In software engineering, containerization is operating-system-level virtualization or application-level virtualization over multiple resources so that software applications can run in isolated user spaces called containers in any cloud or non-cloud environment, regardless of type or vendor. The term "container" has different meanings in different contexts, and it is important to ensure that the intended definition aligns with the audience's understanding. == Usage == Each container is basically a fully functional and portable cloud or non-cloud computing environment surrounding the application and keeping it independent of other environments running in parallel. Individually, each container simulates a different software application and runs isolated processes by bundling related configuration files, libraries and dependencies. But, collectively, multiple containers share a common operating system kernel (OS). In recent times, containerization technology has been widely adopted by cloud computing platforms like Amazon Web Services, Microsoft Azure, Google Cloud Platform, and IBM Cloud. Containerization has also been pursued by the U.S. Department of Defense as a way of more rapidly developing and fielding software updates, with first application in its F-22 air superiority fighter. == History == The concept of containerization in computing originated from early operating system–level isolation mechanisms. One of the earliest implementations was the chroot system call introduced in Version 7 Unix in 1979, which changed the apparent root directory for a process and its children, providing a basic form of filesystem isolation. In the early 2000s, more advanced forms of operating system–level virtualization were developed. FreeBSD introduced "jails" in 2000, which extended isolation by restricting processes to a subset of system resources. Around the same time, Solaris introduced "zones" (also known as Solaris Containers), providing similar capabilities with resource management and isolation features. Linux later incorporated comparable functionality through kernel features such as namespaces and control groups (cgroups), which enabled isolation of process IDs, network stacks, filesystems, and resource allocation. These features formed the foundation for Linux Containers (LXC), which provided a userspace interface for managing containers. The widespread adoption of containerization accelerated with the release of Docker in 2013, which introduced a standardized format for packaging applications and their dependencies, along with tooling for image distribution and container management. == Types of containers == OS containers Application containers == Security issues == Because of the shared OS, security threats can affect the whole containerized system. In containerized environments, security scanners generally protect the OS, but not the application containers, which adds unwanted vulnerability. == Container management, orchestration, clustering == Container orchestration or container management is mostly used in the context of application containers. Implementations providing such orchestration include Kubernetes and Docker swarm. == Container cluster management == Container clusters need to be managed. This includes functionality to create a cluster, to upgrade the software or repair it, balance the load between existing instances, scale by starting or stopping instances to adapt to the number of users, to log activities and monitor produced logs or the application itself by querying sensors. Open-source implementations of such software include OKD and Rancher. Quite a number of companies provide container cluster management as a managed service, like Alibaba, Amazon, Google, and Microsoft.
Decorrelation
Decorrelation is a general term for any process that is used to reduce autocorrelation within a signal, or cross-correlation within a set of signals, while preserving other aspects of the signal. A frequently used method of decorrelation is the use of a matched linear filter to reduce the autocorrelation of a signal as far as possible. Since the minimum possible autocorrelation for a given signal energy is achieved by equalising the power spectrum of the signal to be similar to that of a white noise signal, this is often referred to as signal whitening. == Process == === Signal processing === Most decorrelation algorithms are linear, but there are also non-linear decorrelation algorithms. Many data compression algorithms incorporate a decorrelation stage. For example, many transform coders first apply a fixed linear transformation that would, on average, have the effect of decorrelating a typical signal of the class to be coded, prior to any later processing. This is typically a Karhunen–Loève transform, or a simplified approximation such as the discrete cosine transform. By comparison, sub-band coders do not generally have an explicit decorrelation step, but instead exploit the already-existing reduced correlation within each of the sub-bands of the signal, due to the relative flatness of each sub-band of the power spectrum in many classes of signals. Linear predictive coders can be modelled as an attempt to decorrelate signals by subtracting the best possible linear prediction from the input signal, leaving a whitened residual signal. Decorrelation techniques can also be used for many other purposes, such as reducing crosstalk in a multi-channel signal, or in the design of echo cancellers. In image processing decorrelation techniques can be used to enhance or stretch, colour differences found in each pixel of an image. This is generally termed as 'decorrelation stretching'. === Neuroscience === In neuroscience, decorrelation is used in the analysis of the neural networks in the human visual system. The raw inputs from cone cells and rod cells under go many steps of processing before it is handled by the visual cortex. These steps generally perform decorrelation, both spatial (surround suppression in the retina) and temporal (handling of movement in the lateral geniculate nucleus). === Cryptography === In cryptography, decorrelation is used in cipher design (see Decorrelation theory) and in the design of hardware random number generators.
DeepL Translator
DeepL is a German AI research company known for its language AI platform, which includes DeepL Translator and DeepL Voice, and for DeepL Agent, an AI agent capable of planning workflows and using office systems and tools autonomously, in response to natural language instructions. Its algorithm uses the transformer architecture. It offers a paid subscription for additional features and access to its translation application programming interface. DeepL was founded in 2017 by Jaroslaw Kutylowski and is a unicorn, valued at $2 billion after a Series C funding round raised $300 million in May 2024. Its more than 200,000 business customers include a large proportion of the Fortune 500. == History == The translating system was first developed within Linguee by a team led by Chief Technology Officer Jarosław Kutyłowski in 2016. It was launched as DeepL Translator on 28 August 2017 and offered translations between English, German, French, Spanish, Italian, Polish and Dutch. At its launch, it claimed to have surpassed its competitors in blind tests and BLEU scores, including Google Translate, Amazon Translate, Microsoft Translator and Facebook's translation feature. With the release of DeepL in 2017, Linguee's company name was changed to DeepL GmbH, and it is also financed by advertising on its sister site, linguee.com. Support for Portuguese and Russian was added on 5 December 2018. In July 2019, Jarosław Kutyłowski became the CEO of DeepL GmbH and restructured the company into a Societas Europaea in 2021. Translation software for Microsoft Windows and macOS was released in September 2019. Support for Chinese (simplified) and Japanese was added on 19 March 2020, which the company claimed to have surpassed the aforementioned competitors as well as Baidu and Youdao. Then, 13 more European languages were added in March 2021: Bulgarian, Czech, Danish, Estonian, Finnish, Greek, Hungarian, Latvian, Lithuanian, Romanian, Slovak, Slovenian, and Swedish, bringing the total number of supported languages to 24. On 25 May 2022, support for Indonesian and Turkish was added, and support for Ukrainian was added on 14 September 2022. In January 2023, the company reached a valuation of 1 billion euro and became the most valued startup company in Cologne. At the end of the month, support for Korean and Norwegian (Bokmål) was also added. In May 2024, the company announced an investment of US$300 million at AI. In January 2026, more languages were supported, including Luxembourgish and Irish. == Services == === Translation method === The service uses a proprietary algorithm with convolutional neural networks (CNNs) that have been trained with the Linguee database. According to the developers, the service uses a newer improved architecture of neural networks, resulting in a more natural sound of translations than by competing services. The translation is generated using a supercomputer that reaches 5.1 petaflops and is operated in Iceland with hydropower. DeepL's data centers are located at the EcoDataCenter in Falun, Sweden, which is a data center for sustainability. In general, CNNs are slightly more suitable for long coherent word sequences, but they have so far not been used by the competition because of their weaknesses compared to recurrent neural networks. The weaknesses of DeepL are compensated for by supplemental techniques, some of which are publicly known. === Translator and subscription === The translator can be used for free with a maximum limit of 1,500 characters per translation. Microsoft Word and PowerPoint files in Office Open XML file formats (.docx and .pptx) and PDF files up to 5MB in size can also be translated. It offers paid subscription DeepL Pro, which has been available since March 2018 and includes application programming interface access and a software plug-in for computer-assisted translation tools, including SDL Trados Studio. Unlike the free version, translated texts are stated to not be saved on the server; also, the character limit is removed. The monthly pricing model includes a set amount of text, with texts beyond that being calculated according to the number of characters. ==== Supported languages ==== As of May 2026, the translation service supports the following languages: Additionally, these languages are currently in beta, indicated by an asterisk after their name in the language picker: === DeepL Write === In November 2022, DeepL launched a tool to improve monolingual texts in English and German, called DeepL Write. In December, the company removed access and informed journalists that it was only for internal use and that DeepL Write would be relaunched in early 2023. The public beta version was then released on January 17, 2023. In the summer of 2024, DeepL announced the availability of two more languages in DeepL Write: French and Spanish. By January 2024, DeepL had added an additional two: Portuguese (European and Brazilian) and Italian. === DeepL Agent === In November 2025, DeepL launched an AI agent called DeepL Agent which is capable of operating business applications in a human-like manner. == Reception == The reception of DeepL has been generally positive. TechCrunch appreciates it for the accuracy of its translations and stating that it was more accurate and nuanced than Google Translate. Le Monde thanks its developers for translating French text into more "French-sounding" expressions. RTL Z stated that DeepL Translator "offers better translations […] when it comes to Dutch to English and vice versa". La Repubblica, and a Latin American website, "WWWhat's new?", showed praise as well. A 2018 paper by the University of Bologna evaluated the Italian-to-German translation capabilities and found the preliminary results to be similar in quality to Google Translate. In September 2021, Slator remarked that the language industry response was more measured than the press and noted that DeepL is still highly regarded by users. A reviewer noted in 2018 that DeepL had far fewer languages available for translation than competing products. == Awards and honors == DeepL won the 2020 Webby Award for Best Practices and the 2020 Webby Award for Technical Achievement (Apps, Mobile, and Features), both in the category Apps, Mobile & Voice. In April 2025, DeepL was featured in the Forbes AI 50 list.
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Muller automaton
In automata theory, a Muller automaton is a type of an ω-automaton. The acceptance condition separates a Muller automaton from other ω-automata. The Muller automaton is defined using a Muller acceptance condition, i.e. the set of all states visited infinitely often must be an element of the acceptance set. Both deterministic and non-deterministic Muller automata recognize the ω-regular languages. They are named after David E. Muller, an American mathematician and computer scientist, who invented them in 1963. == Formal definition == Formally, a deterministic Muller-automaton is a tuple A = (Q,Σ,δ,q0,F) that consists of the following information: Q is a finite set. The elements of Q are called the states of A. Σ is a finite set called the alphabet of A. δ: Q × Σ → Q is a function, called the transition function of A. q0 is an element of Q, called the initial state. F is a set of sets of states. Formally, F ⊆ P(Q) where P(Q) is powerset of Q. F defines the acceptance condition. A accepts exactly those runs in which the set of infinitely often occurring states is an element of F In a non-deterministic Muller automaton, the transition function δ is replaced with a transition relation Δ that returns a set of states and the initial state q0 is replaced by a set of initial states Q0. Generally, 'Muller automaton' refers to a non-deterministic Muller automaton. For more comprehensive formalisation look at ω-automaton. == Equivalence with other ω-automata == The Muller automata are equally expressive as parity automata, Rabin automata, Streett automata, and non-deterministic Büchi automata, to mention some, and strictly more expressive than the deterministic Büchi automata. The equivalence of the above automata and non-deterministic Muller automata can be shown very easily as the accepting conditions of these automata can be emulated using the acceptance condition of Muller automata and vice versa. McNaughton's theorem demonstrates the equivalence of non-deterministic Büchi automaton and deterministic Muller automaton. Thus, deterministic and non-deterministic Muller automata are equivalent in terms of the languages they can accept. == Transformation to non-deterministic Muller automata == Following is a list of automata constructions that each transforms a type of ω-automata to a non-deterministic Muller automaton. From Büchi automata If B is the set of final states in a Büchi automaton with the set of states Q, we can construct a Muller automaton with same set of states, transition function and initial state with the Muller accepting condition as F = { X | X ∈ P(Q) ∧ X ∩ B ≠ ∅}. From Rabin automata/parity automata Similarly, the Rabin conditions ( E j , F j ) {\displaystyle (E_{j},F_{j})} can be emulated by constructing the acceptance set in the Muller automaton as all sets F ⊆ Q {\displaystyle F\subseteq Q} that satisfy F ∩ E j = ∅ {\displaystyle F\cap E_{j}=\emptyset } and F ∩ F j ≠ ∅ {\displaystyle F\cap F_{j}\neq \emptyset } , for some j. Note that this covers the case of parity automata too, as the parity acceptance condition can be expressed as a Rabin acceptance condition easily. From Streett automata The Streett conditions ( E j , F j ) {\displaystyle (E_{j},F_{j})} can be emulated by constructing the acceptance set in the Muller automaton as all sets F ⊆ Q {\displaystyle F\subseteq Q} that satisfy F ∩ F j = ∅ ⟹ F ∩ E j = ∅ {\displaystyle F\cap F_{j}=\emptyset \implies F\cap E_{j}=\emptyset } , for all j. == Transformation to deterministic Muller automata == From Büchi automaton McNaughton's theorem provides a procedure to transform any non-deterministic Büchi automaton into a deterministic Muller automaton.
Connected-component labeling
Connected-component labeling (CCL), connected-component analysis (CCA), blob extraction, region labeling, blob discovery, or region extraction is an algorithmic application of graph theory, where subsets of connected components are uniquely labeled based on a given heuristic. Connected-component labeling is not to be confused with segmentation. Connected-component labeling is used in computer vision to detect connected regions in binary digital images, although color images and data with higher dimensionality can also be processed. When integrated into an image recognition system or human-computer interaction interface, connected component labeling can operate on a variety of information. Blob extraction is generally performed on the resulting binary image from a thresholding step, but it can be applicable to gray-scale and color images as well. Blobs may be counted, filtered, and tracked. Blob extraction is related to but distinct from blob detection. == Overview == A graph, containing vertices and connecting edges, is constructed from relevant input data. The vertices contain information required by the comparison heuristic, while the edges indicate connected 'neighbors'. An algorithm traverses the graph, labeling the vertices based on the connectivity and relative values of their neighbors. Connectivity is determined by the medium; image graphs, for example, can be 4-connected neighborhood or 8-connected neighborhood. Following the labeling stage, the graph may be partitioned into subsets, after which the original information can be recovered and processed . == Definition == The usage of the term connected-component labeling (CCL) and its definition is quite consistent in the academic literature, whereas connected-component analysis (CCA) varies both in terminology and in its definition of the problem. Rosenfeld et al. define connected components labeling as the “[c]reation of a labeled image in which the positions associated with the same connected component of the binary input image have a unique label.” Shapiro et al. define CCL as an operator whose “input is a binary image and [...] output is a symbolic image in which the label assigned to each pixel is an integer uniquely identifying the connected component to which that pixel belongs.” There is no consensus on the definition of CCA in the academic literature. It is often used interchangeably with CCL. A more extensive definition is given by Shapiro et al.: “Connected component analysis consists of connected component labeling of the black pixels followed by property measurement of the component regions and decision making.” The definition for connected-component analysis presented here is more general, taking the thoughts expressed in into account. == Algorithms == The algorithms discussed can be generalised to arbitrary dimensions, albeit with increased time and space complexity. === One component at a time === This is a fast and very simple method to implement and understand. It is based on graph traversal methods in graph theory. In short, once the first pixel of a connected component is found, all the connected pixels of that connected component are labelled before going onto the next pixel in the image. This algorithm is part of Vincent and Soille's watershed segmentation algorithm, other implementations also exist. In order to do that a linked list is formed that will keep the indexes of the pixels that are connected to each other, steps (2) and (3) below. The method of defining the linked list specifies the use of a depth or a breadth first search. For this particular application, there is no difference which strategy to use. The simplest kind of a last in first out queue implemented as a singly linked list will result in a depth first search strategy. It is assumed that the input image is a binary image, with pixels being either background or foreground and that the connected components in the foreground pixels are desired. The algorithm steps can be written as: Start from the first pixel in the image. Set current label to 1. Go to (2). If this pixel is a foreground pixel and it is not already labelled, give it the current label and add it as the first element in a queue, then go to (3). If it is a background pixel or it was already labelled, then repeat (2) for the next pixel in the image. Pop out an element from the queue, and look at its neighbours (based on any type of connectivity). If a neighbour is a foreground pixel and is not already labelled, give it the current label and add it to the queue. Repeat (3) until there are no more elements in the queue. Go to (2) for the next pixel in the image and increment current label by 1. Note that the pixels are labelled before being put into the queue. The queue will only keep a pixel to check its neighbours and add them to the queue if necessary. This algorithm only needs to check the neighbours of each foreground pixel once and doesn't check the neighbours of background pixels. The pseudocode is: algorithm OneComponentAtATime(data) input : imageData[xDim][yDim] initialization : label = 0, labelArray[xDim][yDim] = 0, statusArray[xDim][yDim] = false, queue1, queue2; for i = 0 to xDim do for j = 0 to yDim do if imageData[i][j] has not been processed do if imageData[i][j] is a foreground pixel do check its four neighbors(north, south, east, west) : if neighbor is not processed do if neighbor is a foreground pixel do add it to queue1 else update its status to processed end if labelArray[i][j] = label (give label) statusArray[i][j] = true (update status) while queue1 is not empty do For each pixel in the queue do : check its four neighbors if neighbor is not processed do if neighbor is a foreground pixel do add it to queue2 else update its status to processed end if give it the current label update its status to processed remove the current element from queue1 copy queue2 into queue1 end While increase the label end if else update its status to processed end if end if end if end for end for === Two-pass === Relatively simple to implement and understand, the two-pass algorithm, (also known as the Hoshen–Kopelman algorithm) iterates through 2-dimensional binary data. The algorithm makes two passes over the image: the first pass to assign temporary labels and record equivalences, and the second pass to replace each temporary label by the smallest label of its equivalence class. The input data can be modified in situ (which carries the risk of data corruption), or labeling information can be maintained in an additional data structure. Connectivity checks are carried out by checking neighbor pixels' labels (neighbor elements whose labels are not assigned yet are ignored), or say, the north-east, the north, the north-west and the west of the current pixel (assuming 8-connectivity). 4-connectivity uses only north and west neighbors of the current pixel. The following conditions are checked to determine the value of the label to be assigned to the current pixel (4-connectivity is assumed) Conditions to check: Does the pixel to the left (west) have the same value as the current pixel? Yes – We are in the same region. Assign the same label to the current pixel No – Check next condition Do both pixels to the north and west of the current pixel have the same value as the current pixel but not the same label? Yes – We know that the north and west pixels belong to the same region and must be merged. Assign the current pixel the minimum of the north and west labels, and record their equivalence relationship No – Check next condition Does the pixel to the left (west) have a different value and the one to the north the same value as the current pixel? Yes – Assign the label of the north pixel to the current pixel No – Check next condition Do the pixel's north and west neighbors have different pixel values than current pixel? Yes – Create a new label id and assign it to the current pixel The algorithm continues this way, and creates new region labels whenever necessary. The key to a fast algorithm, however, is how this merging is done. This algorithm uses the union-find data structure which provides excellent performance for keeping track of equivalence relationships. Union-find essentially stores labels which correspond to the same blob in a disjoint-set data structure, making it easy to remember the equivalence of two labels by the use of an interface method E.g.: findSet(l). findSet(l) returns the minimum label value that is equivalent to the function argument 'l'. Once the initial labeling and equivalence recording is completed, the second pass merely replaces each pixel label with its equivalent disjoint-set representative element. A faster-scanning algorithm for connected-region extraction is presented below. On the first pass: Iterate through each element of the data by column, then by row (Raster Scanning) If the element is not the background Get the neighboring elements of the current element If there are no neighbors, uniquely
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