBN models are also known as context-specific Bayesian networks. The flexibility in the definition of conditioning subsets of variables turns out to be a real advantage in classification and analysis applications, as the statistical dependencies between random variables in a sequence of variables (not necessarily adjacent) may be taken into account efficiently, and in a position-specific and context-specific manner.