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  Empowerment (artificial intelligence)

  Empowerment in the field of artificial intelligence formalises and quantifies (via information theory) the potential an agent perceives that it has to influence its environment. An agent which follows an empowerment maximising policy, acts to maximise future options (typically up to some limited horizon). Empowerment can be used as a (pseudo) utility function that depends only on information gathered from the local environment to guide action, rather than seeking an externally imposed goal, thus is a form of intrinsic motivation. The empowerment formalism depends on a probabilistic model commonly used in artificial intelligence. An autonomous agent operates in the world by taking in sensory information and acting to change its state, or that of the environment, in a cycle of perceiving and acting known as the perception-action loop. Agent state and actions are modelled by random variables ( S : s ∈ S , A : a ∈ A {\displaystyle S:s\in {\mathcal {S}},A:a\in {\mathcal {A}}} ) and time ( t {\displaystyle t} ). The choice of action depends on the current state, and the future state depends on the choice of action, thus the perception-action loop unrolled in time forms a causal bayesian network. == Definition == Empowerment ( E {\displaystyle {\mathfrak {E}}} ) is defined as the channel capacity ( C {\displaystyle C} ) of the actuation channel of the agent, and is formalised as the maximal possible information flow between the actions of the agent and the effect of those actions some time later. Empowerment can be thought of as the future potential of the agent to affect its environment, as measured by its sensors. E := C ( A t ⟶ S t + 1 ) ≡ max p ( a t ) I ( A t ; S t + 1 ) {\displaystyle {\mathfrak {E}}:=C(A_{t}\longrightarrow S_{t+1})\equiv \max _{p(a_{t})}I(A_{t};S_{t+1})} In a discrete time model, Empowerment can be computed for a given number of cycles into the future, which is referred to in the literature as 'n-step' empowerment. E ( A t n ⟶ S t + n ) = max p ( a t , . . . , a t + n − 1 ) I ( A t , . . . , A t + n − 1 ; S t + n ) {\displaystyle {\mathfrak {E}}(A_{t}^{n}\longrightarrow S_{t+n})=\max _{p(a_{t},...,a_{t+n-1})}I(A_{t},...,A_{t+n-1};S_{t+n})} The unit of empowerment depends on the logarithm base. Base 2 is commonly used in which case the unit is bits. === Contextual Empowerment === In general the choice of action (action distribution) that maximises empowerment varies from state to state. Knowing the empowerment of an agent in a specific state is useful, for example to construct an empowerment maximising policy. State-specific empowerment can be found using the more general formalism for 'contextual empowerment'. C {\displaystyle C} is a random variable describing the context (e.g. state). E ( A t n ⟶ S t + n ∣ C ) = ∑ c ∈ C p ( c ) E ( A t n ⟶ S t + n ∣ C = c ) {\displaystyle {\mathfrak {E}}(A_{t}^{n}\longrightarrow S_{t+n}{\mid }C)=\sum _{c{\in }C}p(c){\mathfrak {E}}(A_{t}^{n}\longrightarrow S_{t+n}{\mid }C=c)} == Application == Empowerment maximisation can be used as a pseudo-utility function to enable agents to exhibit intelligent behaviour without requiring the definition of external goals, for example balancing a pole in a cart-pole balancing scenario where no indication of the task is provided to the agent. Empowerment has been applied in studies of collective behaviour and in continuous domains. As is the case with Bayesian methods in general, computation of empowerment becomes computationally expensive as the number of actions and time horizon extends, but approaches to improve efficiency have led to usage in real-time control. Empowerment has been used for intrinsically motivated reinforcement learning agents playing video games, and in the control of underwater vehicles.

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  Application-release automation

  Application-release automation (ARA) refers to the process of packaging and deploying an application or update of an application from development, across various environments, and ultimately to production. ARA solutions must combine the capabilities of deployment automation, environment management and modeling, and release coordination. == Relationship with DevOps == ARA tools help cultivate DevOps best practices by providing a combination of automation, environment modeling and workflow-management capabilities. These practices help teams deliver software rapidly, reliably and responsibly. ARA tools achieve a key DevOps goal of implementing continuous delivery with a large quantity of releases quickly. == Relationship with deployment == ARA is more than just software-deployment automation – it deploys applications using structured release-automation techniques that allow for an increase in visibility for the whole team. It combines workload automation and release-management tools as they relate to release packages, as well as movement through different environments within the DevOps pipeline. ARA tools help regulate deployments, how environments are created and deployed, and how and when releases are deployed. == ARA Solutions == All ARA solutions must include capabilities in automation, environment modeling, and release coordination. Additionally, the solution must provide this functionality without reliance on other tools.

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  CLAWS (linguistics)

  The Constituent Likelihood Automatic Word-tagging System (CLAWS) is a program that performs part-of-speech tagging. It was developed in the 1980s at Lancaster University by the University Centre for Computer Corpus Research on Language. It has an overall accuracy rate of 96–97% with the latest version (CLAWS4) tagging around 100 million words of the British National Corpus. == History == A Part-Of-Speech Tagger (POS Tagger) is a piece of software that reads text in some language and assigns parts of speech to each word (and other token), such as noun, verb, adjective, etc., although generally computational applications use more fine-grained POS tags like 'noun-plural'. Developed in the early 1980s, CLAWS was built to fill the ever-growing gap created by always-changing POS necessities. Originally created to add part-of-speech tags to the LOB corpus of British English, the CLAWS tagset has since been adapted to other languages as well, including Urdu and Arabic. Since its inception, CLAWS has been hailed for its functionality and adaptability. Still, it is not without flaws, and though it boasts an error-rate of only 1.5% when judged in major categories, CLAWS still remains with c.3.3% ambiguities unresolved. Ambiguity arises in cases such as with the word flies, and whether it should be classified as a noun or a verb. It's these ambiguities that will require the various upgrades and tagsets that CLAWS will endure. == Rules and processing == CLAWS uses a Hidden Markov model to determine the likelihood of sequences of words in anticipating each part-of-speech label. === Sample output === This excerpt from Bram Stoker's Dracula (1897) has been tagged using both the CLAWS C5 and C7 tagsets. This is what a CLAWS output will generally look like, with the most likely part-of-speech tag following each word. == Tagsets == === CLAWS1 tagset === The first tagset developed in CLAWS, CLAWS1 tagset, has 132 word tags. In terms of form and application, C1 tagset is similar to Brown Corpus tags. See Table of tags in C1 tagset here. === CLAWS2 tagset === From 1983 to 1986, updated versions leading to CLAWS2 were part of a larger attempt to deal with aspects such as recognizing sentence breaks, in order to avoid the need for manual pre-processing of a text before the tags were applied, moving instead to optional manual post-editing to adjust the output of the automatic annotation, if needed. The CLAWS2 tagset has 166 word tags. See Table of tags in C2 tagset here. === CLAWS4 tagset === The CLAWS4 was used for the 100-million-word British National Corpus (BNC). A general-purpose grammatical tagger, it is a successor of the CLAWS1 tagger. In tagging the BNC, the many rounds of work that went into CLAWS4 focused on making the CLAWS program independent from the tagsets. For example, the BNC project used two tagset versions: "a main tagset (C5) with 62 tags with which the whole of the corpus has been tagged, and a larger (C7) tagset with 152 tags, which has been used to make a selected 'core' sample corpus of two million words." The latest version of CLAWS4 is offered by UCREL, a research center of Lancaster University. === CLAWS5 tagset === The CLAWS5 tagset, which was used for BNC, has over 60 tags. See Table of tags in C5 tagset here. === CLAWS6 tagset === The CLAWS6 tagset was used for the BNC sampler corpus and the COLT corpus. It has over 160 tags, including 13 determiner subtypes. See Table of tags in C6 tagset here. === CLAWS7 tagset === The standard CLAWS7 tagset is used currently. It is only different in the punctuation tags when compared to the CLAWS6 tagset. See Table of tags in C7 tagset here. === CLAWS8 tagset === CLAWS8 tagset was extended from C7 tagset with further distinctions in the determiner and pronoun categories, as well as 37 new auxiliary tags for forms of be, do, and have. See Table of tags in C8 tagset here

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  Transduction (machine learning)

  In logic, statistical inference, and supervised learning, transduction or transductive inference is reasoning from observed, specific (training) cases to specific (test) cases. In contrast, induction is reasoning from observed training cases to general rules, which are then applied to the test cases. The distinction is most interesting in cases where the predictions of the transductive model are not achievable by any inductive model. Note that this is caused by transductive inference on different test sets producing mutually inconsistent predictions. Transduction was introduced in a computer science context by Vladimir Vapnik in the 1990s, motivated by his view that transduction is preferable to induction since, according to him, induction requires solving a more general problem (inferring a function) before solving a more specific problem (computing outputs for new cases): "When solving a problem of interest, do not solve a more general problem as an intermediate step. Try to get the answer that you really need but not a more general one.". An example of learning which is not inductive would be in the case of binary classification, where the inputs tend to cluster in two groups. A large set of test inputs may help in finding the clusters, thus providing useful information about the classification labels. The same predictions would not be obtainable from a model which induces a function based only on the training cases. Some people may call this an example of the closely related semi-supervised learning, since Vapnik's motivation is quite different. The most well-known example of a case-bases learning algorithm is the k-nearest neighbor algorithm, which is related to transductive learning algorithms. Another example of an algorithm in this category is the Transductive Support Vector Machine (TSVM). A third possible motivation of transduction arises through the need to approximate. If exact inference is computationally prohibitive, one may at least try to make sure that the approximations are good at the test inputs. In this case, the test inputs could come from an arbitrary distribution (not necessarily related to the distribution of the training inputs), which wouldn't be allowed in semi-supervised learning. An example of an algorithm falling in this category is the Bayesian Committee Machine (BCM). == Historical context == The mode of inference from particulars to particulars, which Vapnik came to call transduction, was already distinguished from the mode of inference from particulars to generalizations in part III of the Cambridge philosopher and logician W.E. Johnson's 1924 textbook, Logic. In Johnson's work, the former mode was called 'eduction' and the latter was called 'induction'. Bruno de Finetti developed a purely subjective form of Bayesianism in which claims about objective chances could be translated into empirically respectable claims about subjective credences with respect to observables through exchangeability properties. An early statement of this view can be found in his 1937 La Prévision: ses Lois Logiques, ses Sources Subjectives and a mature statement in his 1970 Theory of Probability. Within de Finetti's subjective Bayesian framework, all inductive inference is ultimately inference from particulars to particulars. == Example problem == The following example problem contrasts some of the unique properties of transduction against induction. A collection of points is given, such that some of the points are labeled (A, B, or C), but most of the points are unlabeled (?). The goal is to predict appropriate labels for all of the unlabeled points. The inductive approach to solving this problem is to use the labeled points to train a supervised learning algorithm, and then have it predict labels for all of the unlabeled points. With this problem, however, the supervised learning algorithm will only have five labeled points to use as a basis for building a predictive model. It will certainly struggle to build a model that captures the structure of this data. For example, if a nearest-neighbor algorithm is used, then the points near the middle will be labeled "A" or "C", even though it is apparent that they belong to the same cluster as the point labeled "B", compared to semi-supervised learning. Transduction has the advantage of being able to consider all of the points, not just the labeled points, while performing the labeling task. In this case, transductive algorithms would label the unlabeled points according to the clusters to which they naturally belong. The points in the middle, therefore, would most likely be labeled "B", because they are packed very close to that cluster. An advantage of transduction is that it may be able to make better predictions with fewer labeled points, because it uses the natural breaks found in the unlabeled points. One disadvantage of transduction is that it builds no predictive model. If a previously unknown point is added to the set, the entire transductive algorithm would need to be repeated with all of the points in order to predict a label. This can be computationally expensive if the data is made available incrementally in a stream. Further, this might cause the predictions of some of the old points to change (which may be good or bad, depending on the application). A supervised learning algorithm, on the other hand, can label new points instantly, with very little computational cost. == Transduction algorithms == Transduction algorithms can be broadly divided into two categories: those that seek to assign discrete labels to unlabeled points, and those that seek to regress continuous labels for unlabeled points. Algorithms that seek to predict discrete labels tend to be derived by adding partial supervision to a clustering algorithm. Two classes of algorithms can be used: flat clustering and hierarchical clustering. The latter can be further subdivided into two categories: those that cluster by partitioning, and those that cluster by agglomerating. Algorithms that seek to predict continuous labels tend to be derived by adding partial supervision to a manifold learning algorithm. === Partitioning transduction === Partitioning transduction can be thought of as top-down transduction. It is a semi-supervised extension of partition-based clustering. It is typically performed as follows: Consider the set of all points to be one large partition. While any partition P contains two points with conflicting labels: Partition P into smaller partitions. For each partition P: Assign the same label to all of the points in P. Of course, any reasonable partitioning technique could be used with this algorithm. Max flow min cut partitioning schemes are very popular for this purpose. === Agglomerative transduction === Agglomerative transduction can be thought of as bottom-up transduction. It is a semi-supervised extension of agglomerative clustering. It is typically performed as follows: Compute the pair-wise distances, D, between all the points. Sort D in ascending order. Consider each point to be a cluster of size 1. For each pair of points {a,b} in D: If (a is unlabeled) or (b is unlabeled) or (a and b have the same label) Merge the two clusters that contain a and b. Label all points in the merged cluster with the same label. === Continuous Label Transduction === These methods seek to regress continuous labels, often via manifold learning techniques. The idea is to learn a low-dimensional representation of the data and infer values smoothly across the manifold. == Applications and related concepts == Transduction is closely related to: Semi-supervised learning – uses both labeled and unlabeled data but typically induces a model. Case-based reasoning – such as the k-nearest neighbor (k-NN) algorithm, often considered a transductive method. Transductive Support Vector Machines (TSVM) – extend standard SVMs to incorporate unlabeled test data during training. Bayesian Committee Machine (BCM) – an approximation method that makes transductive predictions when exact inference is too costly.

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  CrewAI

  CrewAI is an open-source software framework and platform for building AI agents and multi-agent systems. Written primarily in Python, it is used to define artificial-intelligence agents, assign tasks to them, and coordinate their work through agent teams and workflows. The framework is associated with CrewAI Inc., a startup developing enterprise tools for automating business workflows with large language model-based agents. == History == CrewAI was first released on the Python Package Index in December 2023. The project was created by João Moura and later developed by CrewAI Inc. and open-source contributors. In October 2024, TechCrunch reported that CrewAI had raised $18 million across seed and Series A funding rounds from investors including Boldstart Ventures, Craft Ventures, Earl Grey Capital, and Insight Partners. The report also stated that Andrew Ng and HubSpot co-founder Dharmesh Shah had invested in the company. SiliconANGLE described the company as the developer of an open-source framework for building artificial-intelligence agents and reported that the funding consisted of a seed round led by Boldstart Ventures and a Series A led by Insight Partners. By late 2024, CrewAI had introduced commercial enterprise products built on top of its open-source components. TechCrunch reported that the company's enterprise offering added access controls, analytics, support, and templates for workflow automation. == Features == CrewAI is designed around groups of agents, sometimes called "crews", that can be assigned roles, goals, and tasks. The framework supports agent collaboration, task delegation, tool use, memory, and knowledge sources for retrieval-augmented generation workflows. The project describes two main building blocks: "Crews", which are used for autonomous agent collaboration, and "Flows", which are used for more controlled event-driven workflows. The framework is independent of LangChain and is released under the MIT License. It can be installed as a Python package and is commonly used with external large language model APIs or local models, depending on the developer's configuration. == Business model == CrewAI combines an open-source framework with commercial enterprise products. Its enterprise products are intended for organizations that need to build, monitor, and manage agent-based automations with additional security, observability, and administrative controls.

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  Example-based machine translation

  Example-based machine translation (EBMT) is a method of machine translation often characterized by its use of a bilingual corpus with parallel texts as its main knowledge base at run-time. It is essentially a translation by analogy and can be viewed as an implementation of a case-based reasoning approach to machine learning. == Translation by analogy == At the foundation of example-based machine translation is the idea of translation by analogy. When applied to the process of human translation, the idea that translation takes place by analogy is a rejection of the idea that people translate sentences by doing deep linguistic analysis. Instead, it is founded on the belief that people translate by first decomposing a sentence into certain phrases, then by translating these phrases, and finally by properly composing these fragments into one long sentence. Phrasal translations are translated by analogy to previous translations. The principle of translation by analogy is encoded to example-based machine translation through the example translations that are used to train such a system. Other approaches to machine translation, including statistical machine translation, also use bilingual corpora to learn the process of translation. == History == Example-based machine translation was first suggested by Makoto Nagao in 1984. He pointed out that it is especially adapted to translation between two totally different languages, such as English and Japanese. In this case, one sentence can be translated into several well-structured sentences in another language, therefore, it is no use to do the deep linguistic analysis characteristic of rule-based machine translation. == Example == Example-based machine translation systems are trained from bilingual parallel corpora containing sentence pairs like the example shown in the table above. Sentence pairs contain sentences in one language with their translations into another. The particular example shows an example of a minimal pair, meaning that the sentences vary by just one element. These sentences make it simple to learn translations of portions of a sentence. For example, an example-based machine translation system would learn three units of translation from the above example: How much is that X ? corresponds to Ano X wa ikura desu ka. red umbrella corresponds to akai kasa small camera corresponds to chiisai kamera Composing these units can be used to produce novel translations in the future. For example, if we have been trained using some text containing the sentences: President Kennedy was shot dead during the parade. and The convict escaped on July 15th., then we could translate the sentence The convict was shot dead during the parade. by substituting the appropriate parts of the sentences. == Phrasal verbs == Example-based machine translation is best suited for sub-language phenomena like phrasal verbs. Phrasal verbs have highly context-dependent meanings. They are common in English, where they comprise a verb followed by an adverb and/or a preposition, which are called the particle to the verb. Phrasal verbs produce specialized context-specific meanings that may not be derived from the meaning of the constituents. There is almost always an ambiguity during word-to-word translation from source to the target language. As an example, consider the phrasal verb "put on" and its Hindustani translation. It may be used in any of the following ways: Ram put on the lights. (Switched on) (Hindustani translation: Jalana) Ram put on a cap. (Wear) (Hindustani translation: Pahenna)

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  Artificial intelligence in fraud detection

  Artificial intelligence is used by many different businesses and organizations. It is widely used in the financial sector, especially by accounting firms, to help detect fraud. In 2022, PricewaterhouseCoopers reported that fraud has impacted 46% of all businesses in the world. The shift from working in person to working from home has brought increased access to data. According to an FTC (Federal Trade Commission) study from 2022, customers reported fraud of approximately $5.8 billion in 2021, an increase of 70% from the year before. The majority of these scams were imposter scams and online shopping frauds. Furthermore, artificial intelligence plays a crucial role in developing advanced algorithms and machine learning models that enhance fraud detection systems, enabling businesses to stay ahead of evolving fraudulent tactics in an increasingly digital landscape. == Tools == === Expert systems === Expert systems were first designed in the 1970s as an expansion into artificial intelligence technologies. Their design is based on the premise of decreasing potential user error in decision-making and emulating mental reasoning used by experts in a particular field. They differentiate themselves from traditional linear reasoning models by separating identified points in data and processing them individually at the same time. Though, these systems do not rely purely on machine-learned intelligence. Information regarding rules, practices, and procedures in the form of "if-then" statements are implemented into the programming of the system. Users interact with the system by feeding information into the system either through direct entry or import of external data. An inference system compares the information provided by the user with corresponding rules that are believed to specifically apply to the situation. Using this information and the corresponding rules will be used to create a solution to the user's query. Expert systems will generally not operate properly when the common procedures for a specified situation are ambiguous due to the need for well-defined rules. Implementation of expert systems in accounting procedures is feasible in areas where professional judgment is required. Situations where expert systems are applicable include investigations into transactions that involve potential fraudulent entries, instances of going concern, and the evaluation of risk in the planning stages of an audit. === Continuous auditing === Continuous auditing is a set of processes that assess various aspects of information gathered in an audit to classify areas of risk and potential weaknesses in financial Internal controls at a more frequent rate than traditional methods. Instead of analyzing recorded transactions and journal entries periodically, continuous auditing focuses on interpreting the character of these actions more frequently. The frequency of these processes being undertaken as well as highlighting areas of importance is up to the discretion of their implementer, who commonly makes such decisions based on the level of risk in the accounts being evaluated and the goals of implementing the system. Performance of these processes can occur as frequently as being nearly instantaneous with an entry being posted. The processes involved with analyzing financial data in continuous auditing can include the creation of spreadsheets to allow for interactive information gathering, calculation of financial ratios for comparison with previously created models, and detection of errors in entered figures. A primary goal of this practice is to allow for quicker and easier detection of instances of faulty controls, errors, and instances of fraud. === Machine learning and deep learning === The ability of machine learning and deep learning to swiftly and effectively sort through vast volumes of data in the forms of various documents relevant to companies and documents being audited makes them applicable to the domains of audit and fraud detection. Examples of this include recognizing key language in contracts, identifying levels of risk of fraud in transactions, and assessing journal entries for misstatement. == Applications == === 'Big 4' Accounting Firms === Deloitte created an Al-enabled document-reviewing system in 2014. The system automates the method of reviewing and extracting relevant information from different business documents. Deloitte claims that this innovation has made a difference by reducing time spent going through lawful contract documents, invoices, money-related articulations, and board minutes by up to 50%. Working with IBM's Watson, Deloitte is developing cognitive-technology-enhanced commerce arrangements for its clients. LeasePoint is fueled by IBM TRIRIGA (this product evolved into IBM Maximo Real Estate and Facilities) and uses Deloitte's industrial information to create an end-to-end leasing portfolio. Automated Cognitive Resource Assessment employs IBM's Maximo innovation to progress the proficiency of asset inspection. Ernst and Young (EY) connected Al to the investigation of lease contracts. EY (Australia) has also received Al-enabled auditing technology. Collaborating with H20.ai, PwC developed an Al-enabled framework (GL.ai) capable of analyzing reports and preparing reports. PwC claims to have made a significant investment in normal dialect processing (NLP), an Al-enabled innovation to process unstructured information efficiently. KPMG built a portfolio of Al instruments, called KPMG Ignite, to upgrade trade decisions and forms. Working with Microsoft and IBM Watson, KPMG is creating instruments to coordinate Al, data analytics, Cognitive Technologies, and RPA. == Advantages == === Efficiency === The process of auditing an entity in an attempt to detect fraudulent activity requires the repeating of investigatory processes until an error or misstatement may be identified. Under traditional methods, these processes would be carried out by a human being. Proponents of artificial intelligence in fraud detection have stated that these traditional methods are inefficient and can be more quickly accomplished with the aid of an intelligent computing system. A survey of 400 chief executive officers created by KPMG in 2016 found that approximately 58% believed that artificial intelligence would play a key role in making audits more efficient in the future. === Data interpretation === Higher levels of fraud detection entail the use of professional judgement to interpret data. Supporters of artificial intelligence being used in financial audits have claimed that increased risks from instances of higher data interpretation can be minimized through such technologies. One necessary element of an audit of financial statements that requires professional judgement is the implementation of thresholds for materiality. Materiality entails the distinction between errors and transactions in financial statements that would impact decisions made by users of those financial statements. The threshold for materiality in an audit is set by the auditor based on various factors. Artificial intelligence has been used to interpret data and suggest materiality thresholds to be implemented through the use of expert systems. === Decreased costs === Those in favor of using artificial intelligence to complete investigations of fraud have stated that such technologies decrease the amount of time required to complete tasks that are repetitive. The claim further states that such efficiencies allow for lowered resource requirements, which can then be further spent on tasks that have not been fully automated. The audit firm Ernst & Young has posited these claims by declaring that their deep learning systems have been used to reduce time spent on administrative tasks by analyzing relevant audit documents. According to the firm, this has allowed their employees to focus more on judgement and analysis. == Disadvantages == === Job Displacement === The inescapable reception of computer based intelligence and robotization advancements might prompt critical work relocation across different enterprises. As artificial intelligence frameworks become more equipped for performing undertakings customarily completed by people, there is a worry that specific work jobs could become out of date, prompting joblessness and financial imbalance. === Initial investment requirement === Along with a knowledge of coding and building systems through computer programs, we are seeing the advantages of these systems, but since they are so new, they require a large investment to start building such a system. Any firm that is planning on implementing an AI system to detect fraud must hire a team of data scientists, along with upgrading their cloud system and data storage. The system must be consistently monitored and updated to be the most efficient form of itself, otherwise the likelihood of fraud being involved in those transactions increases. If one does not initially invest in such a syst

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  Image fusion

  The image fusion process is defined as gathering all the important information from multiple images, and their inclusion into fewer images, usually a single one. This single image is more informative and accurate than any single source image, and it consists of all the necessary information. The purpose of image fusion is not only to reduce the amount of data but also to construct images that are more appropriate and understandable for the human and machine perception. In computer vision, multisensor image fusion is the process of combining relevant information from two or more images into a single image. The resulting image will be more informative than any of the input images. In remote sensing applications, the increasing availability of space borne sensors gives a motivation for different image fusion algorithms. Several situations in image processing require high spatial and high spectral resolution in a single image. Most of the available equipment is not capable of providing such data convincingly. Image fusion techniques allow the integration of different information sources. The fused image can have complementary spatial and spectral resolution characteristics. However, the standard image fusion techniques can distort the spectral information of the multispectral data while merging. In satellite imaging, two types of images are available. The panchromatic image acquired by satellites is transmitted with the maximum resolution available and the multispectral data are transmitted with coarser resolution. This will usually be two or four times lower. At the receiver station, the panchromatic image is merged with the multispectral data to convey more information. Many methods exist to perform image fusion. The very basic one is the high-pass filtering technique. Later techniques are based on Discrete Wavelet Transform, uniform rational filter bank, and Laplacian pyramid. == Motivation == Multi sensor data fusion has become a discipline which demands more general formal solutions to a number of application cases. Several situations in image processing require both high spatial and high spectral information in a single image. This is important in remote sensing. However, the instruments are not capable of providing such information either by design or because of observational constraints. One possible solution for this is data fusion. == Methods == Image fusion methods can be broadly classified into two groups – spatial domain fusion and transform domain fusion. The fusion methods such as averaging, Brovey method, principal component analysis (PCA) and IHS based methods fall under spatial domain approaches. Another important spatial domain fusion method is the high-pass filtering based technique. Here the high frequency details are injected into upsampled version of MS images. The disadvantage of spatial domain approaches is that they produce spatial distortion in the fused image. Spectral distortion becomes a negative factor while we go for further processing, such as classification problem. Spatial distortion can be very well handled by frequency-domain approaches on image fusion. The multiresolution analysis has become a very useful tool for analysing remote sensing images. The discrete wavelet transform has become a very useful tool for fusion. Some other fusion methods are also there, such as Laplacian pyramid based, curvelet transform based etc. These methods show a better performance in spatial and spectral quality of the fused image compared to other spatial methods of fusion. The images used in image fusion should already be registered. Misregistration is a major source of error in image fusion. Some well-known image fusion methods are: High-pass filtering technique IHS transform based image fusion PCA-based image fusion Wavelet transform image fusion Pair-wise spatial frequency matching Comparative analysis of image fusion methods demonstrates that different metrics support different user needs, sensitive to different image fusion methods, and need to be tailored to the application. Categories of image fusion metrics are based on information theory features, structural similarity, or human perception. === Multi-focus image fusion === Multi-focus image fusion is used to collect useful and necessary information from input images with different focus depths in order to create an output image that ideally has all information from input images. In visual sensor network (VSN), sensors are cameras which record images and video sequences. In many applications of VSN, a camera can’t give a perfect illustration including all details of the scene. This is because of the limited depth of focus exists in the optical lens of cameras. Therefore, just the object located in the focal length of camera is focused and cleared and the other parts of image are blurred. VSN has an ability to capture images with different depth of focuses in the scene using several cameras. Due to the large amount of data generated by camera compared to other sensors such as pressure and temperature sensors and some limitation such as limited band width, energy consumption and processing time, it is essential to process the local input images to decrease the amount of transmission data. The aforementioned reasons emphasize the necessary of multi-focus images fusion. Multi-focus image fusion is a process which combines the input multi-focus images into a single image including all important information of the input images and it’s more accurate explanation of the scene than every single input image. == Applications == === In remote sensing === Image fusion in remote sensing has several application domains. An important domain is the multi-resolution image fusion (commonly referred to pan-sharpening). In satellite imagery we can have two types of images: Panchromatic images – An image collected in the broad visual wavelength range but rendered in black and white. Multispectral images – Images optically acquired in more than one spectral or wavelength interval. Each individual image is usually of the same physical area and scale but of a different spectral band. The SPOT PAN satellite provides high resolution (10m pixel) panchromatic data. While the LANDSAT TM satellite provides low resolution (30m pixel) multispectral images. Image fusion attempts to merge these images and produce a single high resolution multispectral image. The standard merging methods of image fusion are based on Red–Green–Blue (RGB) to Intensity–Hue–Saturation (IHS) transformation. The usual steps involved in satellite image fusion are as follows: Resize the low resolution multispectral images to the same size as the panchromatic image. Transform the R, G and B bands of the multispectral image into IHS components. Modify the panchromatic image with respect to the multispectral image. This is usually performed by histogram matching of the panchromatic image with Intensity component of the multispectral images as reference. Replace the intensity component by the panchromatic image and perform inverse transformation to obtain a high resolution multispectral image. Pan-sharpening can be done with Photoshop. Other applications of image fusion in remote sensing are available. === In medical imaging === Image fusion has become a common term used within medical diagnostics and treatment. The term is used when multiple images of a patient are registered and overlaid or merged to provide additional information. Fused images may be created from multiple images from the same imaging modality, or by combining information from multiple modalities, such as magnetic resonance image (MRI), computed tomography (CT), positron emission tomography (PET), and single-photon emission computed tomography (SPECT). In radiology and radiation oncology, these images serve different purposes. For example, CT images are used more often to ascertain differences in tissue density while MRI images are typically used to diagnose brain tumors. For accurate diagnosis, radiologists must integrate information from multiple image formats. Fused, anatomically consistent images are especially beneficial in diagnosing and treating cancer. With the advent of these new technologies, radiation oncologists can take full advantage of intensity modulated radiation therapy (IMRT). Being able to overlay diagnostic images into radiation planning images results in more accurate IMRT target tumor volumes.

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  Biopython

  Biopython is an open-source collection of non-commercial Python modules for computational biology and bioinformatics. It makes robust and well-tested code easily accessible to researchers. Python is an object-oriented programming language and is a suitable choice for automation of common tasks. The availability of reusable libraries saves development time and lets researchers focus on addressing scientific questions. Biopython is constantly updated and maintained by a large team of volunteers across the globe. Biopython contains parsers for diverse bioinformatic sequence, alignment, and structure formats. Sequence formats include FASTA, FASTQ, GenBank, and EMBL. Alignment formats include Clustal, BLAST, PHYLIP, and NEXUS. Structural formats include the PDB, which contains the 3D atomic coordinates of the macromolecules. It has provisions to access information from biological databases like NCBI, Expasy, PBD, and BioSQL. This can be used in scripts or incorporated into their software. Biopython contains a standard sequence class, sequence alignment, and motif analysis tools. It also has clustering algorithms, a module for structural biology, and a module for phylogenetics analysis. == History == The development of Biopython began in 1999, and it was first released in July 2000. First "semi-complete" and "semi-stable" release was done in March 2001 and December 2002 respectively. It was developed during a similar time frame and with analogous goals to other projects that added bioinformatics capabilities to their respective programming languages, including BioPerl, BioRuby and BioJava. Early developers on the project included Jeff Chang, Andrew Dalke and Brad Chapman, though over 100 people have made contributions to date. In 2007, a similar Python project, namely PyCogent, was established. The initial scope of Biopython involved accessing, indexing and processing biological sequence files. The retrieved data from common biological databases will then be parsed into a python data structure. While this is still a major focus, over the following years added modules have extended its functionality to cover additional areas of biology. The key challenge in the design of parsers for bioinformatics file formats is the frequency at which the data formats change. This is due to inadequate curation of the structure of the data, and changes in the database contents. This problem is overcome by the application of a standard event-oriented parser design (see Key features and examples). As of version 1.77, Biopython no longer supports Python 2. The current stable release of Biopython version 1.85 was released on 15 January 2025. It only supports Python 3 and the recent releases of Biopython require NumPy (and not Numeric). == Design == Wherever possible, Biopython follows the conventions used by the Python programming language to make it easier for users familiar with Python. For example, Seq and SeqRecord objects can be manipulated via slicing, in a manner similar to Python's strings and lists. It is also designed to be functionally similar to other Bio projects, such as BioPerl. It is organized into modular sub-packages, e.g., Bio.Seq, Bio.Align, Bio.PDB, Bio.Entrez each of them useful in a different bioinformatics domain. It used principles, like encapsulation and polymorphism, notably in classes Seq, SeqRecord, and Bio.PDB.Structure. It can also interoperate with other Python tools (Pandas, Matplotlib and SciPy). Biopython can read and write most common file formats for each of its functional areas, and its license is permissive and compatible with most other software licenses, which allows Biopython to be used in a variety of software projects. == Requirements == Biopython is currently supported and tested with the following Python implementations: Python 3 or PyPy3 NumPy == Key features and examples == === Input and output === Biopython can read and write to a number of common formats. When reading files, descriptive information in the file is used to populate the members of Biopython classes, such as SeqRecord. This allows records of one file format to be converted into others. Very large sequence files can exceed a computer's memory resources, so Biopython provides various options for accessing records in large files. They can be loaded entirely into memory in Python data structures, such as lists or dictionaries, providing fast access at the cost of memory usage. Alternatively, the files can be read from disk as needed, with slower performance but lower memory requirements. === Sequences === A core concept in Biopython is the biological sequence, and this is represented by the Seq class. A Biopython Seq object is similar to a Python string in many respects: it supports the Python slice notation, can be concatenated with other sequences and is immutable. This object includes both general string-like and biological sequence-specific methods. It is best to store information about the biological type (DNA, RNA, protein) separately from the sequence, rather than using an explicit alphabet argument. === Sequence annotation === The SeqRecord class describes sequences, along with information such as name, description and features in the form of SeqFeature objects. Each SeqFeature object specifies the type of the feature and its location. Feature types can be ‘gene’, ‘CDS’ (coding sequence), ‘repeat_region’, ‘mobile_element’ or others, and the position of features in the sequence can be exact or approximate. === Accessing online databases === Through the Bio.Entrez module, users of Biopython can download biological data from NCBI databases. Each of the functions provided by the Entrez search engine is available through functions in this module, including searching for and downloading records. === Phylogeny === The Bio.Phylo module provides tools for working with and visualising phylogenetic trees. A variety of file formats are supported for reading and writing, including Newick, NEXUS and phyloXML. Common tree manipulations and traversals are supported via the Tree and Clade objects. Examples include converting and collating tree files, extracting subsets from a tree, changing a tree's root, and analysing branch features such as length or score. Rooted trees can be drawn in ASCII or using matplotlib (see Figure 1), and the Graphviz library can be used to create unrooted layouts (see Figure 2). === Genome diagrams === The GenomeDiagram module provides methods of visualising sequences within Biopython. Sequences can be drawn in a linear or circular form (see Figure 3), and many output formats are supported, including PDF and PNG. Diagrams are created by making tracks and then adding sequence features to those tracks. By looping over a sequence's features and using their attributes to decide if and how they are added to the diagram's tracks, one can exercise much control over the appearance of the final diagram. Cross-links can be drawn between different tracks, allowing one to compare multiple sequences in a single diagram. === Macromolecular structure === The Bio.PDB module can load molecular structures from PDB and mmCIF files, and was added to Biopython in 2003. The Structure object is central to this module, and it organises macromolecular structure in a hierarchical fashion: Structure objects contain Model objects which contain Chain objects which contain Residue objects which contain Atom objects. Disordered residues and atoms get their own classes, DisorderedResidue and DisorderedAtom, that describe their uncertain positions. Using Bio.PDB, one can navigate through individual components of a macromolecular structure file, such as examining each atom in a protein. Common analyses can be carried out, such as measuring distances or angles, comparing residues and calculating residue depth. === Population genetics === The Bio.PopGen module adds support to Biopython for Genepop, a software package for statistical analysis of population genetics. This allows for analyses of Hardy–Weinberg equilibrium, linkage disequilibrium and other features of a population's allele frequencies. This module can also carry out population genetic simulations using coalescent theory with the fastsimcoal2 program. === Wrappers for command line tools === Biopython previously included command-line wrappers for tools such as BLAST, Clustal, EMBOSS, and SAMtools. This option allowed users to run external tool commands from within the code using specialized Biopython classes. However, Bio.Application modules and their wrappers have deprecated and will be removed in future Biopython releases. The main reason for this is the high maintenance burden of updating them with the evolving external tools. The recommended approach is to directly construct and execute command-line tool commands using Python’s built-in subprocess module. This method provides flexibility and removes the dependency on the Biopython wrappers. subprocess is a native Python module useful for running ext

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  Calais (Reuters product)

  Calais is a service created by Thomson Reuters that automatically extracts semantic information from web pages in a format that can be used on the semantic web. Calais was launched in January 2008, and is free to use. The technology is now available via the website of Refinitiv, a provider of financial market data and infrastructure founded in 2018, that is a subsidiary of London Stock Exchange Group. The Calais Web service reads unstructured text and returns Resource Description Framework formatted results identifying entities, facts and events within the text. The service appears to be based on technology acquired when Reuters purchased ClearForest in 2007. The technology has also been used to automatically tag blog articles, and organize museum collections. Calais uses natural language processing technologies delivered via a web service interface.

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  KidDesk

  KidDesk is an alternative desktop software application. The early childhood learning company Hatch Early Childhood created KidDesk; it subsequently went to Edmark, which was bought by IBM then sold to Riverdeep (now Houghton Mifflin Harcourt Learning Technology). KidDesk is compatible with Microsoft Windows 95 and newer, as well as Apple System 7 and newer. KidDesk can be set to start when the computer starts up, and can only be exited through password entry. Adults choose what programs are included for the child to use, what icon represented the desk, and customize the software programs available for use. == History == Edmark first started shipping KidDesk in 1992. In 1993, Edmark updated KidDesk with KidDesk Family Edition for Macintosh and DOS, adding more desk accessories and desk styles (Sometimes included as a free exclusive offer with the Early Learning House and Thinkin' Things Series). In 1995, KidDesk Family Edition was enhanced for Windows 95, and released one month after the new operating system shipped. In 1998, Edmark developed KidDesk Internet Safe. The Internet Safe edition was written for Windows 95, Windows 98, and Macintosh (including OS8). In 2008, HMH ported KidDesk Family Edition was to run on Windows Vista and in 2011 version 3.07 of KidDesk Family Edition was released as part of the 'Young Explorer' suite which is fully supported on Windows XP, Windows Vista and Windows 7. == Features == A picture editor incorporated into the desk. Used both in the Adult settings menu and in the desk itself. KidDesk users can edit their user logo with a pixel grid paint program. A calendar incorporated into the desk. This allows the user to set dates that the user finds important, and allows the date to be marked with a picture or text. A password exit feature. For security reasons, the adult can set a password so that KidDesk can only be exited if it is entered. As an extra security measure, the password exit function could only be accessed if the user pressed the ctrl + alt + A keyboard buttons simultaneously. A skin changer with several themes - farm, princess, sports, ocean, etc. These themes can be changed. The e-mail and voicemail features are customizable depending on the KidDesk installation. The ability to add websites that can be accessed on KidDesk, and the ability to block hyperlinks, JavaScript, data entry, etc., on said sites was an added for the 'Internet Safe' edition released in 1998. KidDesk Internet Safe edition is available in Spanish and Brazilian-Portuguese versions. == Reception == KidDesk was given a platinum award at the 1994 Oppenheim Toy Portfolio Awards. The judges praised the program's security features allowing "configur[ation] so that kids never have access to the possibly destructive DOS prompt", and concluded that "[i]f you and your kids share a computer, you need to install Kiddesk immediately!" === Awards === Since 1992, KidDesk has won 15 major awards.

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  Superquadrics

  In mathematics, the superquadrics or super-quadrics (also superquadratics) are a family of geometric shapes defined by formulas that resemble those of ellipsoids and other quadrics, except that the squaring operations are replaced by arbitrary powers. They can be seen as the three-dimensional relatives of the superellipses. The term may refer to the solid object or to its surface, depending on the context. The equations below specify the surface; the solid is specified by replacing the equality signs by less-than-or-equal signs. The superquadrics include many shapes that resemble cubes, octahedra, cylinders, lozenges and spindles, with rounded or sharp corners. Because of their flexibility and relative simplicity, they are popular geometric modeling tools, especially in computer graphics. It becomes an important geometric primitive widely used in computer vision, robotics, and physical simulation. Some authors, such as Alan Barr, define "superquadrics" as including both the superellipsoids and the supertoroids. In modern computer vision literatures, superquadrics and superellipsoids are used interchangeably, since superellipsoids are the most representative and widely utilized shape among all the superquadrics. Comprehensive coverage of geometrical properties of superquadrics and methods of their recovery from range images and point clouds are covered in several computer vision literatures. == Formulas == === Implicit equation === The surface of the basic superquadric is given by | x | r + | y | s + | z | t = 1 {\displaystyle \left|x\right|^{r}+\left|y\right|^{s}+\left|z\right|^{t}=1} where r, s, and t are positive real numbers that determine the main features of the superquadric. Namely: less than 1: a pointy octahedron modified to have concave faces and sharp edges. exactly 1: a regular octahedron. between 1 and 2: an octahedron modified to have convex faces, blunt edges and blunt corners. exactly 2: a sphere greater than 2: a cube modified to have rounded edges and corners. infinite (in the limit): a cube Each exponent can be varied independently to obtain combined shapes. For example, if r=s=2, and t=4, one obtains a solid of revolution which resembles an ellipsoid with round cross-section but flattened ends. This formula is a special case of the superellipsoid's formula if (and only if) r = s. If any exponent is allowed to be negative, the shape extends to infinity. Such shapes are sometimes called super-hyperboloids. The basic shape above spans from -1 to +1 along each coordinate axis. The general superquadric is the result of scaling this basic shape by different amounts A, B, C along each axis. Its general equation is | x A | r + | y B | s + | z C | t = 1. {\displaystyle \left|{\frac {x}{A}}\right|^{r}+\left|{\frac {y}{B}}\right|^{s}+\left|{\frac {z}{C}}\right|^{t}=1.} === Parametric description === Parametric equations in terms of surface parameters u and v (equivalent to longitude and latitude if m equals 2) are x ( u , v ) = A g ( v , 2 r ) g ( u , 2 r ) y ( u , v ) = B g ( v , 2 s ) f ( u , 2 s ) z ( u , v ) = C f ( v , 2 t ) − π 2 ≤ v ≤ π 2 , − π ≤ u < π , {\displaystyle {\begin{aligned}x(u,v)&{}=Ag\left(v,{\frac {2}{r}}\right)g\left(u,{\frac {2}{r}}\right)\\y(u,v)&{}=Bg\left(v,{\frac {2}{s}}\right)f\left(u,{\frac {2}{s}}\right)\\z(u,v)&{}=Cf\left(v,{\frac {2}{t}}\right)\\&-{\frac {\pi }{2}}\leq v\leq {\frac {\pi }{2}},\quad -\pi \leq u<\pi ,\end{aligned}}} where the auxiliary functions are f ( ω , m ) = sgn ⁡ ( sin ⁡ ω ) | sin ⁡ ω | m g ( ω , m ) = sgn ⁡ ( cos ⁡ ω ) | cos ⁡ ω | m {\displaystyle {\begin{aligned}f(\omega ,m)&{}=\operatorname {sgn}(\sin \omega )\left|\sin \omega \right|^{m}\\g(\omega ,m)&{}=\operatorname {sgn}(\cos \omega )\left|\cos \omega \right|^{m}\end{aligned}}} and the sign function sgn(x) is sgn ⁡ ( x ) = { − 1 , x < 0 0 , x = 0 + 1 , x > 0. {\displaystyle \operatorname {sgn}(x)={\begin{cases}-1,&x<0\\0,&x=0\\+1,&x>0.\end{cases}}} === Spherical product === Barr introduces the spherical product which given two plane curves produces a 3D surface. If f ( μ ) = ( f 1 ( μ ) f 2 ( μ ) ) , g ( ν ) = ( g 1 ( ν ) g 2 ( ν ) ) {\displaystyle f(\mu )={\begin{pmatrix}f_{1}(\mu )\\f_{2}(\mu )\end{pmatrix}},\quad g(\nu )={\begin{pmatrix}g_{1}(\nu )\\g_{2}(\nu )\end{pmatrix}}} are two plane curves then the spherical product is h ( μ , ν ) = f ( μ ) ⊗ g ( ν ) = ( f 1 ( μ ) g 1 ( ν ) f 1 ( μ ) g 2 ( ν ) f 2 ( μ ) ) {\displaystyle h(\mu ,\nu )=f(\mu )\otimes g(\nu )={\begin{pmatrix}f_{1}(\mu )\ g_{1}(\nu )\\f_{1}(\mu )\ g_{2}(\nu )\\f_{2}(\mu )\end{pmatrix}}} This is similar to the typical parametric equation of a sphere: x = x 0 + r sin ⁡ θ cos ⁡ φ y = y 0 + r sin ⁡ θ sin ⁡ φ ( 0 ≤ θ ≤ π , 0 ≤ φ < 2 π ) z = z 0 + r cos ⁡ θ {\displaystyle {\begin{aligned}x&=x_{0}+r\sin \theta \;\cos \varphi \\y&=y_{0}+r\sin \theta \;\sin \varphi \qquad (0\leq \theta \leq \pi ,\;0\leq \varphi <2\pi )\\z&=z_{0}+r\cos \theta \end{aligned}}} which give rise to the name spherical product. Barr uses the spherical product to define quadric surfaces, like ellipsoids, and hyperboloids as well as the torus, superellipsoid, superquadric hyperboloids of one and two sheets, and supertoroids. == Plotting code == The following GNU Octave code generates a mesh approximation of a superquadric:

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  Mix automation

  In music recording, mix automation allows the mixing console to remember the mixing engineer's dynamic adjustment of faders during a musical piece in the post-production editing process. A timecode is necessary for the synchronization of automation. Modern mixing consoles and digital audio workstations use comprehensive mix automation. The need for automated mixing originated from the late 1970s transition form 8-track to 16-track and then 24-track multitrack recording, as mixing could be laborious and require multiple people and hands, and the results could be almost impossible to reproduce. With 48-track recording - synchronized twin 24-track recorders (for a net 46 audio tracks, with one on each machine for SMPTE timecode) - came larger recording and mixing consoles with even more channel faders to manage during mixdown. Manufacturers, such as Neve Electronics (now AMS Neve) and Solid State Logic (SSL), both English companies, developed systems that enabled one engineer to oversee every detail of a complex mix, although the computers required to power these desks remained a rarity into the late 1970s. According to record producer Roy Thomas Baker, Queen's 1975 single "Bohemian Rhapsody" was one of the first mixes to be done with automation. == Types == Voltage Controlled Automation fader levels are regulated by voltage-controlled amplifiers (VCA). VCAs control the audio level and not the actual fader. Moving Fader Automation a motor is attached to the fader, which then can be controlled by the console, digital audio workstation (DAW), or user. Software Controlled Automation the software can be internal to the console, or external as part of a DAW. The virtual fader can be adjusted in the software by the user. MIDI Automation the communications protocol MIDI can be used to send messages to the console to control automation. == Modes == Auto Write used the first time automation is created or when writing over existing automation Auto Touch writes automation data only while a fader is touched/faders return to any previously automated position after release Auto Latch starts writing automation data when a fader is touched/stays in position after release Auto Read digital Audio Workstation performs the written automation Auto Off automation is temporarily disabled All of these include the mute button. If mute is pressed during writing of automation, the audio track will be muted during playback of that automation. Depending on software, other parameters such as panning, sends, and plug-in controls can be automated as well. In some cases, automation can be written using a digital potentiometer instead of a fader.

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  Multi-agent reinforcement learning

  Multi-agent reinforcement learning (MARL) is a sub-field of reinforcement learning. It focuses on studying the behavior of multiple learning agents that coexist in a shared environment. Each agent is motivated by its own rewards, and does actions to advance its own interests; in some environments these interests are opposed to the interests of other agents, resulting in complex group dynamics. Multi-agent reinforcement learning is closely related to game theory and especially repeated games, as well as multi-agent systems. Its study combines the pursuit of finding ideal algorithms that maximize rewards with a more sociological set of concepts. While research in single-agent reinforcement learning is concerned with finding the algorithm that gets the biggest number of points for one agent, research in multi-agent reinforcement learning evaluates and quantifies social metrics, such as cooperation, reciprocity, equity, social influence, language and discrimination. == Definition == Similarly to single-agent reinforcement learning, multi-agent reinforcement learning is modeled as some form of a Markov decision process (MDP). Fix a set of agents I = { 1 , . . . , N } {\displaystyle I=\{1,...,N\}} . We then define: A set S {\displaystyle S} of environment states. One set A i {\displaystyle {\mathcal {A}}_{i}} of actions for each of the agents i ∈ I = { 1 , … , N } {\displaystyle i\in I=\{1,\dots ,N\}} . P a → ( s , s ′ ) = Pr ( s t + 1 = s ′ ∣ s t = s , a → t = a → ) {\displaystyle P_{\vec {a}}(s,s')=\Pr(s_{t+1}=s'\mid s_{t}=s,{\vec {a}}_{t}={\vec {a}})} is the probability of transition (at time t {\displaystyle t} ) from state s {\displaystyle s} to state s ′ {\displaystyle s'} under joint action a → {\displaystyle {\vec {a}}} . R → a → ( s , s ′ ) {\displaystyle {\vec {R}}_{\vec {a}}(s,s')} is the immediate joint reward after the transition from s {\displaystyle s} to s ′ {\displaystyle s'} with joint action a → {\displaystyle {\vec {a}}} . In settings with perfect information, such as the games of chess and Go, the MDP would be fully observable. In settings with imperfect information, especially in real-world applications like self-driving cars, each agent would access an observation that only has part of the information about the current state. In the partially observable setting, the core model is the partially observable stochastic game in the general case, and the decentralized POMDP in the cooperative case. == Cooperation vs. competition == When multiple agents are acting in a shared environment their interests might be aligned or misaligned. MARL allows exploring all the different alignments and how they affect the agents' behavior: In pure competition settings, the agents' rewards are exactly opposite to each other, and therefore they are playing against each other. Pure cooperation settings are the other extreme, in which agents get the exact same rewards, and therefore they are playing with each other. Mixed-sum settings cover all the games that combine elements of both cooperation and competition. === Pure competition settings === When two agents are playing a zero-sum game, they are in pure competition with each other. Many traditional games such as chess and Go fall under this category, as do two-player variants of video games like StarCraft. Because each agent can only win at the expense of the other agent, many complexities are stripped away. There is no prospect of communication or social dilemmas, as neither agent is incentivized to take actions that benefit its opponent. The Deep Blue and AlphaGo projects demonstrate how to optimize the performance of agents in pure competition settings. One complexity that is not stripped away in pure competition settings is autocurricula. As the agents' policy is improved using self-play, multiple layers of learning may occur. === Pure cooperation settings === MARL is used to explore how separate agents with identical interests can communicate and work together. Pure cooperation settings are explored in recreational cooperative games such as Overcooked, as well as real-world scenarios in robotics. In pure cooperation settings all the agents get identical rewards, which means that social dilemmas do not occur. In pure cooperation settings, oftentimes there are an arbitrary number of coordination strategies, and agents converge to specific "conventions" when coordinating with each other. The notion of conventions has been studied in language and also alluded to in more general multi-agent collaborative tasks. === Mixed-sum settings === Most real-world scenarios involving multiple agents have elements of both cooperation and competition. For example, when multiple self-driving cars are planning their respective paths, each of them has interests that are diverging but not exclusive: Each car is minimizing the amount of time it's taking to reach its destination, but all cars have the shared interest of avoiding a traffic collision. Zero-sum settings with three or more agents often exhibit similar properties to mixed-sum settings, since each pair of agents might have a non-zero utility sum between them. Mixed-sum settings can be explored using classic matrix games such as prisoner's dilemma, more complex sequential social dilemmas, and recreational games such as Among Us, Diplomacy and StarCraft II. Mixed-sum settings can give rise to communication and social dilemmas. == Social dilemmas == As in game theory, much of the research in MARL revolves around social dilemmas, such as prisoner's dilemma, chicken and stag hunt. While game theory research might focus on Nash equilibria and what an ideal policy for an agent would be, MARL research focuses on how the agents would learn these ideal policies using a trial-and-error process. The reinforcement learning algorithms that are used to train the agents are maximizing the agent's own reward; the conflict between the needs of the agents and the needs of the group is a subject of active research. Various techniques have been explored in order to induce cooperation in agents: Modifying the environment rules, adding intrinsic rewards, and more. === Sequential social dilemmas === Social dilemmas like prisoner's dilemma, chicken and stag hunt are "matrix games". Each agent takes only one action from a choice of two possible actions, and a simple 2x2 matrix is used to describe the reward that each agent will get, given the actions that each agent took. In humans and other living creatures, social dilemmas tend to be more complex. Agents take multiple actions over time, and the distinction between cooperating and defecting is not as clear cut as in matrix games. The concept of a sequential social dilemma (SSD) was introduced in 2017 as an attempt to model that complexity. There is ongoing research into defining different kinds of SSDs and showing cooperative behavior in the agents that act in them. == Autocurricula == An autocurriculum (plural: autocurricula) is a reinforcement learning concept that's salient in multi-agent experiments. As agents improve their performance, they change their environment; this change in the environment affects themselves and the other agents. The feedback loop results in several distinct phases of learning, each depending on the previous one. The stacked layers of learning are called an autocurriculum. Autocurricula are especially apparent in adversarial settings, where each group of agents is racing to counter the current strategy of the opposing group. The Hide and Seek game is an accessible example of an autocurriculum occurring in an adversarial setting. In this experiment, a team of seekers is competing against a team of hiders. Whenever one of the teams learns a new strategy, the opposing team adapts its strategy to give the best possible counter. When the hiders learn to use boxes to build a shelter, the seekers respond by learning to use a ramp to break into that shelter. The hiders respond by locking the ramps, making them unavailable for the seekers to use. The seekers then respond by "box surfing", exploiting a glitch in the game to penetrate the shelter. Each "level" of learning is an emergent phenomenon, with the previous level as its premise. This results in a stack of behaviors, each dependent on its predecessor. Autocurricula in reinforcement learning experiments are compared to the stages of the evolution of life on Earth and the development of human culture. A major stage in evolution happened 2-3 billion years ago, when photosynthesizing life forms started to produce massive amounts of oxygen, changing the balance of gases in the atmosphere. In the next stages of evolution, oxygen-breathing life forms evolved, eventually leading up to land mammals and human beings. These later stages could only happen after the photosynthesis stage made oxygen widely available. Similarly, human culture could not have gone through the Industrial Revolution in the 18th century without the resources and insights gaine

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  Point-set registration

  In computer vision, pattern recognition, and robotics, point-set registration, also known as point-cloud registration or scan matching, is the process of finding a spatial transformation (e.g., scaling, rotation and translation) that aligns two point clouds. The purpose of finding such a transformation includes merging multiple data sets into a globally consistent model (or coordinate frame), and mapping a new measurement to a known data set to identify features or to estimate its pose. Raw 3D point cloud data are typically obtained from Lidars and RGB-D cameras. 3D point clouds can also be generated from computer vision algorithms such as triangulation, bundle adjustment, and more recently, monocular image depth estimation using deep learning. For 2D point set registration used in image processing and feature-based image registration, a point set may be 2D pixel coordinates obtained by feature extraction from an image, for example corner detection. Point cloud registration has extensive applications in autonomous driving, motion estimation and 3D reconstruction, object detection and pose estimation, robotic manipulation, simultaneous localization and mapping (SLAM), panorama stitching, virtual and augmented reality, and medical imaging. As a special case, registration of two point sets that only differ by a 3D rotation (i.e., there is no scaling and translation), is called the Wahba Problem and also related to the orthogonal procrustes problem. == Formulation == The problem may be summarized as follows: Let { M , S } {\displaystyle \lbrace {\mathcal {M}},{\mathcal {S}}\rbrace } be two finite size point sets in a finite-dimensional real vector space R d {\displaystyle \mathbb {R} ^{d}} , which contain M {\displaystyle M} and N {\displaystyle N} points respectively (e.g., d = 3 {\displaystyle d=3} recovers the typical case of when M {\displaystyle {\mathcal {M}}} and S {\displaystyle {\mathcal {S}}} are 3D point sets). The problem is to find a transformation to be applied to the moving "model" point set M {\displaystyle {\mathcal {M}}} such that the difference (typically defined in the sense of point-wise Euclidean distance) between M {\displaystyle {\mathcal {M}}} and the static "scene" set S {\displaystyle {\mathcal {S}}} is minimized. In other words, a mapping from R d {\displaystyle \mathbb {R} ^{d}} to R d {\displaystyle \mathbb {R} ^{d}} is desired which yields the best alignment between the transformed "model" set and the "scene" set. The mapping may consist of a rigid or non-rigid transformation. The transformation model may be written as T {\displaystyle T} , using which the transformed, registered model point set is: The output of a point set registration algorithm is therefore the optimal transformation T ⋆ {\displaystyle T^{\star }} such that M {\displaystyle {\mathcal {M}}} is best aligned to S {\displaystyle {\mathcal {S}}} , according to some defined notion of distance function dist ⁡ ( ⋅ , ⋅ ) {\displaystyle \operatorname {dist} (\cdot ,\cdot )} : where T {\displaystyle {\mathcal {T}}} is used to denote the set of all possible transformations that the optimization tries to search for. The most popular choice of the distance function is to take the square of the Euclidean distance for every pair of points: where ‖ ⋅ ‖ 2 {\displaystyle \|\cdot \|_{2}} denotes the vector 2-norm, s m {\displaystyle s_{m}} is the corresponding point in set S {\displaystyle {\mathcal {S}}} that attains the shortest distance to a given point m {\displaystyle m} in set M {\displaystyle {\mathcal {M}}} after transformation. Minimizing such a function in rigid registration is equivalent to solving a least squares problem. == Types of algorithms == When the correspondences (i.e., s m ↔ m {\displaystyle s_{m}\leftrightarrow m} ) are given before the optimization, for example, using feature matching techniques, then the optimization only needs to estimate the transformation. This type of registration is called correspondence-based registration. On the other hand, if the correspondences are unknown, then the optimization is required to jointly find out the correspondences and transformation together. This type of registration is called simultaneous pose and correspondence registration. === Rigid registration === Given two point sets, rigid registration yields a rigid transformation which maps one point set to the other. A rigid transformation is defined as a transformation that does not change the distance between any two points. Typically such a transformation consists of translation and rotation. In rare cases, the point set may also be mirrored. In robotics and computer vision, rigid registration has the most applications. === Non-rigid registration === Given two point sets, non-rigid registration yields a non-rigid transformation which maps one point set to the other. Non-rigid transformations include affine transformations such as scaling and shear mapping. However, in the context of point set registration, non-rigid registration typically involves nonlinear transformation. If the eigenmodes of variation of the point set are known, the nonlinear transformation may be parametrized by the eigenvalues. A nonlinear transformation may also be parametrized as a thin plate spline. === Other types === Some approaches to point set registration use algorithms that solve the more general graph matching problem. However, the computational complexity of such methods tend to be high and they are limited to rigid registrations. In this article, we will only consider algorithms for rigid registration, where the transformation is assumed to contain 3D rotations and translations (possibly also including a uniform scaling). The PCL (Point Cloud Library) is an open-source framework for n-dimensional point cloud and 3D geometry processing. It includes several point registration algorithms. == Correspondence-based registration == Correspondence-based methods assume the putative correspondences m ↔ s m {\displaystyle m\leftrightarrow s_{m}} are given for every point m ∈ M {\displaystyle m\in {\mathcal {M}}} . Therefore, we arrive at a setting where both point sets M {\displaystyle {\mathcal {M}}} and S {\displaystyle {\mathcal {S}}} have N {\displaystyle N} points and the correspondences m i ↔ s i , i = 1 , … , N {\displaystyle m_{i}\leftrightarrow s_{i},i=1,\dots ,N} are given. === Outlier-free registration === In the simplest case, one can assume that all the correspondences are correct, meaning that the points m i , s i ∈ R 3 {\displaystyle m_{i},s_{i}\in \mathbb {R} ^{3}} are generated as follows:where l > 0 {\displaystyle l>0} is a uniform scaling factor (in many cases l = 1 {\displaystyle l=1} is assumed), R ∈ SO ( 3 ) {\displaystyle R\in {\text{SO}}(3)} is a proper 3D rotation matrix ( SO ( d ) {\displaystyle {\text{SO}}(d)} is the special orthogonal group of degree d {\displaystyle d} ), t ∈ R 3 {\displaystyle t\in \mathbb {R} ^{3}} is a 3D translation vector and ϵ i ∈ R 3 {\displaystyle \epsilon _{i}\in \mathbb {R} ^{3}} models the unknown additive noise (e.g., Gaussian noise). Specifically, if the noise ϵ i {\displaystyle \epsilon _{i}} is assumed to follow a zero-mean isotropic Gaussian distribution with standard deviation σ i {\displaystyle \sigma _{i}} , i.e., ϵ i ∼ N ( 0 , σ i 2 I 3 ) {\displaystyle \epsilon _{i}\sim {\mathcal {N}}(0,\sigma _{i}^{2}I_{3})} , then the following optimization can be shown to yield the maximum likelihood estimate for the unknown scale, rotation and translation:Note that when the scaling factor is 1 and the translation vector is zero, then the optimization recovers the formulation of the Wahba problem. Despite the non-convexity of the optimization (cb.2) due to non-convexity of the set SO ( 3 ) {\displaystyle {\text{SO}}(3)} , seminal work by Berthold K.P. Horn showed that (cb.2) actually admits a closed-form solution, by decoupling the estimation of scale, rotation and translation. Similar results were discovered by Arun et al. In addition, in order to find a unique transformation ( l , R , t ) {\displaystyle (l,R,t)} , at least N = 3 {\displaystyle N=3} non-collinear points in each point set are required. More recently, Briales and Gonzalez-Jimenez have developed a semidefinite relaxation using Lagrangian duality, for the case where the model set M {\displaystyle {\mathcal {M}}} contains different 3D primitives such as points, lines and planes (which is the case when the model M {\displaystyle {\mathcal {M}}} is a 3D mesh). Interestingly, the semidefinite relaxation is empirically tight, i.e., a certifiably globally optimal solution can be extracted from the solution of the semidefinite relaxation. === Robust registration === The least squares formulation (cb.2) is known to perform arbitrarily badly in the presence of outliers. An outlier correspondence is a pair of measurements s i ↔ m i {\displaystyle s_{i}\leftrightarrow m_{i}} that departs from the generative model (cb.1). In this case, one can consider a differen

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