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  JAUS Tool Set

  The JAUS Tool Set (JTS) is a software engineering tool for the design of software services used in a distributed computing environment. JTS provides a graphical user interface (GUI) and supporting tools for the rapid design, documentation, and implementation of service interfaces that adhere to the Society of Automotive Engineers' standard AS5684A, the JAUS Service Interface Design Language (JSIDL). JTS is designed to support the modeling, analysis, implementation, and testing of the protocol for an entire distributed system. == Overview == The JAUS Tool Set (JTS) is a set of open source software specification and development tools accompanied by an open source software framework to develop Joint Architecture for Unmanned Systems (JAUS) designs and compliant interface implementations for simulations and control of robotic components per SAE-AS4 standards. JTS consists of the components: GUI based Service Editor: The Service Editor (referred to as the GUI in this document) provides a user friendly interface with which a system designer can specify and analyze formal specifications of Components and Services defined using the JAUS Service Interface Definition Language (JSIDL). Validator: A syntactic and semantic validator provides on-the-fly validation of specifications entered (or imported) by the user with respect to JSIDL syntax and semantics is integrated into the GUI. Specification Repository: A repository (or database) that is integrated into the GUI that allows for the storage of and encourages the reuse of existing formal specifications. C++ Code Generator: The Code Generator automatically generates C++ code that has a 1:1 mapping to the formal specifications. The generated code includes all aspects of the service, including the implementations of marshallers and unmarshallers for messages, and implementations of finite-state machines for protocol behavior that are effectively decoupled from application behavior. Document Generator: The Document Generator automatically generates documentation for sets of Service Definitions. Documents may be generated in several formats. Software Framework: The software framework implements the transport layer specification AS5669A, and provides the interfaces necessary to integrate the auto-generated C++ code with the transport layer implementation. Present transport options include UDP and TCP in wired or wireless networks, as well as serial connections. The transport layer itself is modular, and allows end-users to add additional support as needed. Wireshark Plugin: The Wireshark plugin implements a plugin to the popular network protocol analyzer called Wireshark. This plugin allows for the live capture and offline analysis of JAUS message-based communication at runtime. A built-in repository facilitates easy reuse of service interfaces and implementations traffic across the wire. The JAUS Tool Set can be downloaded from www.jaustoolset.org User documentation and community forum are also available at the site. == Release history == Following a successful Beta test, Version 1.0 of the JAUS Tool Set was released in July 2010. The initial offering focused on core areas of User Interface, HTML document generation, C++ code generation, and the software framework. The Version 1.1 update was released in October 2010. In addition to bug fixes and UI improvements, this version offered several important upgrades including enhancement to the Validator, Wireshark plug-in, and generated code. The JTS 2.0 release is scheduled for the second quarter of 2011 and further refines the Tool Set functionality: Protocol Validation: Currently, JTS provides validation for message creation, to ensure users cannot create invalid messages specifications. That capability does not currently exist for protocol definitions, but is being added. This will help ensure that users create all necessary elements of a service definition, and reduce user error. C# and Java Code Generation: Currently, JTS generates cross-platform C++ code. However, other languages including Java and C# are seeing a dramatic increase in their use in distributed systems, particularly in the development of graphical clients to embedded services. MS Word Document Generation: HTML and JSIDL output is supported, but native Office-Open-XML (OOXML) based MS Word generation has advantages in terms of output presentation, and ease of use for integration with other documents. Therefore, we plan to integrate MS Word service document generation. In addition, the development team has several additional goals that are not-yet-scheduled for a particular release window: Protocol Verification: This involves converting the JSIDL definition of a service into a PROMELA model, for validation by the SPIN model checking tool. Using PROMELA to model client and server interfaces will allow developers to formally validate JAUS services. End User Experience: We plan to conduct formal User Interface testing. This involves defining a set of tasks and use cases, asking users with various levels of JAUS experience to accomplish those tasks, and measuring performance and collecting feedback, to look for areas where the overall user experience can be improved. Improved Service Re-Use: JSIDL allows for inheritance of protocol descriptions, much like object-oriented programming languages allow child classes to re-use and extend behaviors defined by the parent class. At present, the generated code 'flattens' these state machines into a series of nested states which gives the correct interface behavior, but only if each single leaf (child) service is generated within its own component. This limits service re-use and can lead to a copy-and-paste of the same implementation across multiple components. The team is evaluating other inheritance solutions that would allow for multiple leaf (child) services to share access to a common parent, but at present the approach is sufficient to address the requirements of the JAUS Core Service Set. == Domains and application == The JAUS Tool Set is based on the JAUS Service Interface Definition Language (JSIDL), which was originally developed for application within the unmanned systems, or robotics, communities. As such, JTS has quickly gained acceptance as a tool for generation of services and interfaces compliant with the SAE AS-4 "JAUS" publications. Although usage statistics are not available, the Tool Set has been downloaded by representatives of US Army, Navy, Marines, and numerous defense contractors. It was also used in a commercial product called the JAUS Expansion Module sold by DeVivo AST, Inc. Since the JSIDL schema is independent of the data being exchanged, however, the Tool Set can be used for the design and implementation of a Service Oriented Architecture for any distributed systems environment that uses binary encoded message exchange. JSIDL is built on a two-layered architecture that separates the application layer and the transport layer, effectively decoupling the data being exchanges from the details of how that data moves from component to component. Furthermore, since the schema itself is widely generic, it's possible to define messages for any number of domains including but not limited to industrial control systems, remote monitoring and diagnostics, and web-based applications. == Licensing == JTS is released under the open source BSD license. The JSIDL Standard is available from the SAE. The Jr Middleware on which the Software Framework (Transport Layer) is based is open source under LGPL. Other packages distributed with JTS may have different licenses. == Sponsors == Development of the JAUS Tool Set was sponsored by several United States Department of Defense organizations: Office of Under Secretary of Defense for Acquisition, Technology & Logistics / Unmanned Warfare. Navy Program Executive Officer Littoral and Mine Navy Program Executive Officer Unmanned Aviation and Strike Weapons Office of Naval Research Air Force Research Lab

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  Modern Hopfield network

  Modern Hopfield networks (also known as Dense Associative Memories) are generalizations of the classical Hopfield networks that break the linear scaling relationship between the number of input features and the number of stored memories. This is achieved by introducing stronger non-linearities (either in the energy function or neurons’ activation functions) leading to super-linear (even an exponential) memory storage capacity as a function of the number of feature neurons. The network still requires a sufficient number of hidden neurons. The key theoretical idea behind the modern Hopfield networks is to use an energy function and an update rule that is more sharply peaked around the stored memories in the space of neuron’s configurations compared to the classical Hopfield network. == Classical Hopfield networks == Hopfield networks are recurrent neural networks with dynamical trajectories converging to fixed point attractor states and described by an energy function. The state of each model neuron i {\textstyle i} is defined by a time-dependent variable V i {\displaystyle V_{i}} , which can be chosen to be either discrete or continuous. A complete model describes the mathematics of how the future state of activity of each neuron depends on the known present or previous activity of all the neurons. In the original Hopfield model of associative memory, the variables were binary, and the dynamics were described by a one-at-a-time update of the state of the neurons. An energy function quadratic in the V i {\displaystyle V_{i}} was defined, and the dynamics consisted of changing the activity of each single neuron i {\displaystyle i} only if doing so would lower the total energy of the system. This same idea was extended to the case of V i {\displaystyle V_{i}} being a continuous variable representing the output of neuron i {\displaystyle i} , and V i {\displaystyle V_{i}} being a monotonic function of an input current. The dynamics became expressed as a set of first-order differential equations for which the "energy" of the system always decreased. The energy in the continuous case has one term which is quadratic in the V i {\displaystyle V_{i}} (as in the binary model), and a second term which depends on the gain function (neuron's activation function). While having many desirable properties of associative memory, both of these classical systems suffer from a small memory storage capacity, which scales linearly with the number of input features. == Discrete variables == A simple example of the Modern Hopfield network can be written in terms of binary variables V i {\displaystyle V_{i}} that represent the active V i = + 1 {\displaystyle V_{i}=+1} and inactive V i = − 1 {\displaystyle V_{i}=-1} state of the model neuron i {\displaystyle i} . E = − ∑ μ = 1 N mem F ( ∑ i = 1 N f ξ μ i V i ) {\displaystyle E=-\sum \limits _{\mu =1}^{N_{\text{mem}}}F{\Big (}\sum \limits _{i=1}^{N_{f}}\xi _{\mu i}V_{i}{\Big )}} In this formula the weights ξ μ i {\textstyle \xi _{\mu i}} represent the matrix of memory vectors (index μ = 1... N mem {\displaystyle \mu =1...N_{\text{mem}}} enumerates different memories, and index i = 1... N f {\displaystyle i=1...N_{f}} enumerates the content of each memory corresponding to the i {\displaystyle i} -th feature neuron), and the function F ( x ) {\displaystyle F(x)} is a rapidly growing non-linear function. The update rule for individual neurons (in the asynchronous case) can be written in the following form V i ( t + 1 ) = sign ⁡ [ ∑ μ = 1 N mem ( F ( ξ μ i + ∑ j ≠ i ξ μ j V j ( t ) ) − F ( − ξ μ i + ∑ j ≠ i ξ μ j V j ( t ) ) ) ] {\displaystyle V_{i}^{(t+1)}=\operatorname {sign} {\bigg [}\sum \limits _{\mu =1}^{N_{\text{mem}}}{\bigg (}F{\Big (}\xi _{\mu i}+\sum \limits _{j\neq i}\xi _{\mu j}V_{j}^{(t)}{\Big )}-F{\Big (}-\xi _{\mu i}+\sum \limits _{j\neq i}\xi _{\mu j}V_{j}^{(t)}{\Big )}{\bigg )}{\bigg ]}} which states that in order to calculate the updated state of the i {\textstyle i} -th neuron the network compares two energies: the energy of the network with the i {\displaystyle i} -th neuron in the ON state and the energy of the network with the i {\displaystyle i} -th neuron in the OFF state, given the states of the remaining neuron. The updated state of the i {\displaystyle i} -th neuron selects the state that has the lowest of the two energies. In the limiting case when the non-linear energy function is quadratic F ( x ) = x 2 {\displaystyle F(x)=x^{2}} these equations reduce to the familiar energy function and the update rule for the classical binary Hopfield network. The memory storage capacity of these networks can be calculated for random binary patterns. For the power energy function F ( x ) = x n {\displaystyle F(x)=x^{n}} the maximal number of memories that can be stored and retrieved from this network without errors is given by N mem max ≈ 1 2 ( 2 n − 3 ) ! ! N f n − 1 ln ⁡ ( N f ) {\displaystyle N_{\text{mem}}^{\max }\approx {\frac {1}{2(2n-3)!!}}{\frac {N_{f}^{n-1}}{\ln(N_{f})}}} For an exponential energy function F ( x ) = e x {\textstyle F(x)=e^{x}} the memory storage capacity is exponential in the number of feature neurons N mem max ≈ 2 N f / 2 {\displaystyle N_{\text{mem}}^{\max }\approx 2^{N_{f}/2}} == Continuous variables == Modern Hopfield networks or Dense Associative Memories can be best understood in continuous variables and continuous time. Consider the network architecture, shown in Fig.1, and the equations for the neurons' state evolutionwhere the currents of the feature neurons are denoted by x i {\textstyle x_{i}} , and the currents of the memory neurons are denoted by h μ {\displaystyle h_{\mu }} ( h {\displaystyle h} stands for hidden neurons). There are no synaptic connections among the feature neurons or the memory neurons. A matrix ξ μ i {\displaystyle \xi _{\mu i}} denotes the strength of synapses from a feature neuron i {\displaystyle i} to the memory neuron μ {\displaystyle \mu } . The synapses are assumed to be symmetric, so that the same value characterizes a different physical synapse from the memory neuron μ {\displaystyle \mu } to the feature neuron i {\displaystyle i} . The outputs of the memory neurons and the feature neurons are denoted by f μ {\displaystyle f_{\mu }} and g i {\displaystyle g_{i}} , which are non-linear functions of the corresponding currents. In general these outputs can depend on the currents of all the neurons in that layer so that f μ = f ( { h μ } ) {\displaystyle f_{\mu }=f(\{h_{\mu }\})} and g i = g ( { x i } ) {\textstyle g_{i}=g(\{x_{i}\})} . It is convenient to define these activation function as derivatives of the Lagrangian functions for the two groups of neuronsThis way the specific form of the equations for neuron's states is completely defined once the Lagrangian functions are specified. Finally, the time constants for the two groups of neurons are denoted by τ f {\displaystyle \tau _{f}} and τ h {\displaystyle \tau _{h}} , I i {\displaystyle I_{i}} is the input current to the network that can be driven by the presented data. General systems of non-linear differential equations can have many complicated behaviors that can depend on the choice of the non-linearities and the initial conditions. For Hopfield networks, however, this is not the case - the dynamical trajectories always converge to a fixed point attractor state. This property is achieved because these equations are specifically engineered so that they have an underlying energy function The terms grouped into square brackets represent a Legendre transform of the Lagrangian function with respect to the states of the neurons. If the Hessian matrices of the Lagrangian functions are positive semi-definite, the energy function is guaranteed to decrease on the dynamical trajectory This property makes it possible to prove that the system of dynamical equations describing temporal evolution of neurons' activities will eventually reach a fixed point attractor state. In certain situations one can assume that the dynamics of hidden neurons equilibrates at a much faster time scale compared to the feature neurons, τ h ≪ τ f {\textstyle \tau _{h}\ll \tau _{f}} . In this case the steady state solution of the second equation in the system (1) can be used to express the currents of the hidden units through the outputs of the feature neurons. This makes it possible to reduce the general theory (1) to an effective theory for feature neurons only. The resulting effective update rules and the energies for various common choices of the Lagrangian functions are shown in Fig.2. In the case of log-sum-exponential Lagrangian function the update rule (if applied once) for the states of the feature neurons is the attention mechanism commonly used in many modern AI systems (see Ref. for the derivation of this result from the continuous time formulation). == Relationship to classical Hopfield network with continuous variables == Classical formulation of continuous Hopfield networks can be understood as a

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  Multidimensional scaling

  Multidimensional scaling (MDS) is a means of visualizing the level of similarity of individual cases of a data set. MDS is used to translate distances between each pair of n {\textstyle n} objects in a set into a configuration of n {\textstyle n} points mapped into an abstract Cartesian space. More technically, MDS refers to a set of related ordination techniques used in information visualization, in particular to display the information contained in a distance matrix. It is a form of non-linear dimensionality reduction. Given a distance matrix with the distances between each pair of objects in a set, and a chosen number of dimensions, N, an MDS algorithm places each object into N-dimensional space (a lower-dimensional representation) such that the between-object distances are preserved as well as possible. For N = 1, 2, and 3, the resulting points can be visualized on a scatter plot. Core theoretical contributions to MDS were made by James O. Ramsay of McGill University, who is also regarded as the founder of functional data analysis. == Types == MDS algorithms fall into a taxonomy, depending on the meaning of the input matrix: === Classical multidimensional scaling === It is also known as Principal Coordinates Analysis (PCoA), Torgerson Scaling or Torgerson–Gower scaling. It takes an input matrix giving dissimilarities between pairs of items and outputs a coordinate matrix whose configuration minimizes a loss function called strain, which is given by Strain D ( x 1 , x 2 , . . . , x n ) = ( ∑ i , j ( b i j − x i T x j ) 2 ∑ i , j b i j 2 ) 1 / 2 , {\displaystyle {\text{Strain}}_{D}(x_{1},x_{2},...,x_{n})={\Biggl (}{\frac {\sum _{i,j}{\bigl (}b_{ij}-x_{i}^{T}x_{j}{\bigr )}^{2}}{\sum _{i,j}b_{ij}^{2}}}{\Biggr )}^{1/2},} where x i {\displaystyle x_{i}} denote vectors in N-dimensional space, x i T x j {\displaystyle x_{i}^{T}x_{j}} denotes the scalar product between x i {\displaystyle x_{i}} and x j {\displaystyle x_{j}} , and b i j {\displaystyle b_{ij}} are the elements of the matrix B {\displaystyle B} defined on step 2 of the following algorithm, which are computed from the distances. Steps of a Classical MDS algorithm: Classical MDS uses the fact that the coordinate matrix X {\displaystyle X} can be derived by eigenvalue decomposition from B = X X ′ {\textstyle B=XX'} . And the matrix B {\textstyle B} can be computed from proximity matrix D {\textstyle D} by using double centering. Set up the squared proximity matrix D ( 2 ) = [ d i j 2 ] {\textstyle D^{(2)}=[d_{ij}^{2}]} Apply double centering: B = − 1 2 C D ( 2 ) C {\textstyle B=-{\frac {1}{2}}CD^{(2)}C} using the centering matrix C = I − 1 n J n {\textstyle C=I-{\frac {1}{n}}J_{n}} , where n {\textstyle n} is the number of objects, I {\textstyle I} is the n × n {\textstyle n\times n} identity matrix, and J n {\textstyle J_{n}} is an n × n {\textstyle n\times n} matrix of all ones. Determine the m {\textstyle m} largest eigenvalues λ 1 , λ 2 , . . . , λ m {\textstyle \lambda _{1},\lambda _{2},...,\lambda _{m}} and corresponding eigenvectors e 1 , e 2 , . . . , e m {\textstyle e_{1},e_{2},...,e_{m}} of B {\textstyle B} (where m {\textstyle m} is the number of dimensions desired for the output). Now, X = E m Λ m 1 / 2 {\textstyle X=E_{m}\Lambda _{m}^{1/2}} , where E m {\textstyle E_{m}} is the matrix of m {\textstyle m} eigenvectors and Λ m {\textstyle \Lambda _{m}} is the diagonal matrix of m {\textstyle m} eigenvalues of B {\textstyle B} . Classical MDS assumes metric distances. So this is not applicable for direct dissimilarity ratings. === Metric multidimensional scaling (mMDS) === It is a superset of classical MDS that generalizes the optimization procedure to a variety of loss functions and input matrices of known distances with weights and so on. A useful loss function in this context is called stress, which is often minimized using a procedure called stress majorization. Metric MDS minimizes the cost function called “stress” which is a residual sum of squares: Stress D ( x 1 , x 2 , . . . , x n ) = ∑ i ≠ j = 1 , . . . , n ( d i j − ‖ x i − x j ‖ ) 2 . {\displaystyle {\text{Stress}}_{D}(x_{1},x_{2},...,x_{n})={\sqrt {\sum _{i\neq j=1,...,n}{\bigl (}d_{ij}-\|x_{i}-x_{j}\|{\bigr )}^{2}}}.} Metric scaling uses a power transformation with a user-controlled exponent p {\textstyle p} : d i j p {\textstyle d_{ij}^{p}} and − d i j 2 p {\textstyle -d_{ij}^{2p}} for distance. In classical scaling p = 1. {\textstyle p=1.} Non-metric scaling is defined by the use of isotonic regression to nonparametrically estimate a transformation of the dissimilarities. === Non-metric multidimensional scaling (NMDS) === In contrast to metric MDS, non-metric MDS finds both a non-parametric monotonic relationship between the dissimilarities in the item-item matrix and the Euclidean distances between items, and the location of each item in the low-dimensional space. Let d i j {\displaystyle d_{ij}} be the dissimilarity between points i , j {\displaystyle i,j} . Let d ^ i j = ‖ x i − x j ‖ {\displaystyle {\hat {d}}_{ij}=\|x_{i}-x_{j}\|} be the Euclidean distance between embedded points x i , x j {\displaystyle x_{i},x_{j}} . Now, for each choice of the embedded points x i {\displaystyle x_{i}} and is a monotonically increasing function f {\displaystyle f} , define the "stress" function: S ( x 1 , . . . , x n ; f ) = ∑ i < j ( f ( d i j ) − d ^ i j ) 2 ∑ i < j d ^ i j 2 . {\displaystyle S(x_{1},...,x_{n};f)={\sqrt {\frac {\sum _{i Read more →

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  Local tangent space alignment

  Local tangent space alignment (LTSA) is a method for manifold learning, which can efficiently learn a nonlinear embedding into low-dimensional coordinates from high-dimensional data, and can also reconstruct high-dimensional coordinates from embedding coordinates. It is based on the intuition that when a manifold is correctly unfolded, all of the tangent hyperplanes to the manifold will become aligned. It begins by computing the k-nearest neighbors of every point. It computes the tangent space at every point by computing the d-first principal components in each local neighborhood. It then optimizes to find an embedding that aligns the tangent spaces, but it ignores the label information conveyed by data samples, and thus can not be used for classification directly.

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  Database

  In computing, a database is an organized collection of data or a type of data store based on the use of a database management system (DBMS), the software that interacts with end users, applications, and the database itself to capture and analyze the data. The DBMS additionally encompasses the core facilities provided to administer the database. The sum total of the database, the DBMS and the associated applications can be referred to as a database system. Often the term "database" is also used loosely to refer to any of the DBMS, the database system or an application associated with the database. Before digital storage and retrieval of data became widespread, index cards were used for data storage in a wide range of applications and environments: in the home to record and store recipes, shopping lists, contact information and other organizational data; in business to record presentation notes, project research and notes, and contact information; in schools as flash cards or other visual aids; and in academic research to hold data such as bibliographical citations or notes in a card file. Professional book indexers used index cards in the creation of book indexes until they were replaced by indexing software in the 1980s and 1990s. Small databases can be stored on a file system, while large databases are hosted on computer clusters or cloud storage. The design of databases spans formal techniques and practical considerations, including data modeling, efficient data representation and storage, query languages, security and privacy of sensitive data, and distributed computing issues, including supporting concurrent access and fault tolerance. Computer scientists may classify database management systems according to the database models that they support. Relational databases became dominant in the 1980s. These model data as rows and columns in a series of tables, and the vast majority use SQL for writing and querying data. In the 2000s, non-relational databases became popular, collectively referred to as NoSQL, because they use different query languages. == Terminology and overview == Formally, a "database" refers to a set of related data accessed through the use of a "database management system" (DBMS), which is an integrated set of computer software that allows users to interact with one or more databases and provides access to all of the data contained in the database (although restrictions may exist that limit access to particular data). The DBMS provides various functions that allow entry, storage and retrieval of large quantities of information and provides ways to manage how that information is organized. Because of the close relationship between them, the term "database" is often used casually to refer to both a database and the DBMS used to manipulate it. Outside the world of professional information technology, the term database is often used to refer to any collection of related data (such as a spreadsheet or a card index) as size and usage requirements typically necessitate use of a database management system. Existing DBMSs provide various functions that allow management of a database and its data which can be classified into four main functional groups: Data definition – Creation, modification and removal of definitions that detail how the data is to be organized. Update – Insertion, modification, and deletion of the data itself. Retrieval – Selecting data according to specified criteria (e.g., a query, a position in a hierarchy, or a position in relation to other data) and providing that data either directly to the user, or making it available for further processing by the database itself or by other applications. The retrieved data may be made available in a more or less direct form without modification, as it is stored in the database, or in a new form obtained by altering it or combining it with existing data from the database. Administration – Registering and monitoring users, enforcing data security, monitoring performance, maintaining data integrity, dealing with concurrency control, and recovering information that has been corrupted by some event such as an unexpected system failure. Both a database and its DBMS conform to the principles of a particular database model. "Database system" refers collectively to the database model, database management system, and database. Physically, database servers are dedicated computers that hold the actual databases and run only the DBMS and related software. Database servers are usually multiprocessor computers, with generous memory and RAID disk arrays used for stable storage. Hardware database accelerators, connected to one or more servers via a high-speed channel, are also used in large-volume transaction processing environments. DBMSs are found at the heart of most database applications. DBMSs may be built around a custom multitasking kernel with built-in networking support, but modern DBMSs typically rely on a standard operating system to provide these functions. Since DBMSs comprise a significant market, computer and storage vendors often take into account DBMS requirements in their own development plans. Databases and DBMSs can be categorized according to the database model(s) that they support (such as relational or XML), the type(s) of computer they run on (from a server cluster to a mobile phone), the query language(s) used to access the database (such as SQL or XQuery), and their internal engineering, which affects performance, scalability, resilience, and security. == History == The sizes, capabilities, and performance of databases and their respective DBMSs have grown in orders of magnitude. These performance increases were enabled by the technology progress in the areas of processors, computer memory, computer storage, and computer networks. The concept of a database was made possible by the emergence of direct access storage media such as magnetic disks, which became widely available in the mid-1960s; earlier systems relied on sequential storage of data on magnetic tape. The subsequent development of database technology can be divided into three eras based on data model or structure: navigational, SQL/relational, and post-relational. The two main early navigational data models were the hierarchical model and the CODASYL model (network model). These were characterized by the use of pointers (often physical disk addresses) to follow relationships from one record to another. The relational model, first proposed in 1970 by Edgar F. Codd, departed from this tradition by insisting that applications should search for data by content, rather than by following links. The relational model employs sets of ledger-style tables, each used for a different type of entity. Only in the mid-1980s did computing hardware become powerful enough to allow the wide deployment of relational systems (DBMSs plus applications). By the early 1990s, however, relational systems dominated in all large-scale data processing applications, and as of 2018 they remain dominant: IBM Db2, Oracle, MySQL, and Microsoft SQL Server are the most searched DBMS. The dominant database language, standardized SQL for the relational model, has influenced database languages for other data models. Object databases were developed in the 1980s to overcome the inconvenience of object–relational impedance mismatch, which led to the coining of the term "post-relational" and also the development of hybrid object–relational databases. The next generation of post-relational databases in the late 2000s became known as NoSQL databases, introducing fast key–value stores and document-oriented databases. A competing "next generation" known as NewSQL databases attempted new implementations that retained the relational/SQL model while aiming to match the high performance of NoSQL compared to commercially available relational DBMSs. === 1960s, navigational DBMS === The introduction of the term database coincided with the availability of direct-access storage (disks and drums) from the mid-1960s onwards. The term represented a contrast with the tape-based systems of the past, allowing shared interactive use rather than daily batch processing. The Oxford English Dictionary cites a 1962 report by the System Development Corporation of California as the first to use the term "data-base" in a specific technical sense. As computers grew in speed and capability, a number of general-purpose database systems emerged; by the mid-1960s a number of such systems had come into commercial use. Interest in a standard began to grow, and Charles Bachman, author of one such product, the Integrated Data Store (IDS), founded the Database Task Group within CODASYL, the group responsible for the creation and standardization of COBOL. In 1971, the Database Task Group delivered their standard, which generally became known as the CODASYL approach, and soon a number of commercial products based on this approach entered the market. The CODASYL approach of

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  Huber loss

  In statistics, the Huber loss is a loss function used in robust regression, that is less sensitive to outliers in data than the squared error loss. A variant for classification is also sometimes used. == Definition == The Huber loss function describes the penalty incurred by an estimation procedure f. Huber (1964) defines the loss function piecewise by L δ ( a ) = { 1 2 a 2 for | a | ≤ δ , δ ⋅ ( | a | − 1 2 δ ) , otherwise. {\displaystyle L_{\delta }(a)={\begin{cases}{\frac {1}{2}}{a^{2}}&{\text{for }}|a|\leq \delta ,\\[4pt]\delta \cdot \left(|a|-{\frac {1}{2}}\delta \right),&{\text{otherwise.}}\end{cases}}} This function is quadratic for small values of a, and linear for large values, with equal values and slopes of the different sections at the two points where | a | = δ {\displaystyle |a|=\delta } . The variable a often refers to the residuals, that is to the difference between the observed and predicted values a = y − f ( x ) {\displaystyle a=y-f(x)} , so the former can be expanded to L δ ( y , f ( x ) ) = { 1 2 ( y − f ( x ) ) 2 for | y − f ( x ) | ≤ δ , δ ⋅ ( | y − f ( x ) | − 1 2 δ ) , otherwise. {\displaystyle L_{\delta }(y,f(x))={\begin{cases}{\frac {1}{2}}{\left(y-f(x)\right)}^{2}&{\text{for }}\left|y-f(x)\right|\leq \delta ,\\[4pt]\delta \ \cdot \left(\left|y-f(x)\right|-{\frac {1}{2}}\delta \right),&{\text{otherwise.}}\end{cases}}} The Huber loss is the convolution of the absolute value function with the rectangular function, scaled and translated. Thus it "smoothens out" the former's corner at the origin. == Motivation == Two very commonly used loss functions are the squared loss, L ( a ) = a 2 {\displaystyle L(a)=a^{2}} , and the absolute loss, L ( a ) = | a | {\displaystyle L(a)=|a|} . The squared loss function results in an arithmetic mean-unbiased estimator, and the absolute-value loss function results in a median-unbiased estimator (in the one-dimensional case, and a geometric median-unbiased estimator for the multi-dimensional case). The squared loss has the disadvantage that it has the tendency to be dominated by outliers—when summing over a set of a {\displaystyle a} 's (as in ∑ i = 1 n L ( a i ) {\textstyle \sum _{i=1}^{n}L(a_{i})} ), the sample mean is influenced too much by a few particularly large a {\displaystyle a} -values when the distribution is heavy tailed: in terms of estimation theory, the asymptotic relative efficiency of the mean is poor for heavy-tailed distributions. As defined above, the Huber loss function is strongly convex in a uniform neighborhood of its minimum a = 0 {\displaystyle a=0} ; at the boundary of this uniform neighborhood, the Huber loss function has a differentiable extension to an affine function at points a = − δ {\displaystyle a=-\delta } and a = δ {\displaystyle a=\delta } . These properties allow it to combine much of the sensitivity of the mean-unbiased, minimum-variance estimator of the mean (using the quadratic loss function) and the robustness of the median-unbiased estimator (using the absolute value function). == Pseudo-Huber loss function == The Pseudo-Huber loss function can be used as a smooth approximation of the Huber loss function. It combines the best properties of L2 squared loss and L1 absolute loss by being strongly convex when close to the target/minimum and less steep for extreme values. The scale at which the Pseudo-Huber loss function transitions from L2 loss for values close to the minimum to L1 loss for extreme values and the steepness at extreme values can be controlled by the δ {\displaystyle \delta } value. The Pseudo-Huber loss function ensures that derivatives are continuous for all degrees. It is defined as L δ ( a ) = δ 2 ( 1 + ( a / δ ) 2 − 1 ) . {\displaystyle L_{\delta }(a)=\delta ^{2}\left({\sqrt {1+(a/\delta )^{2}}}-1\right).} As such, this function approximates a 2 / 2 {\displaystyle a^{2}/2} for small values of a {\displaystyle a} , and approximates a straight line with slope δ {\displaystyle \delta } for large values of a {\displaystyle a} . While the above is the most common form, other smooth approximations of the Huber loss function also exist. == Variant for classification == For classification purposes, a variant of the Huber loss called modified Huber is sometimes used. Given a prediction f ( x ) {\displaystyle f(x)} (a real-valued classifier score) and a true binary class label y ∈ { + 1 , − 1 } {\displaystyle y\in \{+1,-1\}} , the modified Huber loss is defined as L ( y , f ( x ) ) = { max ( 0 , 1 − y f ( x ) ) 2 for y f ( x ) > − 1 , − 4 y f ( x ) otherwise. {\displaystyle L(y,f(x))={\begin{cases}\max(0,1-y\,f(x))^{2}&{\text{for }}\,\,y\,f(x)>-1,\\[4pt]-4y\,f(x)&{\text{otherwise.}}\end{cases}}} The term max ( 0 , 1 − y f ( x ) ) {\displaystyle \max(0,1-y\,f(x))} is the hinge loss used by support vector machines; the quadratically smoothed hinge loss is a generalization of L {\displaystyle L} . == Applications == The Huber loss function is used in robust statistics, M-estimation and additive modelling.

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  Bondy's theorem

  In mathematics, Bondy's theorem is a bound on the number of elements needed to distinguish the sets in a family of sets from each other. It belongs to the field of combinatorics, and is named after John Adrian Bondy, who published it in 1972. == Statement == The theorem is as follows: Let X be a set with n elements and let A1, A2, ..., An be distinct subsets of X. Then there exists a subset S of X with n − 1 elements such that the sets Ai ∩ S are all distinct. In other words, if we have a 0-1 matrix with n rows and n columns such that each row is distinct, we can remove one column such that the rows of the resulting n × (n − 1) matrix are distinct. == Example == Consider the 4 × 4 matrix [ 1 1 0 1 0 1 0 1 0 0 1 1 0 1 1 0 ] {\displaystyle {\begin{bmatrix}1&1&0&1\\0&1&0&1\\0&0&1&1\\0&1&1&0\end{bmatrix}}} where all rows are pairwise distinct. If we delete, for example, the first column, the resulting matrix [ 1 0 1 1 0 1 0 1 1 1 1 0 ] {\displaystyle {\begin{bmatrix}1&0&1\\1&0&1\\0&1&1\\1&1&0\end{bmatrix}}} no longer has this property: the first row is identical to the second row. Nevertheless, by Bondy's theorem we know that we can always find a column that can be deleted without introducing any identical rows. In this case, we can delete the third column: all rows of the 3 × 4 matrix [ 1 1 1 0 1 1 0 0 1 0 1 0 ] {\displaystyle {\begin{bmatrix}1&1&1\\0&1&1\\0&0&1\\0&1&0\end{bmatrix}}} are distinct. Another possibility would have been deleting the fourth column. == Learning theory application == From the perspective of computational learning theory, Bondy's theorem can be rephrased as follows: Let C be a concept class over a finite domain X. Then there exists a subset S of X with the size at most |C| − 1 such that S is a witness set for every concept in C. This implies that every finite concept class C has its teaching dimension bounded by |C| − 1.

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  Chromosome (evolutionary algorithm)

  A chromosome or genotype in evolutionary algorithms (EA) is a set of parameters which define a proposed solution of the problem that the evolutionary algorithm is trying to solve. The set of all solutions, also called individuals according to the biological model, is known as the population. The genome of an individual consists of one, more rarely of several, chromosomes and corresponds to the genetic representation of the task to be solved. A chromosome is composed of a set of genes, where a gene consists of one or more semantically connected parameters, which are often also called decision variables. They determine one or more phenotypic characteristics of the individual or at least have an influence on them. In the basic form of genetic algorithms, the chromosome is represented as a binary string, while in later variants and in EAs in general, a wide variety of other data structures are used. == Chromosome design == When creating the genetic representation of a task, it is determined which decision variables and other degrees of freedom of the task should be improved by the EA and possible additional heuristics and how the genotype-phenotype mapping should look like. The design of a chromosome translates these considerations into concrete data structures for which an EA then has to be selected, configured, extended, or, in the worst case, created. Finding a suitable representation of the problem domain for a chromosome is an important consideration, as a good representation will make the search easier by limiting the search space; similarly, a poorer representation will allow a larger search space. In this context, suitable mutation and crossover operators must also be found or newly defined to fit the chosen chromosome design. An important requirement for these operators is that they not only allow all points in the search space to be reached in principle, but also make this as easy as possible. The following requirements must be met by a well-suited chromosome: It must allow the accessibility of all admissible points in the search space. Design of the chromosome in such a way that it covers only the search space and no additional areas. so that there is no redundancy or only as little redundancy as possible. Observance of strong causality: small changes in the chromosome should only lead to small changes in the phenotype. This is also called locality of the relationship between search and problem space. Designing the chromosome in such a way that it excludes prohibited regions in the search space completely or as much as possible. While the first requirement is indispensable, depending on the application and the EA used, one usually only has to be satisfied with fulfilling the remaining requirements as far as possible. The evolutionary search is supported and possibly considerably accelerated by a fulfillment as complete as possible. == Examples of chromosomes == === Chromosomes for binary codings === In their classical form, GAs use bit strings and map the decision variables to be optimized onto them. An example for one Boolean and three integer decision variables with the value ranges 0 ≤ D 1 ≤ 60 {\displaystyle 0\leq D_{1}\leq 60} , 28 ≤ D 2 ≤ 30 {\displaystyle 28\leq D_{2}\leq 30} and − 12 ≤ D 3 ≤ 14 {\displaystyle -12\leq D_{3}\leq 14} may illustrate this: Note that the negative number here is given in two's complement. This straight forward representation uses five bits to represent the three values of D 2 {\displaystyle D_{2}} , although two bits would suffice. This is a significant redundancy. An improved alternative, where 28 is to be added for the genotype-phenotype mapping, could look like this: with D 2 = 28 + D 2 ′ = 29 {\displaystyle D_{2}=28+D'_{2}=29} . === Chromosomes with real-valued or integer genes === For the processing of tasks with real-valued or mixed-integer decision variables, EAs such as the evolution strategy or the real-coded GAs are suited. In the case of mixed-integer values, rounding is often used, but this represents some violation of the redundancy requirement. If the necessary precisions of the real values can be reasonably narrowed down, this violation can be remedied by using integer-coded GAs. For this purpose, the valid digits of real values are mapped to integers by multiplication with a suitable factor. For example, 12.380 becomes the integer 12380 by multiplying by 1000. This must of course be taken into account in genotype-phenotype mapping for evaluation and result presentation. A common form is a chromosome consisting of a list or an array of integer or real values. === Chromosomes for permutations === Combinatorial problems are mainly concerned with finding an optimal sequence of a set of elementary items. As an example, consider the problem of the traveling salesman who wants to visit a given number of cities exactly once on the shortest possible tour. The simplest and most obvious mapping onto a chromosome is to number the cities consecutively, to interpret a resulting sequence as permutation and to store it directly in a chromosome, where one gene corresponds to the ordinal number of a city. Then, however, the variation operators may only change the gene order and not remove or duplicate any genes. The chromosome thus contains the path of a possible tour to the cities. As an example the sequence 3 , 5 , 7 , 1 , 4 , 2 , 9 , 6 , 8 {\displaystyle 3,5,7,1,4,2,9,6,8} of nine cities may serve, to which the following chromosome corresponds: In addition to this encoding frequently called path representation, there are several other ways of representing a permutation, for example the ordinal representation or the matrix representation. === Chromosomes for co-evolution === When a genetic representation contains, in addition to the decision variables, additional information that influences evolution and/or the mapping of the genotype to the phenotype and is itself subject to evolution, this is referred to as co-evolution. A typical example is the evolution strategy (ES), which includes one or more mutation step sizes as strategy parameters in each chromosome. Another example is an additional gene to control a selection heuristic for resource allocation in a scheduling tasks. This approach is based on the assumption that good solutions are based on an appropriate selection of strategy parameters or on control gene(s) that influences genotype-phenotype mapping. The success of the ES gives evidence to this assumption. === Chromosomes for complex representations === The chromosomes presented above are well suited for processing tasks of continuous, mixed-integer, pure-integer or combinatorial optimization. For a combination of these optimization areas, on the other hand, it becomes increasingly difficult to map them to simple strings of values, depending on the task. The following extension of the gene concept is proposed by the EA GLEAM (General Learning Evolutionary Algorithm and Method) for this purpose: A gene is considered to be the description of an element or elementary trait of the phenotype, which may have multiple parameters. For this purpose, gene types are defined that contain as many parameters of the appropriate data type as are required to describe the particular element of the phenotype. A chromosome now consists of genes as data objects of the gene types, whereby, depending on the application, each gene type occurs exactly once as a gene or can be contained in the chromosome any number of times. The latter leads to chromosomes of dynamic length, as they are required for some problems. The gene type definitions also contain information on the permissible value ranges of the gene parameters, which are observed during chromosome generation and by corresponding mutations, so they cannot lead to lethal mutations. For tasks with a combinatorial part, there are suitable genetic operators that can move or reposition genes as a whole, i.e. with their parameters. A scheduling task is used as an illustration, in which workflows are to be scheduled that require different numbers of heterogeneous resources. A workflow specifies which work steps can be processed in parallel and which have to be executed one after the other. In this context, heterogeneous resources mean different processing times at different costs in addition to different processing capabilities. Each scheduling operation therefore requires one or more parameters that determine the resource selection, where the value ranges of the parameters depend on the number of alternative resources available for each work step. A suitable chromosome provides one gene type per work step and in this case one corresponding gene, which has one parameter for each required resource. The order of genes determines the order of scheduling operations and, therefore, the precedence in case of allocation conflicts. The exemplary gene type definition of work step 15 with two resources, for which there are four and seven alternatives respectively

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  Qlone

  Qlone is a 3D scanning app based on photogrammetry for creation of 3D models on mobile devices. The resultant 3D models can be exported for external use. Qlone was featured at the Apple Worldwide Developers Conference in 2021. It was also featured on BBC Click. == Qlone features == === 3D scanning === 3D scanning with Qlone requires the use of an included mat design. The user prints the mat onto a sheet of paper, then places the object to be scanned in the centre of the mat. An augmented reality dome within the Qlone app guides the user through the subsequent scanning process. The iOS version of Qlone allows scanning without the mat. === 3D editing === Qlone's editing features allow users to adjust 3D scanned models using texture mapping, polygon mesh size simplification, digital sculpting, cleaning and smoothing, and artistic effects. === File export === Qlone exports directly to multiple 3D platforms including SketchFab, i.materialise, Lens Studio for Snapchat, Shapeways and CGTrader. Models can also be exported in different 3D formats for use in other 3D tools – OBJ, STL, FBX, USDZ, GLB (Binary gLTF), PLY, and X3D. == Use in Science, Education and Academia == Due to its inexpensive, simple and accessible nature for creating 3D models, Qlone was used in many academically educational and scientific research projects. The European Space Agency used Qlone to scan rocks in a Tele-Robotic rock collection experiment. Neurosurgeons from the University of Southern California and surgeons from Tulane University School of Medicine used Qlone to create 3D models of cadaveric specimens and anatomical models with the aim of increasing access to such components for enhancing anatomy training and allowing realistic surgical simulations for neurosurgeons and practitioners worldwide. Archaeologists from Texas A&M University used Qlone to create 3D replicas of artifacts and models and students from Vancouver iTech Preparatory Middle School used Qlone to create 3D scans of more than 100 artifacts from Fort Vancouver National Historic Site.

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  Naive Bayes classifier

  In statistics, naive (sometimes simple or idiot's) Bayes classifiers are a family of "probabilistic classifiers" which assume that the features are conditionally independent, given the target class. In other words, a naive Bayes model assumes the information about the class provided by each variable is unrelated to the information from the others, with no information shared between the predictors. The highly unrealistic nature of this assumption, called the naive independence assumption, is what gives the classifier its name. These classifiers are some of the simplest Bayesian network models. Naive Bayes classifiers generally perform worse than more advanced models like logistic regressions, especially at quantifying uncertainty (with naive Bayes models often producing wildly overconfident probabilities). However, they are highly scalable, requiring only one parameter for each feature or predictor in a learning problem. Maximum-likelihood training can be done by evaluating a closed-form expression (simply by counting observations in each group), rather than the expensive iterative approximation algorithms required by most other models. Despite the use of Bayes' theorem in the classifier's decision rule, naive Bayes is not (necessarily) a Bayesian method, and naive Bayes models can be fit to data using either Bayesian or frequentist methods. == Introduction == Naive Bayes is a simple technique for constructing classifiers: models that assign class labels to problem instances, represented as vectors of feature values, where the class labels are drawn from some finite set. There is not a single algorithm for training such classifiers, but a family of algorithms based on a common principle: all naive Bayes classifiers assume that the value of a particular feature is independent of the value of any other feature, given the class variable. For example, a fruit may be considered to be an apple if it is red, round, and about 10 cm in diameter. A naive Bayes classifier considers each of these features to contribute independently to the probability that this fruit is an apple, regardless of any possible correlations between the color, roundness, and diameter features. In many practical applications, parameter estimation for naive Bayes models uses the method of maximum likelihood; in other words, one can work with the naive Bayes model without accepting Bayesian probability or using any Bayesian methods. Despite their naive design and apparently oversimplified assumptions, naive Bayes classifiers have worked quite well in many complex real-world situations. In 2004, an analysis of the Bayesian classification problem showed that there are sound theoretical reasons for the apparently implausible efficacy of naive Bayes classifiers. Still, a comprehensive comparison with other classification algorithms in 2006 showed that Bayes classification is outperformed by other approaches, such as boosted trees or random forests. An advantage of naive Bayes is that it only requires a small amount of training data to estimate the parameters necessary for classification. == Probabilistic model == Abstractly, naive Bayes is a conditional probability model: it assigns probabilities p ( C k ∣ x 1 , … , x n ) {\displaystyle p(C_{k}\mid x_{1},\ldots ,x_{n})} for each of the K possible outcomes or classes C k {\displaystyle C_{k}} given a problem instance to be classified, represented by a vector x = ( x 1 , … , x n ) {\displaystyle \mathbf {x} =(x_{1},\ldots ,x_{n})} encoding some n features (independent variables). The problem with the above formulation is that if the number of features n is large or if a feature can take on a large number of values, then basing such a model on probability tables is infeasible. The model must therefore be reformulated to make it more tractable. Using Bayes' theorem, the conditional probability can be decomposed as: p ( C k ∣ x ) = p ( C k ) p ( x ∣ C k ) p ( x ) {\displaystyle p(C_{k}\mid \mathbf {x} )={\frac {p(C_{k})\ p(\mathbf {x} \mid C_{k})}{p(\mathbf {x} )}}\,} In plain English, using Bayesian probability terminology, the above equation can be written as posterior = prior × likelihood evidence {\displaystyle {\text{posterior}}={\frac {{\text{prior}}\times {\text{likelihood}}}{\text{evidence}}}\,} In practice, there is interest only in the numerator of that fraction, because the denominator does not depend on C {\displaystyle C} and the values of the features x i {\displaystyle x_{i}} are given, so that the denominator is effectively constant. The numerator is equivalent to the joint probability model p ( C k , x 1 , … , x n ) {\displaystyle p(C_{k},x_{1},\ldots ,x_{n})\,} which can be rewritten as follows, using the chain rule for repeated applications of the definition of conditional probability: p ( C k , x 1 , … , x n ) = p ( x 1 , … , x n , C k ) = p ( x 1 ∣ x 2 , … , x n , C k ) p ( x 2 , … , x n , C k ) = p ( x 1 ∣ x 2 , … , x n , C k ) p ( x 2 ∣ x 3 , … , x n , C k ) p ( x 3 , … , x n , C k ) = ⋯ = p ( x 1 ∣ x 2 , … , x n , C k ) p ( x 2 ∣ x 3 , … , x n , C k ) ⋯ p ( x n − 1 ∣ x n , C k ) p ( x n ∣ C k ) p ( C k ) {\displaystyle {\begin{aligned}p(C_{k},x_{1},\ldots ,x_{n})&=p(x_{1},\ldots ,x_{n},C_{k})\\&=p(x_{1}\mid x_{2},\ldots ,x_{n},C_{k})\ p(x_{2},\ldots ,x_{n},C_{k})\\&=p(x_{1}\mid x_{2},\ldots ,x_{n},C_{k})\ p(x_{2}\mid x_{3},\ldots ,x_{n},C_{k})\ p(x_{3},\ldots ,x_{n},C_{k})\\&=\cdots \\&=p(x_{1}\mid x_{2},\ldots ,x_{n},C_{k})\ p(x_{2}\mid x_{3},\ldots ,x_{n},C_{k})\cdots p(x_{n-1}\mid x_{n},C_{k})\ p(x_{n}\mid C_{k})\ p(C_{k})\\\end{aligned}}} Now the "naive" conditional independence assumptions come into play: assume that all features in x {\displaystyle \mathbf {x} } are mutually independent, conditional on the category C k {\displaystyle C_{k}} . Under this assumption, p ( x i ∣ x i + 1 , … , x n , C k ) = p ( x i ∣ C k ) . {\displaystyle p(x_{i}\mid x_{i+1},\ldots ,x_{n},C_{k})=p(x_{i}\mid C_{k})\,.} Thus, the joint model can be expressed as p ( C k ∣ x 1 , … , x n ) ∝ p ( C k , x 1 , … , x n ) = p ( C k ) p ( x 1 ∣ C k ) p ( x 2 ∣ C k ) p ( x 3 ∣ C k ) ⋯ = p ( C k ) ∏ i = 1 n p ( x i ∣ C k ) , {\displaystyle {\begin{aligned}p(C_{k}\mid x_{1},\ldots ,x_{n})\varpropto \ &p(C_{k},x_{1},\ldots ,x_{n})\\&=p(C_{k})\ p(x_{1}\mid C_{k})\ p(x_{2}\mid C_{k})\ p(x_{3}\mid C_{k})\ \cdots \\&=p(C_{k})\prod _{i=1}^{n}p(x_{i}\mid C_{k})\,,\end{aligned}}} where ∝ {\displaystyle \varpropto } denotes proportionality since the denominator p ( x ) {\displaystyle p(\mathbf {x} )} is omitted. This means that under the above independence assumptions, the conditional distribution over the class variable C {\displaystyle C} is: p ( C k ∣ x 1 , … , x n ) = 1 Z p ( C k ) ∏ i = 1 n p ( x i ∣ C k ) {\displaystyle p(C_{k}\mid x_{1},\ldots ,x_{n})={\frac {1}{Z}}\ p(C_{k})\prod _{i=1}^{n}p(x_{i}\mid C_{k})} where the evidence Z = p ( x ) = ∑ k p ( C k ) p ( x ∣ C k ) {\displaystyle Z=p(\mathbf {x} )=\sum _{k}p(C_{k})\ p(\mathbf {x} \mid C_{k})} is a scaling factor dependent only on x 1 , … , x n {\displaystyle x_{1},\ldots ,x_{n}} , that is, a constant if the values of the feature variables are known. Often, it is only necessary to discriminate between classes. In that case, the scaling factor is irrelevant, and it is sufficient to calculate the log-probability up to a factor: ln ⁡ p ( C k ∣ x 1 , … , x n ) = ln ⁡ p ( C k ) + ∑ i = 1 n ln ⁡ p ( x i ∣ C k ) − ln ⁡ Z ⏟ irrelevant {\displaystyle \ln p(C_{k}\mid x_{1},\ldots ,x_{n})=\ln p(C_{k})+\sum _{i=1}^{n}\ln p(x_{i}\mid C_{k})\underbrace {-\ln Z} _{\text{irrelevant}}} The scaling factor is irrelevant, since discrimination subtracts it away: ln ⁡ p ( C k ∣ x 1 , … , x n ) p ( C l ∣ x 1 , … , x n ) = ( ln ⁡ p ( C k ) + ∑ i = 1 n ln ⁡ p ( x i ∣ C k ) ) − ( ln ⁡ p ( C l ) + ∑ i = 1 n ln ⁡ p ( x i ∣ C l ) ) {\displaystyle \ln {\frac {p(C_{k}\mid x_{1},\ldots ,x_{n})}{p(C_{l}\mid x_{1},\ldots ,x_{n})}}=\left(\ln p(C_{k})+\sum _{i=1}^{n}\ln p(x_{i}\mid C_{k})\right)-\left(\ln p(C_{l})+\sum _{i=1}^{n}\ln p(x_{i}\mid C_{l})\right)} There are two benefits of using log-probability. One is that it allows an interpretation in information theory, where log-probabilities are units of information in nats. Another is that it avoids arithmetic underflow. === Constructing a classifier from the probability model === The discussion so far has derived the independent feature model, that is, the naive Bayes probability model. The naive Bayes classifier combines this model with a decision rule. One common rule is to pick the hypothesis that is most probable so as to minimize the probability of misclassification; this is known as the maximum a posteriori or MAP decision rule. The corresponding classifier, a Bayes classifier, is the function that assigns a class label y ^ = C k {\displaystyle {\hat {y}}=C_{k}} for some k as follows: y ^ = argmax k ∈ { 1 , … , K } p ( C k ) ∏ i = 1 n p ( x i ∣ C k ) . {\displaystyle {\hat {y}}={\underset {k\in \{1,\ldots ,K\}}{\operatorname {argmax} }}\ p(C_{k})\displays

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  Latent class model

  In statistics, a latent class model (LCM) is a model for clustering multivariate discrete data. It assumes that the data arise from a mixture of discrete distributions, within each of which the variables are independent. It is called a latent class model because the class to which each data point belongs is unobserved (or latent). Latent class analysis (LCA) is a subset of structural equation modeling used to find groups or subtypes of cases in multivariate categorical data. These groups or subtypes of cases are called "latent classes". When faced with the following situation, a researcher might opt to use LCA to better understand the data: Symptoms a, b, c, and d have been recorded in a variety of patients diagnosed with diseases X, Y, and Z. Disease X is associated with symptoms a, b, and c; disease Y is linked to symptoms b, c, and d; and disease Z is connected to symptoms a, c, and d. In this context, the LCA would attempt to detect the presence of latent classes (i.e., the disease entities), thus creating patterns of association in the symptoms. As in factor analysis, LCA can also be used to classify cases according to their maximum likelihood class membership probability. The key criterion for resolving the LCA is identifying latent classes in which the observed symptom associations are effectively rendered null. This is because within each class, the diseases responsible for the symptoms create a structure of dependencies. As a result, the symptoms become conditionally independent, meaning that, given the class a case belongs to, the symptoms are no longer related to one another. == Model == Within each latent class, the observed variables are statistically independent—an essential aspect of latent class modeling. Usually, the observed variables are statistically dependent. By introducing the latent variable, independence is restored in the sense that within classes, variables are independent (local independence). Therefore, the association between the observed variables is explained by the classes of the latent variable (McCutcheon, 1987). In one form, the LCM is written as p i 1 , i 2 , … , i N ≈ ∑ t T p t ∏ n N p i n , t n , {\displaystyle p_{i_{1},i_{2},\ldots ,i_{N}}\approx \sum _{t}^{T}p_{t}\,\prod _{n}^{N}p_{i_{n},t}^{n},} where T {\displaystyle T} is the number of latent classes and p t {\displaystyle p_{t}} are the so-called recruitment or unconditional probabilities that should sum to one. p i n , t n {\displaystyle p_{i_{n},t}^{n}} are the marginal or conditional probabilities. For a two-way latent class model, the form is p i j ≈ ∑ t T p t p i t p j t . {\displaystyle p_{ij}\approx \sum _{t}^{T}p_{t}\,p_{it}\,p_{jt}.} This two-way model is related to probabilistic latent semantic analysis and non-negative matrix factorization. The probability model used in LCA is closely related to the Naive Bayes classifier. The main difference is that in LCA, the class membership of an individual is a latent variable, whereas in Naive Bayes classifiers, the class membership is an observed label. == Related methods == There are a number of methods with distinct names and uses that share a common relationship. Cluster analysis is, like LCA, used to discover taxon-like groups of cases in data. Multivariate mixture estimation (MME) is applicable to continuous data and assumes that such data arise from a mixture of distributions, such as a set of heights arising from a mixture of men and women. If a multivariate mixture estimation is constrained so that measures must be uncorrelated within each distribution, it is termed latent profile analysis. Modified to handle discrete data, this constrained analysis is known as LCA. Discrete latent trait models further constrain the classes to form from segments of a single dimension, allocating members to classes based on that dimension. An example would be assigning cases to social classes based on ability or merit. In a practical instance, the variables could be multiple choice items of a political questionnaire. In this case, the data consists of an N-way contingency table with answers to the items for a number of respondents. In this example, the latent variable refers to political opinion, and the latent classes to political groups. Given group membership, the conditional probabilities specify the chance that certain answers are chosen. == Application == LCA may be used in many fields, such as: collaborative filtering, Behavior Genetics and Evaluation of diagnostic tests.

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  Reservoir computing

  Reservoir computing is a framework for computation derived from recurrent neural network theory that maps input signals into higher dimensional computational spaces through the dynamics of a fixed, non-linear system called a reservoir. After the input signal is fed into the reservoir, which is treated as a "black box," a simple readout mechanism is trained to read the state of the reservoir and map it to the desired output. The first key benefit of this framework is that training is performed only at the readout stage, as the reservoir dynamics are fixed. The second is that the computational power of naturally available systems, both classical and quantum mechanical, can be used to reduce the effective computational cost. == History == The first examples of reservoir neural networks demonstrated that randomly connected recurrent neural networks could be used for sensorimotor sequence learning, and simple forms of interval and speech discrimination. In these early models the memory in the network took the form of both short-term synaptic plasticity and activity mediated by recurrent connections. In other early reservoir neural network models the memory of the recent stimulus history was provided solely by the recurrent activity. Overall, the general concept of reservoir computing stems from the use of recursive connections within neural networks to create a complex dynamical system. It is a generalisation of earlier neural network architectures such as recurrent neural networks, liquid-state machines and echo-state networks. Reservoir computing also extends to physical systems that are not networks in the classical sense, but rather continuous systems in space and/or time: e.g. a literal "bucket of water" can serve as a reservoir that performs computations on inputs given as perturbations of the surface. The resultant complexity of such recurrent neural networks was found to be useful in solving a variety of problems including language processing and dynamic system modeling. However, training of recurrent neural networks is challenging and computationally expensive. Reservoir computing reduces those training-related challenges by fixing the dynamics of the reservoir and only training the linear output layer. A large variety of nonlinear dynamical systems can serve as a reservoir that performs computations. In recent years semiconductor lasers have attracted considerable interest as computation can be fast and energy efficient compared to electrical components. Recent advances in both AI and quantum information theory have given rise to the concept of quantum neural networks. These hold promise in quantum information processing, which is challenging to classical networks, but can also find application in solving classical problems. In 2018, a physical realization of a quantum reservoir computing architecture was demonstrated in the form of nuclear spins within a molecular solid. However, the nuclear spin experiments in did not demonstrate quantum reservoir computing per se as they did not involve processing of sequential data. Rather the data were vector inputs, which makes this more accurately a demonstration of quantum implementation of a random kitchen sink algorithm (also going by the name of extreme learning machines in some communities). In 2019, another possible implementation of quantum reservoir processors was proposed in the form of two-dimensional fermionic lattices. In 2020, realization of reservoir computing on gate-based quantum computers was proposed and demonstrated on cloud-based IBM superconducting near-term quantum computers. Reservoir computers have been used for time-series analysis purposes. In particular, some of their usages involve chaotic time-series prediction, separation of chaotic signals, and link inference of networks from their dynamics. == Classical reservoir computing == === Reservoir === The 'reservoir' in reservoir computing is the internal structure of the computer, and must have two properties: it must be made up of individual, non-linear units, and it must be capable of storing information. The non-linearity describes the response of each unit to input, which is what allows reservoir computers to solve complex problems. Reservoirs are able to store information by connecting the units in recurrent loops, where the previous input affects the next response. The change in reaction due to the past allows the computers to be trained to complete specific tasks. Reservoirs can be virtual or physical. Virtual reservoirs are typically randomly generated and are designed like neural networks. Virtual reservoirs can be designed to have non-linearity and recurrent loops, but, unlike neural networks, the connections between units are randomized and remain unchanged throughout computation. Physical reservoirs are possible because of the inherent non-linearity of certain natural systems. The interaction between ripples on the surface of water contains the nonlinear dynamics required in reservoir creation, and a pattern recognition RC was developed by first inputting ripples with electric motors then recording and analyzing the ripples in the readout. === Readout === The readout is a neural network layer that performs a linear transformation on the output of the reservoir. The weights of the readout layer are trained by analyzing the spatiotemporal patterns of the reservoir after excitation by known inputs, and by utilizing a training method such as a linear regression or a Ridge regression. As its implementation depends on spatiotemporal reservoir patterns, the details of readout methods are tailored to each type of reservoir. For example, the readout for a reservoir computer using a container of liquid as its reservoir might entail observing spatiotemporal patterns on the surface of the liquid. === Types === ==== Context reverberation network ==== An early example of reservoir computing was the context reverberation network. In this architecture, an input layer feeds into a high dimensional dynamical system which is read out by a trainable single-layer perceptron. Two kinds of dynamical system were described: a recurrent neural network with fixed random weights, and a continuous reaction–diffusion system inspired by Alan Turing's model of morphogenesis. At the trainable layer, the perceptron associates current inputs with the signals that reverberate in the dynamical system; the latter were said to provide a dynamic "context" for the inputs. In the language of later work, the reaction–diffusion system served as the reservoir. ==== Echo state network ==== The tree echo state network (TreeESN) model represents a generalization of the reservoir computing framework to tree structured data. ==== Liquid-state machine ==== Chaotic liquid state machine The liquid (i.e. reservoir) of a chaotic liquid state machine (CLSM), or chaotic reservoir, is made from chaotic spiking neurons but which stabilize their activity by settling to a single hypothesis that describes the trained inputs of the machine. This is in contrast to general types of reservoirs that don't stabilize. The liquid stabilization occurs via synaptic plasticity and chaos control that govern neural connections inside the liquid. CLSM showed promising results in learning sensitive time series data. ==== Nonlinear transient computation ==== This type of information processing is most relevant when time-dependent input signals depart from the mechanism's internal dynamics. These departures cause transients or temporary altercations which are represented in the device's output. ==== Deep reservoir computing ==== The extension of the reservoir computing framework towards deep learning, with the introduction of deep reservoir computing and of the deep echo state network (DeepESN) model allows to develop efficiently trained models for hierarchical processing of temporal data, at the same time enabling the investigation on the inherent role of layered composition in recurrent neural networks. == Quantum reservoir computing == Quantum reservoir computing may use the nonlinear nature of quantum mechanical interactions or processes to form the characteristic nonlinear reservoirs but may also be done with linear reservoirs when the injection of the input to the reservoir creates the nonlinearity. The marriage of machine learning and quantum devices is leading to the emergence of quantum neuromorphic computing as a new research area. === Types === ==== Gaussian states of interacting quantum harmonic oscillators ==== Gaussian states are a paradigmatic class of states of continuous variable quantum systems. Although they can nowadays be created and manipulated in, e.g, state-of-the-art optical platforms, naturally robust to decoherence, it is well-known that they are not sufficient for, e.g., universal quantum computing because transformations that preserve the Gaussian nature of a state are linear. Normally, linear dynamics would not be sufficient for nontrivial reser

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  Scene text

  Scene text is text that appears in an image captured by a camera in an outdoor environment. The detection and recognition of scene text from camera captured images are computer vision tasks which became important after smart phones with good cameras became ubiquitous. The text in scene images varies in shape, font, colour and position. The recognition of scene text is further complicated sometimes by non-uniform illumination and focus. To improve scene text recognition, the International Conference on Document Analysis and Recognition (ICDAR) conducts a robust reading competition once in two years. The competition was held in 2003, 2005 and during every ICDAR conference. International association for pattern recognition (IAPR) has created a list of datasets as Reading systems. == Text detection == Text detection is the process of detecting the text present in the image, followed by surrounding it with a rectangular bounding box. Text detection can be carried out using image based techniques or frequency based techniques. In image based techniques, an image is segmented into multiple segments. Each segment is a connected component of pixels with similar characteristics. The statistical features of connected components are utilised to group them and form the text. Machine learning approaches such as support vector machine and convolutional neural networks are used to classify the components into text and non-text. In frequency based techniques, discrete Fourier transform (DFT) or discrete wavelet transform (DWT) are used to extract the high frequency coefficients. It is assumed that the text present in an image has high frequency components and selecting only the high frequency coefficients filters the text from the non-text regions in an image. == Word recognition == In word recognition, the text is assumed to be already detected and located and the rectangular bounding box containing the text is available. The word present in the bounding box needs to be recognized. The methods available to perform word recognition can be broadly classified into top-down and bottom-up approaches. In the top-down approaches, a set of words from a dictionary is used to identify which word suits the given image. Images are not segmented in most of these methods. Hence, the top-down approach is sometimes referred as segmentation free recognition. In the bottom-up approaches, the image is segmented into multiple components and the segmented image is passed through a recognition engine. Either an off the shelf Optical character recognition (OCR) engine or a custom-trained one is used to recognise the text.

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  Softplus

  In mathematics and machine learning, the softplus function is f ( x ) = ln ⁡ ( 1 + e x ) . {\displaystyle f(x)=\ln(1+e^{x}).} It is a smooth approximation (in fact, an analytic function) to the ramp function, which is known as the rectifier or ReLU (rectified linear unit) in machine learning. For large negative x {\displaystyle x} it is ln ⁡ ( 1 + e x ) = ln ⁡ ( 1 + ϵ ) ⪆ ln ⁡ 1 = 0 {\displaystyle \ln(1+e^{x})=\ln(1+\epsilon )\gtrapprox \ln 1=0} , so just above 0, while for large positive x {\displaystyle x} it is ln ⁡ ( 1 + e x ) ⪆ ln ⁡ ( e x ) = x {\displaystyle \ln(1+e^{x})\gtrapprox \ln(e^{x})=x} , so just above x {\displaystyle x} . The names softplus and SmoothReLU are used in machine learning. The name "softplus" (2000), by analogy with the earlier softmax (1989) is presumably because it is a smooth (soft) approximation of the positive part of x, which is sometimes denoted with a superscript plus, x + := max ( 0 , x ) {\displaystyle x^{+}:=\max(0,x)} . == Alternative forms == This function can be approximated as: ln ⁡ ( 1 + e x ) ≈ { ln ⁡ 2 , x = 0 , x 1 − e − x / ln ⁡ 2 , x ≠ 0 {\displaystyle \ln \left(1+e^{x}\right)\approx {\begin{cases}\ln 2,&x=0,\\[6pt]{\frac {x}{1-e^{-x/\ln 2}}},&x\neq 0\end{cases}}} By making the change of variables x = y ln ⁡ ( 2 ) {\displaystyle x=y\ln(2)} , this is equivalent to log 2 ⁡ ( 1 + 2 y ) ≈ { 1 , y = 0 , y 1 − e − y , y ≠ 0. {\displaystyle \log _{2}(1+2^{y})\approx {\begin{cases}1,&y=0,\\[6pt]{\frac {y}{1-e^{-y}}},&y\neq 0.\end{cases}}} A sharpness parameter k {\displaystyle k} may be included: f ( x ) = ln ⁡ ( 1 + e k x ) k , f ′ ( x ) = e k x 1 + e k x = 1 1 + e − k x . {\displaystyle f(x)={\frac {\ln(1+e^{kx})}{k}},\qquad \qquad f'(x)={\frac {e^{kx}}{1+e^{kx}}}={\frac {1}{1+e^{-kx}}}.} Additionally, the softplus function is equivalent to the log of the sigmoid function in the following way: − ln ⁡ ( sigmoid ( − x ) ) = − ln ⁡ ( 1 1 + e x ) = ln ⁡ ( 1 + e x ) = softplus ( x ) {\displaystyle -\ln({\text{sigmoid}}(-x))=-\ln \left({\frac {1}{1+e^{x}}}\right)=\ln \left(1+e^{x}\right)={\text{softplus}}(x)} == Related functions == The derivative of softplus is the standard logistic function: f ′ ( x ) = e x 1 + e x = 1 1 + e − x {\displaystyle f'(x)={\frac {e^{x}}{1+e^{x}}}={\frac {1}{1+e^{-x}}}} The logistic function or the sigmoid function is a smooth approximation of the rectifier, the Heaviside step function. === LogSumExp === The multivariable generalization of single-variable softplus is the LogSumExp with the first argument set to zero: L S E 0 + ⁡ ( x 1 , … , x n ) := LSE ⁡ ( 0 , x 1 , … , x n ) = ln ⁡ ( 1 + e x 1 + ⋯ + e x n ) . {\displaystyle \operatorname {LSE_{0}} ^{+}(x_{1},\dots ,x_{n}):=\operatorname {LSE} (0,x_{1},\dots ,x_{n})=\ln(1+e^{x_{1}}+\cdots +e^{x_{n}}).} The LogSumExp function is LSE ⁡ ( x 1 , … , x n ) = ln ⁡ ( e x 1 + ⋯ + e x n ) , {\displaystyle \operatorname {LSE} (x_{1},\dots ,x_{n})=\ln(e^{x_{1}}+\cdots +e^{x_{n}}),} and its gradient is the softmax; the softmax with the first argument set to zero is the multivariable generalization of the logistic function. Both LogSumExp and softmax are used in machine learning. === Convex conjugate === The convex conjugate (specifically, the Legendre transformation) of the softplus function is the negative binary entropy function (with base e). This is because (following the definition of the Legendre transformation: the derivatives are inverse functions) the derivative of softplus is the logistic function, whose inverse function is the logit, which is the derivative of negative binary entropy. Softplus can be interpreted as logistic loss (as a positive number), so, by duality, minimizing logistic loss corresponds to maximizing entropy. This justifies the principle of maximum entropy as loss minimization.

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  Evolutionary attractor

  An evolutionary attractor is a point in an evolutionary space where a selection process will always drive trait values towards that point from the region around it. Because of the importance of evolution through natural selection, often such an evolutionary space will be defined by genetic or phenotypic traits, or possibly both. In this case the selection process will be a form of natural selection. The existence of an evolutionary attractor in a biological evolutionary space does not always imply that it can be reached from all points in that evolutionary space, nor does it identify what will happen when the evolutionary attractor is reached. While an evolutionary attractor may represent a point in evolutionary space that is resistant to further selection, such as an evolutionarily stable strategy, other possibilities are available. Because identification of an evolutionary attractor on its own does not describe everything about the evolutionary space in which it lies, this has led to interest in the evolutionary dynamics surrounding evolutionary attractors and in evolutionary spaces in general. (Theoretical biologists and mathematicians working in the area may prefer the terms adaptive dynamics or evolutionary invasion analysis to evolutionary dynamics.) These fields use differential equations which allows a more complete understanding of the dynamics in evolutionary spaces including the existence or otherwise of evolutionary attractors. Advances in the study of molecular evolution have also led to the identification of evolutionary attractors at a molecular level. Because biological evolutionary processes have been studied using evolutionary game theory, a technique inspired by game theory originally derived to address economic problems, not only can evolutionary attractors be found in biology but economists studying evolutionary economic models have also identified evolutionary attractors. Evolution in biology has also inspired evolutionary computation in computer science. Many algorithms in this field use a form of selection inspired by natural selection to generate results through evolutionary algorithms. This is therefore another area in which evolutionary attractors have been identified. == Evolutionary attractors in biology == It is not probably not surprising that biology is the field where most examples of evolutionary attractors have been identified, given the importance of evolution through natural selection. === Evolutionary attractors in adaptive landscapes === An evolutionary attractor is a point in genetic and/or phenotypic trait space, that evolution will always drive trait values towards via a selection process. The concept of an evolutionary attractor arose in population genetics following the origin of the adaptive landscape originally proposed by Sewall Wright in 1932. The height of a point in an adaptive landscape is a measure of evolutionary fitness. If a point in an adaptive landscape is a peak, then selection will always drive traits towards it and it will be an evolutionary attractor. While population genetics deals with discrete genetic traits, quantitative genetics extended such concepts to deal with continuous genetic traits, where the concept of evolutionary attractor is also valid. === Evolutionary attractors in evolutionary game models === Evolutionary game theory introduced into evolutionary biology concepts originally used in economics, with the advantage that evolution could be studied in relation to strategic choices made in animal conflicts. This is of particular interest because of the concept of the evolutionarily stable strategy or ESS, a strategy that once established is resistant to invasion by other strategies. ESSs will not always be evolutionary attractors, but if they are they will persist over evolutionary time. === Dynamics around evolutionary attractors in biology === Evolutionary attractors in biology do not exist in isolation. By definition they must exist in an evolutionary trait space where selection drives all traits towards them from a region immediately around them. That is, they must be convergence stable. Eshel (1983) modified the definition of an ESS by considering individually advantageous reduction from a majority deviation: he created the term continuous stability. A continuously stable ESS can be shown to be convergence stable, therefore it will act as an evolutionary attractor. But the nature of evolutionary trait spaces in biology means that it is not possible to guarantee that the region of convergence to the evolutionary attractor covers the whole of the trait space, nor that there is only one evolutionary attractor in a particular trait space. These issues have led to the emergence of the related fields of evolutionary dynamics, adaptive dynamics and evolutionary invasion analysis, all of which use differential equations to understand the dynamics in evolutionary trait spaces. Hence, if one or more evolutionary attractor exists in an evolutionary trait space, they provide techniques to understand the dynamics in that trait space around the evolutionary attractor. === Evolutionary attractors in an ecological context === Evolution in biology does not take place in single species in isolation. Ecological interaction of species leads to coevolution. Important examples of this are host-parasite or host-pathogen interaction, which can make both the dynamics around evolutionary attractors more complex, and the occurrence and number of evolutionary attractors more diverse. Evolutionary attractors have been identified in the analysis of evolutionary epidemiology of plant pathogens. In the above study working on plant populations the authors were able to identify evolutionary attractors using methods from adaptive dynamics. A model applied to the analysis of a maize (Zea mays L.) virus identified convergence stable equilibria through simulation modelling. A related model identified evolutionary attractors in the interaction of plants with fungal pathogens. === Evolutionary attractors in molecular genetics === As mentioned above much of the consideration of evolutionary attractors in biology has been through investigation of selection at a genetic or phenotypic level or both, in a single species or in coevolving species. Advances in the study of molecular genetics now allow the study of evolutionary attractors to be taken to a molecular genetic level. Wilson et. al (2019) studied the evolution of gene regulatory networks and identified the emergence of evolutionary attractors. == Evolutionary attractors in economics == Evolutionary game theory as applied in biology was inspired by game theory originally devised for applications in economics. Game theory remains an active field of research outside of biology, and thus it is not surprising that researchers in evolutionary economics use evolutionary game theory. Evolutionary attractors have been demonstrated by economists studying the evolutionary dynamics of market entry with market dynamics based on the replicator dynamics of biological evolutionary games. == Evolutionary attractors in computing == Evolutionary computation is a branch of computer science inspired by biological evolution. Many algorithms in evolutionary computation use a form of selection. Thus evolutionary attractors have been identified in computer science as well as in biology and economics. Evolutionary algorithms have generated evolutionary attractors, probably because of the similarity between adaptive hill-climbing in evolutionary heuristics and the adaptive landscape originated to explain evolution through natural selection.

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