AI Art Discord Server

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  Carrier cloud

  In cloud computing, a carrier cloud is a class of cloud that integrates wide area networks (WAN) and other attributes of communications service providers’ carrier-grade networks to enable the deployment of highly-complex applications in the cloud. In contrast, classic cloud computing focuses on the data center and does not address the network connecting data centers and cloud users. This may result in unpredictable response times and security issues when business-critical data are transferred over the Internet. == History == The advent of virtualization technology, cost-effective computing hardware, and ubiquitous Internet connectivity have enabled the first wave of cloud services starting in the early years of the 21st century. But many businesses and other organizations hesitated to move to more demanding applications, from on-premises dedicated hardware to private or public clouds. As a response, communications service providers started in the 2010/2011 time frame to develop carrier clouds that address perceived weaknesses in existing cloud services. Cited weaknesses vary but often include possible downtime, security issues, high cost of custom software and data transfer, inflexibility of some cloud apps, poor customer and nonfulfillment of service level agreements (SLAs). == Characteristics == To enable the deployment of time-sensitive and business critical applications in the cloud, the carrier cloud is designed to match or even exceed the characteristics of on-premises deployments. Therefore, the carrier cloud is characterized by some or all of the following items: Configurable, elastic network performance: Typical cloud computing solutions use the best effort of the public Internet to connect cloud users and data centers. This approach provides instant connectivity but does not offer control over network capacities, latencies, and jitter. Carrier clouds address these gaps with content delivery networks and/or dedicated virtual private networks (VPN) at OSI layers 1 (optical wavelengths), 2 (data link layer), and 3 (network layer). These VPNs can be configured to offer the desired performance parameters and exhibit the same type of elasticity for the network that regular clouds provide for servers and storage. To achieve the requested performance parameters, such as low latency, cloud applications can be (automatically) allocated to distributed data centers that are close enough to the cloud users. Automatic resource placement: For a cloud with multiple data centers, information about both the data center and the connecting network is relevant for a decision of where to place cloud images and storage volumes. For this decision, carrier clouds can obtain relevant information about the network, e.g., using the Application-Layer Traffic Optimization (ALTO) protocol. High level of security and governance: Cloud application providers are subject to general and domain specific security, privacy, and governance requirements and regulations, such as the European Data Protection Directive and the U.S. Health Insurance Portability and Accountability Act. For added security, the wide area network of the carrier cloud can provide segregated encrypted or unencrypted network links that are not accessible from the general Internet. At the data center, the carrier cloud provides e.g. virtual private servers, management processes, logs, and documentation to fulfill security and governance rules. Location control: Fundamentally, cloud users should not be concerned with the geographic location of their cloud resources. However, privacy and other regulations may mandate that certain types of data must not be sent outside a national jurisdiction or other geographical region. Open APIs: Carrier clouds provide graphical user interfaces and Web application programming interfaces that allow cloud application providers to set up, manage, and monitor both, the data center and the WAN, of their cloud services. == Architecture == Carrier clouds encompass data centers at different network tiers and wide area networks that connect multiple data centers to each other as well as to the cloud users. Links between data centers are used for failover, overflow, backup, and geographic diversity. Carrier clouds can be set up as public, private, or hybrid clouds. The carrier cloud federates these cloud entities by using a single management system to orchestrate, manage, and monitor data center and network resources as a single system.

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  Nearest centroid classifier

  In machine learning, a nearest centroid classifier or nearest prototype classifier is a classification model that assigns to observations the label of the class of training samples whose mean (centroid) is closest to the observation. When applied to text classification using word vectors containing tfidf weights to represent documents, the nearest centroid classifier is known as the Rocchio classifier because of its similarity to the Rocchio algorithm for relevance feedback. An extended version of the nearest centroid classifier has found applications in the medical domain, specifically classification of tumors. == Algorithm == === Training === Given labeled training samples { ( x → 1 , y 1 ) , … , ( x → n , y n ) } {\displaystyle \textstyle \{({\vec {x}}_{1},y_{1}),\dots ,({\vec {x}}_{n},y_{n})\}} with class labels y i ∈ Y {\displaystyle y_{i}\in \mathbf {Y} } , compute the per-class centroids μ → ℓ = 1 | C ℓ | ∑ i ∈ C ℓ x → i {\displaystyle \textstyle {\vec {\mu }}_{\ell }={\frac {1}{|C_{\ell }|}}{\underset {i\in C_{\ell }}{\sum }}{\vec {x}}_{i}} where C ℓ {\displaystyle C_{\ell }} is the set of indices of samples belonging to class ℓ ∈ Y {\displaystyle \ell \in \mathbf {Y} } . === Prediction === The class assigned to an observation x → {\displaystyle {\vec {x}}} is y ^ = arg ⁡ min ℓ ∈ Y ‖ μ → ℓ − x → ‖ {\displaystyle {\hat {y}}={\arg \min }_{\ell \in \mathbf {Y} }\|{\vec {\mu }}_{\ell }-{\vec {x}}\|} .

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  Dominance-based rough set approach

  The dominance-based rough set approach (DRSA) is an extension of rough set theory for multi-criteria decision analysis (MCDA), introduced by Greco, Matarazzo and Słowiński. The main change compared to the classical rough sets is the substitution for the indiscernibility relation by a dominance relation, which permits one to deal with inconsistencies typical to consideration of criteria and preference-ordered decision classes. == Multicriteria classification (sorting) == Multicriteria classification (sorting) is one of the problems considered within MCDA and can be stated as follows: given a set of objects evaluated by a set of criteria (attributes with preference-order domains), assign these objects to some pre-defined and preference-ordered decision classes, such that each object is assigned to exactly one class. Due to the preference ordering, improvement of evaluations of an object on the criteria should not worsen its class assignment. The sorting problem is very similar to the problem of classification, however, in the latter, the objects are evaluated by regular attributes and the decision classes are not necessarily preference ordered. The problem of multicriteria classification is also referred to as ordinal classification problem with monotonicity constraints and often appears in real-life application when ordinal and monotone properties follow from the domain knowledge about the problem. As an illustrative example, consider the problem of evaluation in a high school. The director of the school wants to assign students (objects) to three classes: bad, medium and good (notice that class good is preferred to medium and medium is preferred to bad). Each student is described by three criteria: level in Physics, Mathematics and Literature, each taking one of three possible values bad, medium and good. Criteria are preference-ordered and improving the level from one of the subjects should not result in worse global evaluation (class). As a more serious example, consider classification of bank clients, from the viewpoint of bankruptcy risk, into classes safe and risky. This may involve such characteristics as "return on equity (ROE)", "return on investment (ROI)" and "return on sales (ROS)". The domains of these attributes are not simply ordered but involve a preference order since, from the viewpoint of bank managers, greater values of ROE, ROI or ROS are better for clients being analysed for bankruptcy risk . Thus, these attributes are criteria. Neglecting this information in knowledge discovery may lead to wrong conclusions. == Data representation == === Decision table === In DRSA, data are often presented using a particular form of decision table. Formally, a DRSA decision table is a 4-tuple S = ⟨ U , Q , V , f ⟩ {\displaystyle S=\langle U,Q,V,f\rangle } , where U {\displaystyle U\,\!} is a finite set of objects, Q {\displaystyle Q\,\!} is a finite set of criteria, V = ⋃ q ∈ Q V q {\displaystyle V=\bigcup {}_{q\in Q}V_{q}} where V q {\displaystyle V_{q}\,\!} is the domain of the criterion q {\displaystyle q\,\!} and f : U × Q → V {\displaystyle f\colon U\times Q\to V} is an information function such that f ( x , q ) ∈ V q {\displaystyle f(x,q)\in V_{q}} for every ( x , q ) ∈ U × Q {\displaystyle (x,q)\in U\times Q} . The set Q {\displaystyle Q\,\!} is divided into condition criteria (set C ≠ ∅ {\displaystyle C\neq \emptyset } ) and the decision criterion (class) d {\displaystyle d\,\!} . Notice, that f ( x , q ) {\displaystyle f(x,q)\,\!} is an evaluation of object x {\displaystyle x\,\!} on criterion q ∈ C {\displaystyle q\in C} , while f ( x , d ) {\displaystyle f(x,d)\,\!} is the class assignment (decision value) of the object. An example of decision table is shown in Table 1 below. === Outranking relation === It is assumed that the domain of a criterion q ∈ Q {\displaystyle q\in Q} is completely preordered by an outranking relation ⪰ q {\displaystyle \succeq _{q}} ; x ⪰ q y {\displaystyle x\succeq _{q}y} means that x {\displaystyle x\,\!} is at least as good as (outranks) y {\displaystyle y\,\!} with respect to the criterion q {\displaystyle q\,\!} . Without loss of generality, we assume that the domain of q {\displaystyle q\,\!} is a subset of reals, V q ⊆ R {\displaystyle V_{q}\subseteq \mathbb {R} } , and that the outranking relation is a simple order between real numbers ≥ {\displaystyle \geq \,\!} such that the following relation holds: x ⪰ q y ⟺ f ( x , q ) ≥ f ( y , q ) {\displaystyle x\succeq _{q}y\iff f(x,q)\geq f(y,q)} . This relation is straightforward for gain-type ("the more, the better") criterion, e.g. company profit. For cost-type ("the less, the better") criterion, e.g. product price, this relation can be satisfied by negating the values from V q {\displaystyle V_{q}\,\!} . === Decision classes and class unions === Let T = { 1 , … , n } {\displaystyle T=\{1,\ldots ,n\}\,\!} . The domain of decision criterion, V d {\displaystyle V_{d}\,\!} consist of n {\displaystyle n\,\!} elements (without loss of generality we assume V d = T {\displaystyle V_{d}=T\,\!} ) and induces a partition of U {\displaystyle U\,\!} into n {\displaystyle n\,\!} classes Cl = { C l t , t ∈ T } {\displaystyle {\textbf {Cl}}=\{Cl_{t},t\in T\}} , where C l t = { x ∈ U : f ( x , d ) = t } {\displaystyle Cl_{t}=\{x\in U\colon f(x,d)=t\}} . Each object x ∈ U {\displaystyle x\in U} is assigned to one and only one class C l t , t ∈ T {\displaystyle Cl_{t},t\in T} . The classes are preference-ordered according to an increasing order of class indices, i.e. for all r , s ∈ T {\displaystyle r,s\in T} such that r ≥ s {\displaystyle r\geq s\,\!} , the objects from C l r {\displaystyle Cl_{r}\,\!} are strictly preferred to the objects from C l s {\displaystyle Cl_{s}\,\!} . For this reason, we can consider the upward and downward unions of classes, defined respectively, as: C l t ≥ = ⋃ s ≥ t C l s C l t ≤ = ⋃ s ≤ t C l s t ∈ T {\displaystyle Cl_{t}^{\geq }=\bigcup _{s\geq t}Cl_{s}\qquad Cl_{t}^{\leq }=\bigcup _{s\leq t}Cl_{s}\qquad t\in T} == Main concepts == === Dominance === We say that x {\displaystyle x\,\!} dominates y {\displaystyle y\,\!} with respect to P ⊆ C {\displaystyle P\subseteq C} , denoted by x D p y {\displaystyle xD_{p}y\,\!} , if x {\displaystyle x\,\!} is better than y {\displaystyle y\,\!} on every criterion from P {\displaystyle P\,\!} , x ⪰ q y , ∀ q ∈ P {\displaystyle x\succeq _{q}y,\,\forall q\in P} . For each P ⊆ C {\displaystyle P\subseteq C} , the dominance relation D P {\displaystyle D_{P}\,\!} is reflexive and transitive, i.e. it is a partial pre-order. Given P ⊆ C {\displaystyle P\subseteq C} and x ∈ U {\displaystyle x\in U} , let D P + ( x ) = { y ∈ U : y D p x } {\displaystyle D_{P}^{+}(x)=\{y\in U\colon yD_{p}x\}} D P − ( x ) = { y ∈ U : x D p y } {\displaystyle D_{P}^{-}(x)=\{y\in U\colon xD_{p}y\}} represent P-dominating set and P-dominated set with respect to x ∈ U {\displaystyle x\in U} , respectively. === Rough approximations === The key idea of the rough set philosophy is approximation of one knowledge by another knowledge. In DRSA, the knowledge being approximated is a collection of upward and downward unions of decision classes and the "granules of knowledge" used for approximation are P-dominating and P-dominated sets. The P-lower and the P-upper approximation of C l t ≥ , t ∈ T {\displaystyle Cl_{t}^{\geq },t\in T} with respect to P ⊆ C {\displaystyle P\subseteq C} , denoted as P _ ( C l t ≥ ) {\displaystyle {\underline {P}}(Cl_{t}^{\geq })} and P ¯ ( C l t ≥ ) {\displaystyle {\overline {P}}(Cl_{t}^{\geq })} , respectively, are defined as: P _ ( C l t ≥ ) = { x ∈ U : D P + ( x ) ⊆ C l t ≥ } {\displaystyle {\underline {P}}(Cl_{t}^{\geq })=\{x\in U\colon D_{P}^{+}(x)\subseteq Cl_{t}^{\geq }\}} P ¯ ( C l t ≥ ) = { x ∈ U : D P − ( x ) ∩ C l t ≥ ≠ ∅ } {\displaystyle {\overline {P}}(Cl_{t}^{\geq })=\{x\in U\colon D_{P}^{-}(x)\cap Cl_{t}^{\geq }\neq \emptyset \}} Analogously, the P-lower and the P-upper approximation of C l t ≤ , t ∈ T {\displaystyle Cl_{t}^{\leq },t\in T} with respect to P ⊆ C {\displaystyle P\subseteq C} , denoted as P _ ( C l t ≤ ) {\displaystyle {\underline {P}}(Cl_{t}^{\leq })} and P ¯ ( C l t ≤ ) {\displaystyle {\overline {P}}(Cl_{t}^{\leq })} , respectively, are defined as: P _ ( C l t ≤ ) = { x ∈ U : D P − ( x ) ⊆ C l t ≤ } {\displaystyle {\underline {P}}(Cl_{t}^{\leq })=\{x\in U\colon D_{P}^{-}(x)\subseteq Cl_{t}^{\leq }\}} P ¯ ( C l t ≤ ) = { x ∈ U : D P + ( x ) ∩ C l t ≤ ≠ ∅ } {\displaystyle {\overline {P}}(Cl_{t}^{\leq })=\{x\in U\colon D_{P}^{+}(x)\cap Cl_{t}^{\leq }\neq \emptyset \}} Lower approximations group the objects which certainly belong to class union C l t ≥ {\displaystyle Cl_{t}^{\geq }} (respectively C l t ≤ {\displaystyle Cl_{t}^{\leq }} ). This certainty comes from the fact, that object x ∈ U {\displaystyle x\in U} belongs to the lower approximation P _ ( C l t ≥ ) {\displaystyle {\underline {P}}(Cl_{t}^{\geq })} (respectively P _ ( C l t ≤ ) {\displaystyle {\underl

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  Neural gas

  Neural gas is an artificial neural network, inspired by the self-organizing map and introduced in 1991 by Thomas Martinetz and Klaus Schulten. The neural gas is a simple algorithm for finding optimal data representations based on feature vectors. The algorithm was coined "neural gas" because of the dynamics of the feature vectors during the adaptation process, which distribute themselves like a gas within the data space. It is applied where data compression or vector quantization is an issue, for example speech recognition, image processing or pattern recognition. As a robustly converging alternative to the k-means clustering it is also used for cluster analysis. == Algorithm == Suppose we want to model a probability distribution P ( x ) {\displaystyle P(x)} of data vectors x {\displaystyle x} using a finite number of feature vectors w i {\displaystyle w_{i}} , where i = 1 , ⋯ , N {\displaystyle i=1,\cdots ,N} . For each time step t {\displaystyle t} Sample data vector x {\displaystyle x} from P ( x ) {\displaystyle P(x)} Compute the distance between x {\displaystyle x} and each feature vector. Rank the distances. Let i 0 {\displaystyle i_{0}} be the index of the closest feature vector, i 1 {\displaystyle i_{1}} the index of the second closest feature vector, and so on. Update each feature vector by: w i k t + 1 = w i k t + ε ⋅ e − k / λ ⋅ ( x − w i k t ) , k = 0 , ⋯ , N − 1 {\displaystyle w_{i_{k}}^{t+1}=w_{i_{k}}^{t}+\varepsilon \cdot e^{-k/\lambda }\cdot (x-w_{i_{k}}^{t}),k=0,\cdots ,N-1} In the algorithm, ε {\displaystyle \varepsilon } can be understood as the learning rate, and λ {\displaystyle \lambda } as the neighborhood range. ε {\displaystyle \varepsilon } and λ {\displaystyle \lambda } are reduced with increasing t {\displaystyle t} so that the algorithm converges after many adaptation steps. The adaptation step of the neural gas can be interpreted as gradient descent on a cost function. By adapting not only the closest feature vector but all of them with a step size decreasing with increasing distance order, compared to (online) k-means clustering a much more robust convergence of the algorithm can be achieved. The neural gas model does not delete a node and also does not create new nodes. === Comparison with SOM === Compared to self-organized map, the neural gas model does not assume that some vectors are neighbors. If two vectors happen to be close together, they would tend to move together, and if two vectors happen to be apart, they would tend to not move together. In contrast, in an SOM, if two vectors are neighbors in the underlying graph, then they will always tend to move together, no matter whether the two vectors happen to be neighbors in the Euclidean space. The name "neural gas" is because one can imagine it to be what an SOM would be like if there is no underlying graph, and all points are free to move without the bonds that bind them together. == Variants == A number of variants of the neural gas algorithm exists in the literature so as to mitigate some of its shortcomings. More notable is perhaps Bernd Fritzke's growing neural gas, but also one should mention further elaborations such as the Growing When Required network and also the incremental growing neural gas. A performance-oriented approach that avoids the risk of overfitting is the Plastic Neural gas model. === Growing neural gas === Fritzke describes the growing neural gas (GNG) as an incremental network model that learns topological relations by using a "Hebb-like learning rule", only, unlike the neural gas, it has no parameters that change over time and it is capable of continuous learning, i.e. learning on data streams. GNG has been widely used in several domains, demonstrating its capabilities for clustering data incrementally. The GNG is initialized with two randomly positioned nodes which are initially connected with a zero age edge and whose errors are set to 0. Since in the GNG input data is presented sequentially one by one, the following steps are followed at each iteration: It is calculating the errors (distances) between the two closest nodes to the current input data. The error of the winner node (only the closest one) is respectively accumulated. The winner node and its topological neighbors (connected by an edge) are moving towards the current input by different fractions of their respective errors. The age of all edges connected to the winner node are incremented. If the winner node and the second-winner are connected by an edge, such an edge is set to 0. Else, an edge is created between them. If there are edges with an age larger than a threshold, they are removed. Nodes without connections are eliminated. If the current iteration is an integer multiple of a predefined frequency-creation threshold, a new node is inserted between the node with the largest error (among all) and its topological neighbor presenting the highest error. The link between the former and the latter nodes is eliminated (their errors are decreased by a given factor) and the new node is connected to both of them. The error of the new node is initialized as the updated error of the node which had the largest error (among all). The accumulated error of all nodes is decreased by a given factor. If the stopping criterion is not met, the algorithm takes a following input. The criterion might be a given number of epochs, i.e., a pre-set number of times where all data is presented, or the reach of a maximum number of nodes. === Incremental growing neural gas === Another neural gas variant inspired by the GNG algorithm is the incremental growing neural gas (IGNG). The authors propose the main advantage of this algorithm to be "learning new data (plasticity) without degrading the previously trained network and forgetting the old input data (stability)." === Growing when required === Having a network with a growing set of nodes, like the one implemented by the GNG algorithm was seen as a great advantage, however some limitation on the learning was seen by the introduction of the parameter λ, in which the network would only be able to grow when iterations were a multiple of this parameter. The proposal to mitigate this problem was a new algorithm, the Growing When Required network (GWR), which would have the network grow more quickly, by adding nodes as quickly as possible whenever the network identified that the existing nodes would not describe the input well enough. === Plastic neural gas === The ability to only grow a network may quickly introduce overfitting; on the other hand, removing nodes on the basis of age only, as in the GNG model, does not ensure that the removed nodes are actually useless, because removal depends on a model parameter that should be carefully tuned to the "memory length" of the stream of input data. The "Plastic Neural Gas" model solves this problem by making decisions to add or remove nodes using an unsupervised version of cross-validation, which controls an equivalent notion of "generalization ability" for the unsupervised setting. While growing-only methods only cater for the incremental learning scenario, the ability to grow and shrink is suited to the more general streaming data problem. == Implementations == To find the ranking i 0 , i 1 , … , i N − 1 {\displaystyle i_{0},i_{1},\ldots ,i_{N-1}} of the feature vectors, the neural gas algorithm involves sorting, which is a procedure that does not lend itself easily to parallelization or implementation in analog hardware. However, implementations in both parallel software and analog hardware were actually designed.

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  Construction robots

  Construction robots are a subset of industrial robots used for building and infrastructure construction on site, or in the production of materials and components offsite. A 2021 survey said 55% of construction companies in the United States, Europe, and China used robots in some form. This figure, however, reflects reported use across the construction value chain rather than widespread deployment of robots on active construction sites. Real-world adoption remains limited, with many robotic systems confined to pilot projects, controlled environments, or specific task applications rather than continuous on-site construction use. One of the main challenges in deploying robots on construction sites is the unstructured and variable nature of the environment, which differs fundamentally from controlled factory settings where industrial robots have traditionally operated. Some robots currently deployed on job sites assist with physically demanding or repetitive tasks: excavating, lifting heavy materials, surveying, laying out markers, tying rebar, and installing drywall. More advanced systems are being developed for exterior finishing, steel placement, masonry, and reinforced concrete work. In practice, rather than autonomous systems performing core building tasks, the most widely adopted robot applications on construction sites involve technologies such as aerial drones (or, less frequently, robot 'dogs' - for example, Boston Dynamics' Spot - or humanoid robots) used for surveying, inspection, and progress monitoring (the robots typically carry video and/or 360-degree cameras, LiDar scanners or other data capture devices, with data analysed using artificial intelligence and machine learning). Some emerging systems are designed as multifunctional construction robots, integrating multiple tools and capabilities within a single robotic platform to perform different stages of the construction process. These systems aim to improve operational flexibility and increase automation in complex construction environments. Experimental projects using robotic construction technologies and additive manufacturing have been demonstrated in several countries as part of broader efforts to industrialize the construction sector and improve productivity through automation and digitalization. == Features == Construction robots are generally required to meet the following criteria: Mobility: the ability to navigate around a construction site, including uneven terrain and confined spaces. Adaptability: the ability to handle components of variable size, weight, and shape. Environmental awareness: the ability to sense and respond to changing on-site conditions. Interactivity: the ability to operate alongside human workers and other equipment. Multitasking: the ability to perform several different operations within a single deployment. == Capabilities == Construction robots have been developed and tested for a range of on-site tasks, including: Progress monitoring — robots equipped with cameras and sensors can track construction progress and identify deviations from plans. Inspection — robots are used to investigate infrastructure at dangerous or inaccessible locations, reducing risk to human workers and eliminating human error. Wall construction — robotic systems can lay bricks and blocks with greater speed and consistency than manual labour. Earthmoving and material handling — autonomous excavators and haul trucks use GPS, lidar, and motion sensors to perform digging, trenching, and loading tasks with minimal human input. Grading and dozing — autonomous bulldozers use GPS, gyroscopes, and laser sensors to control blade angle and depth, improving surface finish accuracy and reducing material overuse. 3D printing — additive manufacturing systems can construct walls and structural elements directly from digital models. == Notable construction-related activities undertaken by robots == The distribution of robotic applications in construction varies across the project lifecycle. Most applications are concentrated in structural construction tasks such as masonry, concrete work, and assembly, while other phases, including planning, maintenance, and demolition, remain less represented. === Automated building systems === The Nisseki Yokohama Building (also known as Rail City Yokohama), a 30-storey office building in Yokohama, Japan, was constructed between 1994 and 1997 using the SMART system (Shimizu Manufacturing system by Advanced Robotics Technology), developed by Shimizu Corporation and a consortium of seven other Japanese companies. The system used automated horizontal hoists and vertical lifts to position steel beams, columns, precast concrete floor slabs, and prefabricated facade panels, with welding robots connecting structural elements under laser-guided precision. Each component was tracked by barcode to monitor progress and coordinate just-in-time delivery of materials. Obayashi Corporation developed the Advanced Building Construction System (ABCS), a similar automated platform used in several high-rise projects in Japan in the 1990s, including the NEC Head Office in Kanagawa (1997–2000). === Progress monitoring, inspection === Boston Dynamics' Spot was used in February 2024 to inspect sections of the M5 motorway in England for National Highways. A £15,000 humanoid robot (a G1 model from Chinese manufacturer Unitree) was deployed to capture 360-degree imagery and progress reports to support health and safety monitoring and reporting for UK contractor Tilbury Douglas in April 2026. In the US, Virginia Tech's ARCADE research lab is developing MARIO (Multi-Agent Robotic system for Inspection On-site), a heterogenous robotic system deploying multiple robots capable of different locomotion to perform remote real-time construction progress monitoring in complex construction sites. === Earthmoving === === Concrete works === Obayashi Corporation developed and deployed a robotic system for placing concrete layers in dam construction in Japan. A concrete floor finishing robot was deployed by Kajima and Tokimec in Japan. The MARK series were designed in 1984 to automate the levelling and trowelling of concrete slabs on construction sites, providing consistent finishing accuracy, improved efficiency, and reduced dependence on skilled labour === Masonry === SAM100 (Semi-Automated Mason), developed by Construction Robotics, is one of the first commercially available bricklaying robots for on-site masonry construction. In 2018, it was used in the construction of the University Arts Building at the University of Nevada, Reno — a $35.5 million facility — where it laid over 60,000 of the 100,000 bricks required, reducing the brick veneer installation time by approximately 50%. Hadrian X, developed by the Australian company Fastbrick Robotics, is a fully autonomous mobile bricklaying robot. In November 2022, it completed its first commercial project — five four-bedroom houses in Wellard, Western Australia. In February 2025, PulteGroup, one of the largest homebuilders in the United States, piloted Hadrian X on a site in Florida, constructing an entire house in a single day. === 3D printing === In May 2025, a residential building in Arinaga, Gran Canaria, Spain, was completed using 3D printing construction technology, as part of broader efforts to demonstrate robotic and additive manufacturing methods in the housing sector. In 2026, a three-storey apartment block in France was constructed using concrete 3D printing technology, three months faster than conventional building methods. Finland's Hyperion Robotics has opened a UK factory and used 3D printing with concrete to produce foundations for pipelines and for electricity substation bases, reducing time-consuming and weather-dependent onsite construction processes. == Social impact == The adoption of construction robots varies significantly by region and is shaped by labour market conditions, cultural attitudes, and regulatory frameworks. In Japan, construction robots have been embraced as a response to an ageing workforce and chronic labour shortages, and are generally viewed positively by the industry. In the United States, adoption has historically been slower, partly due to resistance from labour unions concerned about job displacement. Research suggests that the impact of automation on workers is uneven: while robots can create a productivity effect that benefits some workers, displacement effects are most pronounced among younger, less-educated workers in manufacturing-heavy regions. More than 60% of construction firms now report difficulty finding skilled operators, which has increased openness to automation as a practical solution to workforce shortages rather than a replacement for workers. In the UK, during onsite deployment of a humanoid robot for monitoring purposes, there were concerns that staff might think they were being watched ("It's not there to spy on people.... So, we insist that everyone is blurred out. N

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  Sharpness aware minimization

  Sharpness Aware Minimization (SAM) is an optimization algorithm used in machine learning that aims to improve model generalization. The method seeks to find model parameters that are located in regions of the loss landscape with uniformly low loss values, rather than parameters that only achieve a minimal loss value at a single point. This approach is described as finding "flat" minima instead of "sharp" ones. The rationale is that models trained this way are less sensitive to variations between training and test data, which can lead to better performance on unseen data. The algorithm was introduced in a 2020 paper by a team of researchers including Pierre Foret, Ariel Kleiner, Hossein Mobahi, and Behnam Neyshabur. == Underlying Principle == SAM modifies the standard training objective by minimizing a "sharpness-aware" loss. This is formulated as a minimax problem where the inner objective seeks to find the highest loss value in the immediate neighborhood of the current model weights, and the outer objective minimizes this value: min w max ‖ ϵ ‖ p ≤ ρ L train ( w + ϵ ) + λ ‖ w ‖ 2 2 {\displaystyle \min _{w}\max _{\|\epsilon \|_{p}\leq \rho }L_{\text{train}}(w+\epsilon )+\lambda \|w\|_{2}^{2}} In this formulation: w {\displaystyle w} represents the model's parameters (weights). L train {\displaystyle L_{\text{train}}} is the loss calculated on the training data. ϵ {\displaystyle \epsilon } is a perturbation applied to the weights. ρ {\displaystyle \rho } is a hyperparameter that defines the radius of the neighborhood (an L p {\displaystyle L_{p}} ball) to search for the highest loss. An optional L2 regularization term, scaled by λ {\displaystyle \lambda } , can be included. A direct solution to the inner maximization problem is computationally expensive. SAM approximates it by taking a single gradient ascent step to find the perturbation ϵ {\displaystyle \epsilon } . This is calculated as: ϵ ( w ) = ρ ∇ L train ( w ) ‖ ∇ L train ( w ) ‖ 2 {\displaystyle \epsilon (w)=\rho {\frac {\nabla L_{\text{train}}(w)}{\|\nabla L_{\text{train}}(w)\|_{2}}}} The optimization process for each training step involves two stages. First, an "ascent step" computes a perturbed set of weights, w adv = w + ϵ ( w ) {\displaystyle w_{\text{adv}}=w+\epsilon (w)} , by moving towards the direction of the highest local loss. Second, a "descent step" updates the original weights w {\displaystyle w} using the gradient calculated at these perturbed weights, ∇ L train ( w adv ) {\displaystyle \nabla L_{\text{train}}(w_{\text{adv}})} . This update is typically performed using a standard optimizer like SGD or Adam. == Application and Performance == SAM has been applied in various machine learning contexts, primarily in computer vision. Research has shown it can improve generalization performance in models such as Convolutional Neural Networks (CNNs) and Vision Transformers (ViTs) on image datasets including ImageNet, CIFAR-10, and CIFAR-100. The algorithm has also been found to be effective in training models with noisy labels, where it performs comparably to methods designed specifically for this problem. Some studies indicate that SAM and its variants can improve out-of-distribution (OOD) generalization, which is a model's ability to perform well on data from distributions not seen during training. Other areas where it has been applied include gradual domain adaptation and mitigating overfitting in scenarios with repeated exposure to training examples. == Limitations == A primary limitation of SAM is its computational cost. By requiring two gradient computations (one for the ascent and one for the descent) per optimization step, it approximately doubles the training time compared to standard optimizers. The theoretical convergence properties of SAM are still under investigation. Some research suggests that with a constant step size, SAM may not converge to a stationary point. The accuracy of the single gradient step approximation for finding the worst-case perturbation may also decrease during the training process. The effectiveness of SAM can also be domain-dependent. While it has shown benefits for computer vision tasks, its impact on other areas, such as GPT-style language models where each training example is seen only once, has been reported as limited in some studies. Furthermore, while SAM seeks flat minima, some research suggests that not all flat minima necessarily lead to good generalization. The algorithm also introduces the neighborhood size ρ {\displaystyle \rho } as a new hyperparameter, which requires tuning. == Research, Variants, and Enhancements == Active research on SAM focuses on reducing its computational overhead and improving its performance. Several variants have been proposed to make the algorithm more efficient. These include methods that attempt to parallelize the two gradient computations, apply the perturbation to only a subset of parameters, or reduce the number of computation steps required. Other approaches use historical gradient information or apply SAM steps intermittently to lower the computational burden. To improve performance and robustness, variants have been developed that adapt the neighborhood size based on model parameter scales (Adaptive SAM or ASAM) or incorporate information about the curvature of the loss landscape (Curvature Regularized SAM or CR-SAM). Other research explores refining the perturbation step by focusing on specific components of the gradient or combining SAM with techniques like random smoothing. Theoretical work continues to analyze the algorithm's behavior, including its implicit bias towards flatter minima and the development of broader frameworks for sharpness-aware optimization that use different measures of sharpness.

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  Information gain ratio

  In decision tree learning, information gain ratio is a ratio of information gain to the intrinsic information. It was proposed by Ross Quinlan, to reduce a bias towards multi-valued attributes by taking the number and size of branches into account when choosing an attribute. Information gain is also known as mutual information. == Information gain calculation == Information gain is the reduction in entropy produced from partitioning a set with attributes a {\displaystyle a} and finding the optimal candidate that produces the highest value: IG ( T , a ) = H ( T ) − H ( T | a ) , {\displaystyle {\text{IG}}(T,a)=\mathrm {H} {(T)}-\mathrm {H} {(T|a)},} where T {\displaystyle T} is a random variable and H ( T | a ) {\displaystyle \mathrm {H} {(T|a)}} is the entropy of T {\displaystyle T} given the value of attribute a {\displaystyle a} . The information gain is equal to the total entropy for an attribute if for each of the attribute values a unique classification can be made for the result attribute. In this case the relative entropies subtracted from the total entropy are 0. == Split information calculation == The split information value for a test is defined as follows: SplitInformation ( X ) = − ∑ i = 1 n N ( x i ) N ( x ) ∗ log ⁡ 2 N ( x i ) N ( x ) {\displaystyle {\text{SplitInformation}}(X)=-\sum _{i=1}^{n}{{\frac {\mathrm {N} (x_{i})}{\mathrm {N} (x)}}\log {_{2}}{\frac {\mathrm {N} (x_{i})}{\mathrm {N} (x)}}}} where X {\displaystyle X} is a discrete random variable with possible values x 1 , x 2 , . . . , x i {\displaystyle {x_{1},x_{2},...,x_{i}}} and N ( x i ) {\displaystyle N(x_{i})} being the number of times that x i {\displaystyle x_{i}} occurs divided by the total count of events N ( x ) {\displaystyle N(x)} where x {\displaystyle x} is the set of events. The split information value is a positive number that describes the potential worth of splitting a branch from a node. This in turn is the intrinsic value that the random variable possesses and will be used to remove the bias in the information gain ratio calculation. == Information gain ratio calculation == The information gain ratio is the ratio between the information gain and the split information value: IGR ( T , a ) = IG ( T , a ) / SplitInformation ( T ) {\displaystyle {\text{IGR}}(T,a)={\text{IG}}(T,a)/{\text{SplitInformation}}(T)} IGR ( T , a ) = − ∑ i = 1 n P ( T ) log ⁡ P ( T ) − ( − ∑ i = 1 n P ( T | a ) log ⁡ P ( T | a ) ) − ∑ i = 1 n N ( t i ) N ( t ) ∗ log ⁡ 2 N ( t i ) N ( t ) {\displaystyle {\text{IGR}}(T,a)={\frac {-\sum _{i=1}^{n}{\mathrm {P} (T)\log \mathrm {P} (T)}-(-\sum _{i=1}^{n}{\mathrm {P} (T|a)\log \mathrm {P} (T|a)})}{-\sum _{i=1}^{n}{{\frac {\mathrm {N} (t_{i})}{\mathrm {N} (t)}}\log {_{2}}{\frac {\mathrm {N} (t_{i})}{\mathrm {N} (t)}}}}}} == Example == Using weather data published by Fordham University, the table was created below: Using the table above, one can find the entropy, information gain, split information, and information gain ratio for each variable (outlook, temperature, humidity, and wind). These calculations are shown in the tables below: Using the above tables, one can deduce that Outlook has the highest information gain ratio. Next, one must find the statistics for the sub-groups of the Outlook variable (sunny, overcast, and rainy), for this example one will only build the sunny branch (as shown in the table below): One can find the following statistics for the other variables (temperature, humidity, and wind) to see which have the greatest effect on the sunny element of the outlook variable: Humidity was found to have the highest information gain ratio. One will repeat the same steps as before and find the statistics for the events of the Humidity variable (high and normal): Since the play values are either all "No" or "Yes", the information gain ratio value will be equal to 1. Also, now that one has reached the end of the variable chain with Wind being the last variable left, they can build an entire root to leaf node branch line of a decision tree. Once finished with reaching this leaf node, one would follow the same procedure for the rest of the elements that have yet to be split in the decision tree. This set of data was relatively small, however, if a larger set was used, the advantages of using the information gain ratio as the splitting factor of a decision tree can be seen more. == Advantages == Information gain ratio biases the decision tree against considering attributes with a large number of distinct values. For example, suppose that we are building a decision tree for some data describing a business's customers. Information gain ratio is used to decide which of the attributes are the most relevant. These will be tested near the root of the tree. One of the input attributes might be the customer's telephone number. This attribute has a high information gain, because it uniquely identifies each customer. Due to its high amount of distinct values, this will not be chosen to be tested near the root. == Disadvantages == Although information gain ratio solves the key problem of information gain, it creates another problem. If one is considering an amount of attributes that have a high number of distinct values, these will never be above one that has a lower number of distinct values. == Difference from information gain == Information gain's shortcoming is created by not providing a numerical difference between attributes with high distinct values from those that have less. Example: Suppose that we are building a decision tree for some data describing a business's customers. Information gain is often used to decide which of the attributes are the most relevant, so they can be tested near the root of the tree. One of the input attributes might be the customer's credit card number. This attribute has a high information gain, because it uniquely identifies each customer, but we do not want to include it in the decision tree: deciding how to treat a customer based on their credit card number is unlikely to generalize to customers we haven't seen before. Information gain ratio's strength is that it has a bias towards the attributes with the lower number of distinct values. Below is a table describing the differences of information gain and information gain ratio when put in certain scenarios.

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  Radial basis function network

  In the field of mathematical modeling, a radial basis function network is an artificial neural network that uses radial basis functions as activation functions. The output of the network is a linear combination of radial basis functions of the inputs and neuron parameters. Radial basis function networks have many uses, including function approximation, time series prediction, classification, and system control. They were first formulated in a 1988 paper by Broomhead and Lowe, both researchers at the Royal Signals and Radar Establishment. == Network architecture == Radial basis function (RBF) networks typically have three layers: an input layer, a hidden layer with a non-linear RBF activation function and a linear output layer. The input can be modeled as a vector of real numbers x ∈ R n {\displaystyle \mathbf {x} \in \mathbb {R} ^{n}} . The output of the network is then a scalar function of the input vector, φ : R n → R {\displaystyle \varphi :\mathbb {R} ^{n}\to \mathbb {R} } , and is given by φ ( x ) = ∑ i = 1 N a i ρ ( | | x − c i | | ) {\displaystyle \varphi (\mathbf {x} )=\sum _{i=1}^{N}a_{i}\rho (||\mathbf {x} -\mathbf {c} _{i}||)} where N {\displaystyle N} is the number of neurons in the hidden layer, c i {\displaystyle \mathbf {c} _{i}} is the center vector for neuron i {\displaystyle i} , and a i {\displaystyle a_{i}} is the weight of neuron i {\displaystyle i} in the linear output neuron. Functions that depend only on the distance from a center vector are radially symmetric about that vector, hence the name radial basis function. In the basic form, all inputs are connected to each hidden neuron. The norm is typically taken to be the Euclidean distance (although the Mahalanobis distance appears to perform better with pattern recognition) and the radial basis function is commonly taken to be Gaussian ρ ( ‖ x − c i ‖ ) = exp ⁡ [ − β i ‖ x − c i ‖ 2 ] {\displaystyle \rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}=\exp \left[-\beta _{i}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert ^{2}\right]} . The Gaussian basis functions are local to the center vector in the sense that lim | | x | | → ∞ ρ ( ‖ x − c i ‖ ) = 0 {\displaystyle \lim _{||x||\to \infty }\rho (\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert )=0} i.e. changing parameters of one neuron has only a small effect for input values that are far away from the center of that neuron. Given certain mild conditions on the shape of the activation function, RBF networks are universal approximators on a compact subset of R n {\displaystyle \mathbb {R} ^{n}} . This means that an RBF network with enough hidden neurons can approximate any continuous function on a closed, bounded set with arbitrary precision. The parameters a i {\displaystyle a_{i}} , c i {\displaystyle \mathbf {c} _{i}} , and β i {\displaystyle \beta _{i}} are determined in a manner that optimizes the fit between φ {\displaystyle \varphi } and the data. === Normalization === ==== Normalized architecture ==== In addition to the above unnormalized architecture, RBF networks can be normalized. In this case the mapping is φ ( x ) = d e f ∑ i = 1 N a i ρ ( ‖ x − c i ‖ ) ∑ i = 1 N ρ ( ‖ x − c i ‖ ) = ∑ i = 1 N a i u ( ‖ x − c i ‖ ) {\displaystyle \varphi (\mathbf {x} )\ {\stackrel {\mathrm {def} }{=}}\ {\frac {\sum _{i=1}^{N}a_{i}\rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}}{\sum _{i=1}^{N}\rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}}}=\sum _{i=1}^{N}a_{i}u{\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}} where u ( ‖ x − c i ‖ ) = d e f ρ ( ‖ x − c i ‖ ) ∑ j = 1 N ρ ( ‖ x − c j ‖ ) {\displaystyle u{\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}\ {\stackrel {\mathrm {def} }{=}}\ {\frac {\rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}}{\sum _{j=1}^{N}\rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{j}\right\Vert {\big )}}}} is known as a normalized radial basis function. ==== Theoretical motivation for normalization ==== There is theoretical justification for this architecture in the case of stochastic data flow. Assume a stochastic kernel approximation for the joint probability density P ( x ∧ y ) = 1 N ∑ i = 1 N ρ ( ‖ x − c i ‖ ) σ ( | y − e i | ) {\displaystyle P\left(\mathbf {x} \land y\right)={1 \over N}\sum _{i=1}^{N}\,\rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}\,\sigma {\big (}\left\vert y-e_{i}\right\vert {\big )}} where the weights c i {\displaystyle \mathbf {c} _{i}} and e i {\displaystyle e_{i}} are exemplars from the data and we require the kernels to be normalized ∫ ρ ( ‖ x − c i ‖ ) d n x = 1 {\displaystyle \int \rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}\,d^{n}\mathbf {x} =1} and ∫ σ ( | y − e i | ) d y = 1 {\displaystyle \int \sigma {\big (}\left\vert y-e_{i}\right\vert {\big )}\,dy=1} . The probability densities in the input and output spaces are P ( x ) = ∫ P ( x ∧ y ) d y = 1 N ∑ i = 1 N ρ ( ‖ x − c i ‖ ) {\displaystyle P\left(\mathbf {x} \right)=\int P\left(\mathbf {x} \land y\right)\,dy={1 \over N}\sum _{i=1}^{N}\,\rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}} and The expectation of y given an input x {\displaystyle \mathbf {x} } is φ ( x ) = d e f E ( y ∣ x ) = ∫ y P ( y ∣ x ) d y {\displaystyle \varphi \left(\mathbf {x} \right)\ {\stackrel {\mathrm {def} }{=}}\ E\left(y\mid \mathbf {x} \right)=\int y\,P\left(y\mid \mathbf {x} \right)dy} where P ( y ∣ x ) {\displaystyle P\left(y\mid \mathbf {x} \right)} is the conditional probability of y given x {\displaystyle \mathbf {x} } . The conditional probability is related to the joint probability through Bayes' theorem P ( y ∣ x ) = P ( x ∧ y ) P ( x ) {\displaystyle P\left(y\mid \mathbf {x} \right)={\frac {P\left(\mathbf {x} \land y\right)}{P\left(\mathbf {x} \right)}}} which yields φ ( x ) = ∫ y P ( x ∧ y ) P ( x ) d y {\displaystyle \varphi \left(\mathbf {x} \right)=\int y\,{\frac {P\left(\mathbf {x} \land y\right)}{P\left(\mathbf {x} \right)}}\,dy} . This becomes φ ( x ) = ∑ i = 1 N e i ρ ( ‖ x − c i ‖ ) ∑ i = 1 N ρ ( ‖ x − c i ‖ ) = ∑ i = 1 N e i u ( ‖ x − c i ‖ ) {\displaystyle \varphi \left(\mathbf {x} \right)={\frac {\sum _{i=1}^{N}e_{i}\rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}}{\sum _{i=1}^{N}\rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}}}=\sum _{i=1}^{N}e_{i}u{\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}} when the integrations are performed. === Local linear models === It is sometimes convenient to expand the architecture to include local linear models. In that case the architectures become, to first order, φ ( x ) = ∑ i = 1 N ( a i + b i ⋅ ( x − c i ) ) ρ ( ‖ x − c i ‖ ) {\displaystyle \varphi \left(\mathbf {x} \right)=\sum _{i=1}^{N}\left(a_{i}+\mathbf {b} _{i}\cdot \left(\mathbf {x} -\mathbf {c} _{i}\right)\right)\rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}} and φ ( x ) = ∑ i = 1 N ( a i + b i ⋅ ( x − c i ) ) u ( ‖ x − c i ‖ ) {\displaystyle \varphi \left(\mathbf {x} \right)=\sum _{i=1}^{N}\left(a_{i}+\mathbf {b} _{i}\cdot \left(\mathbf {x} -\mathbf {c} _{i}\right)\right)u{\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}} in the unnormalized and normalized cases, respectively. Here b i {\displaystyle \mathbf {b} _{i}} are weights to be determined. Higher order linear terms are also possible. This result can be written φ ( x ) = ∑ i = 1 2 N ∑ j = 1 n e i j v i j ( x − c i ) {\displaystyle \varphi \left(\mathbf {x} \right)=\sum _{i=1}^{2N}\sum _{j=1}^{n}e_{ij}v_{ij}{\big (}\mathbf {x} -\mathbf {c} _{i}{\big )}} where e i j = { a i , if i ∈ [ 1 , N ] b i j , if i ∈ [ N + 1 , 2 N ] {\displaystyle e_{ij}={\begin{cases}a_{i},&{\mbox{if }}i\in [1,N]\\b_{ij},&{\mbox{if }}i\in [N+1,2N]\end{cases}}} and v i j ( x − c i ) = d e f { δ i j ρ ( ‖ x − c i ‖ ) , if i ∈ [ 1 , N ] ( x i j − c i j ) ρ ( ‖ x − c i ‖ ) , if i ∈ [ N + 1 , 2 N ] {\displaystyle v_{ij}{\big (}\mathbf {x} -\mathbf {c} _{i}{\big )}\ {\stackrel {\mathrm {def} }{=}}\ {\begin{cases}\delta _{ij}\rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )},&{\mbox{if }}i\in [1,N]\\\left(x_{ij}-c_{ij}\right)\rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )},&{\mbox{if }}i\in [N+1,2N]\end{cases}}} in the unnormalized case and in the normalized case. Here δ i j {\displaystyle \delta _{ij}} is a Kronecker delta function defined as δ i j = { 1 , if i = j 0 , if i ≠ j {\displaystyle \delta _{ij}={\begin{cases}1,&{\mbox{if }}i=j\\0,&{\mbox{if }}i\neq j\end{cases}}} . == Training == RBF networks are typically trained from pairs of input and target values x ( t ) , y ( t ) {\displaystyle \mathbf {x} (t),y(t)} , t = 1 , … , T {\displaystyle t=1,\dots ,T} by a two-step algorithm. In the first step, the center vectors c i {\displaystyle \mathbf {c} _{i}} of the RBF functions in the hidden layer

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  Altibase

  Altibase is a hybrid database, relational database management system manufactured by the Altibase Corporation. The software's hybrid architecture allows it to access both memory-resident and disk-resident tables using single interface. It supports both synchronous and asynchronous replication and offers real-time ACID compliance. Support is also offered for a variety of SQL standards and programming languages. Other important capabilities include data import and export, data encryption for security, multiple data access command sets, materialized view and temporary tables, and others. == History == From 1991 through 1997 the Mr. RT project was an in-memory database research project, conducted by the Electronics and Telecommunications Research Institute a government-funded research organization in South Korea. Altibase was incorporated in 1999. Altibase acquired an in-memory database engine from the Electronics and Telecommunications Research Institute in February 2000, and commercialized the database in October of the same year. In 2001, Altibase changed the name of the in-memory database product from "Spiner" to "Altibase" in 2001. In 2004, Altibase integrated the in-memory database with a disk-resident database to create a hybrid DBMS, released version 4.0 and renamed it as ALTIBASE HDB. Altibase released version 5.5.1 and 6.1.1 in 2012, version 6.3.1 in November 2013, and 6.5.1 in May 2015. Altibase claims that this is the world's first hybrid DBMS. Altibase released its open source edition version 7.1, however, closed the source in 2023. In August 2023, Altibase released its cloud-optimized version 7.3. === Awards === In 2006, Received the Presidential Award at the Korea Software Awards In 2007, Selected as World-Class Product by the Ministry of Commerce, Industry and Energy In 2009, Awarded the Outstanding Product Award in China's Telecommunications Industry In 2009, Received Outstanding Product Award at the China Billing China 2009 Telecommunication Industry Awards In 2010, Commendation from the Minister of Knowledge Economy for Technological Practicalization In 2011, Received the Grand Prize at the 10th Software Enterprise Competitiveness Award In 2011, Selected as Top 10 Emerging Technologies and received Special Award at the Korea Technology Grand Prize In 2012, Awarded for Contributions to Military Manpower Administration In 2014~2016, Included in Gartner Magic Quadrant for Operational DBMS In 2015, Selected as Outstanding BSS by China Fujian Mobile. In 2023, Awarded as the Excellent Research and Development Institution by the Korean Ministry Science and ICT In 2023, Won the Global Premium Commercial Software Presidential Award at the 9th Global Commercial Software Grand Exhibition in Korea === Release === The first version, called Spiner, was released in 2000 for commercial use. It took half of the in-memory DBMS market share in South Korea. In 2002 the second version was released renamed to Altibase v2.0. By 2003, Altibase v3.0 was released and it entered the Chinese market. Released version 4.0 with hybrid architecture, combining RAM and disk databases, was released in 2004. In 2005 Altibase began working with Chinese telecommunications providers for billing systems, and some financial companies in Taiwan, China, for home trading systems. The software was certified by the Telecommunications Technology Association. The Ministry of Government Administration and Home Affairs gave it an award in 2006. Offices in China and United States opened in 2009. In 2011, version 5.5.1 was renamed it to HDB (for "hybrid database"). The Altibase Data Stream product for complex event processing was renamed DSM. The product received a Korean technology award. Altibase introduced certification services. In 2012, HDB Zeta and Extreme were announced, and DSM renamed to CEP. In 2013, yet another variant called XDB was announced, and the company received ISO/IEC 20000 certification. In 2018, Altibase went open source. Altibase went open source in February, 2018. Altibase Corp has made the decision to discontinue the Altibase 7.1 open source edition, effective March 17, 2023. As a result, the open-source edition of Altibase 7.1 will no longer be available for download or use. Altibase released version 7.3 in September, 2023, its notable feature is the world’s first hybrid partition, allowing data to be stored in both memory and on disk at the partition level. Version 7.3 also added parallel processing capabilities for high-speed performance in both partitioned and non-partitioned scenarios. Improving potential bottlenecks associated with Commit and logging that impact transaction performance, version 7.3 has achieved an approximately 490% enhancement in performance compared to previous versions. === Release history === == Clients == According to marketing research, Altibase have over 700 customers and more than 8,000 of installations and deployments, including 22 Fortune Global 500 Companies. Altibase's clients in the telecommunications, financial services, manufacturing, and utilities sectors include Bloomberg, AT&T, LG, Intel, LGU+, ETRADE, HP, UAT Inc., POSCO, SK Telecom, KT Corporation, Samsung Electronics, Shinhan Bank, Woori Bank, Canon(Toshiba), Hanhwa, The South Korean Ministry of Defense, G-Market, CJ, and Chung-Ang University. === Global clients === Japan FX Prime, a foreign exchange services company Retela Crea Securities United States AT&T Implemented Altibase for its PS-LTE Safety network, where the Presence service plays a vital role. This service handles the reception and storage of user information, conducting real-time checks for online presence and location as needed. Canada Telus One of the major telecommunication companies. Utilizes Altibase for its operations involving real-time user management, processing high volumes of dedicated terminal data, and managing real-time location information (GIS) for terminals. Altibase contributes to the company's in-house solution for maintaining uninterrupted services during national disasters or similar situations, ensuring efficiency and reliability. China China Mobile, China Unicom, China Telecom The three major telecommunications companies. Utilize ALTIBASE HDB in 29 of 31 Chinese provinces. Turkish Ziraat Bank, Halk Bank, Deniz Bank, Garanti BBVA, TEB, Oyak Bank, QNB, Burgan Bank, and others. In 2018, Altibase entered the market through a partnership with ATP-Tradesoft, a subsidiary of Ata Holdings. Collaborating with ATP-Tradesoft. Altibase integrated into the Online Trading System XFront. This integration was well-received by major financial institutions and securities firms in Turkey. Altibase is currently implemented in the XFront Online Trading System, used by 13 significant financial institutions and banks in the Turkey. Thailand Bualuang Securities Altibase has been supplied its DBMS to support the construction of the online stock trading platform. Mongolia MobiCom The Mongolian telecommunication giant, has adopted Altibase’s 7.0 version for its mobile platform for storing the infrequently used data. Azerbaijan M1 highway Altibase has been supplied as the Database Management System (DBMS) for the electronic toll collection system. One of the most crucial transportation networks in the country. India State-owned Karur Vysya Bank In 2013, Altibase provided its hybrid database solution and was deployed for the online banking system === Industries === Telecommunications LGU+ SK Telecom KT Corporation AT&T Telus Financial services Shinhan Bank Woori Bank KakaoPay Securities Implemented Altibase in its stock trading system Leveraging Altibase's replication feature, along with offline replication through shared disk and adapter functionality, the system ensures a high level of availability and consistency, with a reliability rate of 99.999% even in the event of system failures. COREDAX Cryptocurrency market Altibase has entered into a strategic partnership by signing a database management system (DBMS) supply contract with the cryptocurrency exchange Bloomberg ETRADE Manufacturing Samsung Electronics LG POSCO Hanhwa Canon(Toshiba) Intel HP Utilities South Korean Ministry of Defense G-Market CJ UAT Inc. Chung-Ang University == Features == Altibase is a so-called "hybrid DBMS", meaning that it simultaneously supports access to both memory-resident and disk-resident tables via a single interface. It is compatible with Solaris, HP-UX, AIX, Linux, and Windows. It supports the complete SQL standard, features Multiversion concurrency control (MVCC), implements Fuzzy and Ping-Pong Checkpointing for periodically backing up memory-resident data, and ships with Replication and Database Link functionality. High performance, large -capacity service Fast real-time data processing and large amounts of data stable Provide parallel processing architecture for large data management Developed and provided Hybrid Partitioned Table function for efficiency according to data personality High stability

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  Vapnik–Chervonenkis dimension

  In Vapnik–Chervonenkis theory, the Vapnik–Chervonenkis (VC) dimension is a measure of the size (capacity, complexity, expressive power, richness, or flexibility) of a class of sets. The notion can be extended to classes of binary functions. It is defined as the cardinality of the largest set of points that the function class can shatter—that is, for which all possible binary labelings can be realized by some function in the class. It was originally defined by Vladimir Vapnik and Alexey Chervonenkis. Informally, the capacity of a classification model is related to how complicated it can be. For example, consider the thresholding of a high-degree polynomial: if the polynomial evaluates above zero, that point is classified as positive, otherwise as negative. A high-degree polynomial can be wiggly, so that it can fit a given set of training points well. Such a polynomial has a high capacity. A much simpler alternative is to threshold a linear function. This function may not fit the training set well, because it has a low capacity. This notion of capacity is made rigorous below. == Definitions == === VC dimension of a set-family === Let C = { C } C ∈ C {\displaystyle {\mathcal {C}}=\{C\}_{C\in {\mathcal {C}}}} be a family of sets (also called set family, collection of sets or set of sets) and X {\displaystyle X} a set. Their intersection is defined as the following set family: C ∩ X := { C ∩ X ∣ C ∈ C } . {\displaystyle {\mathcal {C}}\cap X:=\{C\cap X\mid C\in {\mathcal {C}}\}.} Here typically X {\displaystyle X} and each C ∈ C {\displaystyle C\in {\mathcal {C}}} are subsets of a big "universe" of possibilities U {\displaystyle U} where intersection takes place. We say that a set X {\displaystyle X} is shattered by C {\displaystyle {\mathcal {C}}} if P ( X ) = C ∩ X {\displaystyle {\mathcal {P}}(X)={\mathcal {C}}\cap X} i.e. the set of intersections contains (hence is equal to) all the subsets of X {\displaystyle X} . For finite sets X {\displaystyle X} this is equivalent to | C ∩ X | = 2 | X | . {\displaystyle |{\mathcal {C}}\cap X|=2^{|X|}.} The VC dimension D {\displaystyle D} of C {\displaystyle {\mathcal {C}}} is the cardinality of the largest set that is shattered by C {\displaystyle {\mathcal {C}}} . If arbitrarily large sets can be shattered, the VC dimension of C {\displaystyle {\mathcal {C}}} is ∞ {\displaystyle \infty } . === VC dimension of a classification model === A binary classification model f {\displaystyle f} with some parameter vector θ {\displaystyle \theta } is said to shatter a set of generally positioned data points ( x 1 , x 2 , … , x n ) {\displaystyle (x_{1},x_{2},\ldots ,x_{n})} if, for every assignment of labels to those points, there exists a θ {\displaystyle \theta } such that the model f {\displaystyle f} makes no errors when evaluating that set of data points. The VC dimension of a model f {\displaystyle f} is the maximum number of points that can be arranged so that f {\displaystyle f} shatters them. More formally, it is the maximum cardinal D {\displaystyle D} such that there exists a generally positioned data point set of cardinality D {\displaystyle D} that can be shattered by f {\displaystyle f} . == Examples == f {\displaystyle f} is a constant classifier (with no parameters); Its VC dimension is 0 since it cannot shatter even a single point. In general, the VC dimension of a finite classification model, which can return at most 2 d {\displaystyle 2^{d}} different classifiers, is at most d {\displaystyle d} (this is an upper bound on the VC dimension; the Sauer–Shelah lemma gives a lower bound on the dimension). f {\displaystyle f} is a single-parametric threshold classifier on real numbers; i.e., for a certain threshold θ {\displaystyle \theta } , the classifier f θ {\displaystyle f_{\theta }} returns 1 if the input number is larger than θ {\displaystyle \theta } and 0 otherwise. The VC dimension of f {\displaystyle f} is 1 because: (a) It can shatter a single point. For every point x {\displaystyle x} , a classifier f θ {\displaystyle f_{\theta }} labels it as 0 if θ > x {\displaystyle \theta >x} and labels it as 1 if θ < x {\displaystyle \theta x + 2 {\displaystyle \theta >x+2} , as (1,0) if θ ∈ [ x − 4 , x − 2 ) {\displaystyle \theta \in [x-4,x-2)} , as (1,1) if θ ∈ [ x − 2 , x ] {\displaystyle \theta \in [x-2,x]} , and as (0,1) if θ ∈ ( x , x + 2 ] {\displaystyle \theta \in (x,x+2]} . (b) It cannot shatter any set of three points. For every set of three numbers, if the smallest and the largest are labeled 1, then the middle one must also be labeled 1, so not all labelings are possible. f {\displaystyle f} is a straight line as a classification model on points in a two-dimensional plane (this is the model used by a perceptron). The line should separate positive data points from negative data points. There exist sets of 3 points that can indeed be shattered using this model (any 3 points that are not collinear can be shattered). However, no set of 4 points can be shattered: by Radon's theorem, any four points can be partitioned into two subsets with intersecting convex hulls, so it is not possible to separate one of these two subsets from the other. Thus, the VC dimension of this particular classifier is 3. It is important to remember that while one can choose any arrangement of points, the arrangement of those points cannot change when attempting to shatter for some label assignment. Note, only 3 of the 23 = 8 possible label assignments are shown for the three points. f {\displaystyle f} is a single-parametric sine classifier, i.e., for a certain parameter θ {\displaystyle \theta } , the classifier f θ {\displaystyle f_{\theta }} returns 1 if the input number x {\displaystyle x} has sin ⁡ ( θ x ) > 0 {\displaystyle \sin(\theta x)>0} and 0 otherwise. The VC dimension of f {\displaystyle f} is infinite, since it can shatter any finite subset of the set { 2 − m ∣ m ∈ N } {\displaystyle \{2^{-m}\mid m\in \mathbb {N} \}} . == Uses == === In statistical learning theory === The VC dimension can predict a probabilistic upper bound on the test error of a classification model. Vapnik proved that the probability of the test error (i.e., risk with 0–1 loss function) distancing from an upper bound (on data that is drawn i.i.d. from the same distribution as the training set) is given by: Pr ( test error ⩽ training error + 1 N [ D ( log ⁡ ( 2 N D ) + 1 ) − log ⁡ ( η 4 ) ] ) = 1 − η , {\displaystyle \Pr \left({\text{test error}}\leqslant {\text{training error}}+{\sqrt {{\frac {1}{N}}\left[D\left(\log \left({\tfrac {2N}{D}}\right)+1\right)-\log \left({\tfrac {\eta }{4}}\right)\right]}}\,\right)=1-\eta ,} where D {\displaystyle D} is the VC dimension of the classification model, 0 < η ⩽ 1 {\displaystyle 0<\eta \leqslant 1} , and N {\displaystyle N} is the size of the training set (restriction: this formula is valid when D ≪ N {\displaystyle D\ll N} . When D {\displaystyle D} is larger, the test-error may be much higher than the training-error. This is due to overfitting). The VC dimension also appears in sample-complexity bounds. A space of binary functions with VC dimension D {\displaystyle D} can be learned with: N = Θ ( D + ln ⁡ 1 δ ε 2 ) {\displaystyle N=\Theta \left({\frac {D+\ln {1 \over \delta }}{\varepsilon ^{2}}}\right)} samples, where ε {\displaystyle \varepsilon } is the learning error and δ {\displaystyle \delta } is the failure probability. Thus, the sample-complexity is a linear function of the VC dimension of the hypothesis space. === In computational geometry === The VC dimension is one of the critical parameters in the size of ε-nets, which determines the complexity of approximation algorithms based on them; range sets without finite VC dimension may not have finite ε-nets at all. == Bounds == The VC dimension of the dual set-family of C {\displaystyle {\mathcal {C}}} is strictly less than 2 vc ⁡ ( C ) + 1 {\displaystyle 2^{\operatorname {vc} ({\mathcal {C}})+1}} , and this is best possible. The VC dimension of a finite set-family C {\displaystyle {\mathcal {C}}} is at most log 2 ⁡ | C | {\displaystyle \log _{2}|{\mathcal {C}}|} . This is because | C ∩ X | ≤ | X | {\displaystyle |{\mathcal {C}}\cap X|\leq |X|} by definition. Given a set-fa

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  Rprop

  Rprop, short for resilient backpropagation, is a learning heuristic for supervised learning in feedforward artificial neural networks. This is a first-order optimization algorithm. This algorithm was created by Martin Riedmiller and Heinrich Braun in 1992. Similarly to the Manhattan update rule, Rprop takes into account only the sign of the partial derivative over all patterns (not the magnitude), and acts independently on each "weight". For each weight, if there was a sign change of the partial derivative of the total error function compared to the last iteration, the update value for that weight is multiplied by a factor η−, where η− < 1. If the last iteration produced the same sign, the update value is multiplied by a factor of η+, where η+ > 1. The update values are calculated for each weight in the above manner, and finally each weight is changed by its own update value, in the opposite direction of that weight's partial derivative, so as to minimise the total error function. η+ is empirically set to 1.2 and η− to 0.5. Rprop can result in very large weight increments or decrements if the gradients are large, which is a problem when using mini-batches as opposed to full batches. RMSprop addresses this problem by keeping the moving average of the squared gradients for each weight and dividing the gradient by the square root of the mean square. RPROP is a batch update algorithm. Next to the cascade correlation algorithm and the Levenberg–Marquardt algorithm, Rprop is one of the fastest weight update mechanisms. == Variations == Martin Riedmiller developed three algorithms, all named RPROP. Igel and Hüsken assigned names to them and added a new variant: RPROP+ is defined at A Direct Adaptive Method for Faster Backpropagation Learning: The RPROP Algorithm. RPROP− is defined at Advanced Supervised Learning in Multi-layer Perceptrons – From Backpropagation to Adaptive Learning Algorithms. Backtracking is removed from RPROP+. iRPROP− is defined in Rprop – Description and Implementation Details and was reinvented by Igel and Hüsken. This variant is very popular and most simple. iRPROP+ is defined at Improving the Rprop Learning Algorithm and is very robust and typically faster than the other three variants.

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  Multimodal learning

  Multimodal learning is a type of deep learning that integrates and processes multiple types of data, referred to as modalities, such as text, audio, images, or video. This integration allows for a more holistic understanding of complex data, improving model performance in tasks like visual question answering, cross-modal retrieval, text-to-image generation, aesthetic ranking, and image captioning. Multimodal learning was proposed in 2011 at the beginning of the deep learning period. Large multimodal models, such as Google Gemini and GPT-4o, have become increasingly popular since 2023, enabling increased versatility and a broader understanding of real-world phenomena. == Motivation == Data usually comes with different modalities which carry different information. For example, it is very common to caption an image to convey the information not presented in the image itself. Similarly, sometimes it is more straightforward to use an image to describe information which may not be obvious from text. As a result, if different words appear in similar images, then these words likely describe the same thing. Conversely, if a word is used to describe seemingly dissimilar images, then these images may represent the same object. Thus, in cases dealing with multi-modal data, it is important to use a model which is able to jointly represent the information such that the model can capture the combined information from different modalities. == Multimodal transformers == Models such as CLIP (Contrastive Language–Image Pretraining) learn joint representations of images and text by optimizing contrastive objectives, allowing the model to match images with their corresponding textual descriptions. == Multimodal deep Boltzmann machines == A Boltzmann machine is a type of stochastic neural network invented by Geoffrey Hinton and Terry Sejnowski in 1985. Boltzmann machines can be seen as the stochastic, generative counterpart of Hopfield nets. They are named after the Boltzmann distribution in statistical mechanics. The units in Boltzmann machines are divided into two groups: visible units and hidden units. Each unit is like a neuron with a binary output that represents whether it is activated or not. General Boltzmann machines allow connection between any units. However, learning is impractical using general Boltzmann Machines because the computational time is exponential to the size of the machine. A more efficient architecture is called restricted Boltzmann machine where connection is only allowed between hidden unit and visible unit, which is described in the next section. Multimodal deep Boltzmann machines can process and learn from different types of information, such as images and text, simultaneously. This can notably be done by having a separate deep Boltzmann machine for each modality, for example one for images and one for text, joined at an additional top hidden layer. == Applications == Multimodal machine learning has numerous applications across various domains: Cross-modal retrieval: cross-modal retrieval allows users to search for data across different modalities (e.g., retrieving images based on text descriptions), improving multimedia search engines and content recommendation systems. Classification and missing data retrieval: multimodal Deep Boltzmann Machines outperform traditional models like support vector machines and latent Dirichlet allocation in classification tasks and can predict missing data in multimodal datasets, such as images and text. Healthcare diagnostics: multimodal models integrate medical imaging, genomic data, and patient records to improve diagnostic accuracy and early disease detection, especially in cancer screening. Content generation: models like DALL·E generate images from textual descriptions, benefiting creative industries, while cross-modal retrieval enables dynamic multimedia searches. Robotics and human-computer interaction: multimodal learning improves interaction in robotics and AI by integrating sensory inputs like speech, vision, and touch, aiding autonomous systems and human-computer interaction. Emotion recognition: combining visual, audio, and text data, multimodal systems enhance sentiment analysis and emotion recognition, applied in customer service, social media, and marketing.

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  DeepRoute.ai

  DeepRoute.ai (Chinese: 元戎启行) is a Chinese autonomous driving company founded in 2019 and headquartered in Shenzhen, China. The company develops full-stack self-driving solutions including perception, decision-making, and control systems. == History == DeepRoute.ai was founded in February 2019 in Shenzhen, China, by Zhou Guang (周光), who serves as the company's CEO. In September 2019, the company collaborated with Dongfeng for a live-streamed autonomous driving demonstration. In October 2019, during the 7th Military World Games, DeepRoute.ai conducted Robotaxi demonstration operations. In November 2019, it obtained an intelligent connected vehicle road test permit for public roads in Shenzhen. In October 2020, DeepRoute.ai signed an "Autonomous Driving Leadership Project" with Dongfeng to build one of China's largest autonomous fleets. In August 2020, DeepRoute.ai announced its partnership with Cao Cao Mobility, a Geely-backed ride-hailing company, to test Robotaxis in Hangzhou for daily operations, planning to provide Robotaxis during the 2022 Asian Games. In September 2021, DeepRoute.ai secured US$300 million in a Series B funding round led by Alibaba. In December 2021, the company unveiled its DeepRoute-Driver 2.0, an L4-level autonomous driving solution comprising five solid-state lidar sensors, eight cameras, a proprietary computing system and an optional millimeter-wave radar. with a production cost of under US$10,000. In June 2022, it partnered with Deppon Express to provide autonomous light truck freight transfer services. In March 2023, the company launched its high-precision map-free intelligent driving solution, DeepRoute-Driver 3.0. In November 2024, Great Wall Motor announced a $100 million Series C funding round for Deeproute. With this, Deeproute has completed five rounds of financing, raising a cumulative total of over $500 million. Its shareholders include Fosun RZ Capital, Yunqi Partners, Alibaba, Vision Plus Capital, and Dongfeng, among others. In the same month, Deeproute.ai emphasised that they were in "deep cooperation" with Nvidia and spoke on being part of the first batch of companies in China to get a hold of Nvidia's newer Thor chip for cars which will be used in a new system released next year. This new system will help manage more complex driving scenarios through visual cues. == Products == === VLA Model === VLA Model is a Vision–language–action model designed for autonomous driving systems. It integrates visual perception, semantic understanding, and action decision-making into a unified framework, aiming to enhance the safety and adaptability of advanced driver-assistance systems (ADAS) in complex road environments. The model was officially launched on August 26, 2025, as the core of DeepRoute.ai's DeepRoute IO 2.0 platform. The VLA model is characterized by its "visual-language-action" architecture, which incorporates a chain-of-thought (CoT) reasoning capability inspired by large language models. This design is intended to address the "black box" limitations of traditional end-to-end autonomous driving systems by enabling the model to analyze information, infer causality, and make decisions in a more transparent and interpretable manner. === Appliance === The company has partnered with several automakers including Dongfeng Motor Corporation and Geely to develop and test autonomous vehicles.

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  Grammatical evolution

  Grammatical evolution (GE) is a genetic programming (GP) technique (or approach) from evolutionary computation pioneered by Conor Ryan, JJ Collins and Michael O'Neill in 1998 at the BDS Group in the University of Limerick. As in any other GP approach, the objective is to find an executable program, program fragment, or function, which will achieve a good fitness value for a given objective function. In most published work on GP, a LISP-style tree-structured expression is directly manipulated, whereas GE applies genetic operators to an integer string, subsequently mapped to a program (or similar) through the use of a grammar, which is typically expressed in Backus–Naur form. One of the benefits of GE is that this mapping simplifies the application of search to different programming languages and other structures. == Problem addressed == In type-free, conventional Koza-style GP, the function set must meet the requirement of closure: all functions must be capable of accepting as their arguments the output of all other functions in the function set. Usually, this is implemented by dealing with a single data-type such as double-precision floating point. While modern Genetic Programming frameworks support typing, such type-systems have limitations that Grammatical Evolution does not suffer from. == GE's solution == GE offers a solution to the single-type limitation by evolving solutions according to a user-specified grammar (usually a grammar in Backus-Naur form). Therefore, the search space can be restricted, and domain knowledge of the problem can be incorporated. The inspiration for this approach comes from a desire to separate the "genotype" from the "phenotype": in GP, the objects the search algorithm operates on and what the fitness evaluation function interprets are one and the same. In contrast, GE's "genotypes" are ordered lists of integers which code for selecting rules from the provided context-free grammar. The phenotype, however, is the same as in Koza-style GP: a tree-like structure that is evaluated recursively. This model is more in line with how genetics work in nature, where there is a separation between an organism's genotype and the final expression of phenotype in proteins, etc. Separating genotype and phenotype allows a modular approach. In particular, the search portion of the GE paradigm needn't be carried out by any one particular algorithm or method. Observe that the objects GE performs search on are the same as those used in genetic algorithms. This means, in principle, that any existing genetic algorithm package, such as the popular GAlib, can be used to carry out the search, and a developer implementing a GE system need only worry about carrying out the mapping from list of integers to program tree. It is also in principle possible to perform the search using some other method, such as particle swarm optimization (see the remark below); the modular nature of GE creates many opportunities for hybrids as the problem of interest to be solved dictates. Brabazon and O'Neill have successfully applied GE to predicting corporate bankruptcy, forecasting stock indices, bond credit ratings, and other financial applications. GE has also been used with a classic predator-prey model to explore the impact of parameters such as predator efficiency, niche number, and random mutations on ecological stability. It is possible to structure a GE grammar that for a given function/terminal set is equivalent to genetic programming. == Criticism == Despite its successes, GE has been the subject of some criticism. One issue is that as a result of its mapping operation, GE's genetic operators do not achieve high locality which is a highly regarded property of genetic operators in evolutionary algorithms. == Variants == Although GE was originally described in terms of using an Evolutionary Algorithm, specifically, a Genetic Algorithm, other variants exist. For example, GE researchers have experimented with using particle swarm optimization to carry out the searching instead of genetic algorithms with results comparable to that of normal GE; this is referred to as a "grammatical swarm"; using only the basic PSO model it has been found that PSO is probably equally capable of carrying out the search process in GE as simple genetic algorithms are. (Although PSO is normally a floating-point search paradigm, it can be discretized, e.g., by simply rounding each vector to the nearest integer, for use with GE.) Yet another possible variation that has been experimented with in the literature is attempting to encode semantic information in the grammar in order to further bias the search process. Other work showed that, with biased grammars that leverage domain knowledge, even random search can be used to drive GE. == Related work == GE was originally a combination of the linear representation as used by the Genetic Algorithm for Developing Software (GADS) and Backus Naur Form grammars, which were originally used in tree-based GP by Wong and Leung in 1995 and Whigham in 1996. Other related work noted in the original GE paper was that of Frederic Gruau, who used a conceptually similar "embryonic" approach, as well as that of Keller and Banzhaf, which similarly used linear genomes. == Implementations == There are several implementations of GE. These include the following.

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  Charge based boundary element fast multipole method

  The charge-based formulation of the boundary element method (BEM) is a dimensionality reduction numerical technique that is used to model quasistatic electromagnetic phenomena in highly complex conducting media (targeting, e.g., the human brain) with a very large (up to approximately 1 billion) number of unknowns. The charge-based BEM solves an integral equation of the potential theory written in terms of the induced surface charge density. This formulation is naturally combined with fast multipole method (FMM) acceleration, and the entire method is known as charge-based BEM-FMM. The combination of BEM and FMM is a common technique in different areas of computational electromagnetics and, in the context of bioelectromagnetism, it provides improvements over the finite element method. == Historical development == Along with more common electric potential-based BEM, the quasistatic charge-based BEM, derived in terms of the single-layer (charge) density, for a single-compartment medium has been known in the potential theory since the beginning of the 20th century. For multi-compartment conducting media, the surface charge density formulation first appeared in discretized form (for faceted interfaces) in the 1964 paper by Gelernter and Swihart. A subsequent continuous form, including time-dependent and dielectric effects, appeared in the 1967 paper by Barnard, Duck, and Lynn. The charge-based BEM has also been formulated for conducting, dielectric, and magnetic media, and used in different applications. In 2009, Greengard et al. successfully applied the charge-based BEM with fast multipole acceleration to molecular electrostatics of dielectrics. A similar approach to realistic modeling of the human brain with multiple conducting compartments was first described by Makarov et al. in 2018. Along with this, the BEM-based multilevel fast multipole method has been widely used in radar and antenna studies at microwave frequencies as well as in acoustics. == Physical background - surface charges in biological media == The charge-based BEM is based on the concept of an impressed (or primary) electric field E i {\displaystyle \mathbf {E} ^{i}} and a secondary electric field E s {\displaystyle \mathbf {E} ^{s}} . The impressed field is usually known a priori or is trivial to find. For the human brain, the impressed electric field can be classified as one of the following: A conservative field E i {\displaystyle \mathbf {E} ^{i}} derived from an impressed density of EEG or MEG current sources in a homogeneous infinite medium with the conductivity σ {\displaystyle \sigma } at the source location; An instantaneous solenoidal field E i {\displaystyle \mathbf {E} ^{i}} of an induction coil obtained from Faraday's law of induction in a homogeneous infinite medium (air), when transcranial magnetic stimulation (TMS) problems are concerned; A surface field E i {\displaystyle \mathbf {E} ^{i}} derived from an impressed surface current density J i = σ E i {\displaystyle \mathbf {J} ^{i}=\sigma \mathbf {E} ^{i}} of current electrodes injecting electric current at a boundary of a compartment with conductivity σ {\displaystyle \sigma } when transcranial direct-current stimulation (tDCS) or deep brain stimulation (DBS) are concerned; A conservative field E i {\displaystyle \mathbf {E} ^{i}} of charges deposited on voltage electrodes for tDCS or DBS. This specific problem requires a coupled treatment since these charges will depend on the environment; In application to multiscale modeling, a field E i {\displaystyle \mathbf {E} ^{i}} obtained from any other macroscopic numerical solution in a small (mesoscale or microscale) spatial domain within the brain. For example, a constant field can be used. When the impressed field is "turned on", free charges located within a conducting volume D immediately begin to redistribute and accumulate at the boundaries (interfaces) of regions of different conductivity in D. A surface charge density ρ ( r ) {\displaystyle \rho (\mathbf {r} )} appears on the conductivity interfaces. This charge density induces a secondary conservative electric field E s {\displaystyle \mathbf {E} ^{s}} following Coulomb's law. One example is a human under a direct current powerline with the known field E i {\displaystyle \mathbf {E} ^{i}} directed down. The superior surface of the human's conducting body will be charged negatively while its inferior portion is charged positively. These surface charges create a secondary electric field that effectively cancels or blocks the primary field everywhere in the body so that no current will flow within the body under DC steady state conditions. Another example is a human head with electrodes attached. At any conductivity interface with a normal vector n {\displaystyle \mathbf {n} } pointing from an "inside" (-) compartment of conductivity σ − {\displaystyle \sigma ^{-}} to an "outside" (+) compartment of conductivity σ + {\displaystyle \sigma ^{+}} , Kirchhoff's current law requires continuity of the normal component of the electric current density. This leads to the interfacial boundary condition in the form for every facet at a triangulated interface. As long as σ ± {\displaystyle \sigma ^{\pm }} are different from each other, the two normal components of the electric field, E ± ⋅ n {\displaystyle \mathbf {E} ^{\pm }\cdot \mathbf {n} } , must also be different. Such a jump across the interface is only possible when a sheet of surface charge exists at that interface. Thus, if an electric current or voltage is applied, the surface charge density follows. The goal of the numerical analysis is to find the unknown surface charge distribution and thus the total electric field E = E i + E s {\displaystyle \mathbf {E} =\mathbf {E} ^{i}+\mathbf {E} ^{s}} (and the total electric potential if required) anywhere in space. == System of equations for surface charges == Below, a derivation is given based on Gauss's law and Coulomb's law. All conductivity interfaces, denoted by S, are discretized into planar triangular facets t m {\displaystyle t_{m}} with centers r m {\displaystyle \mathbf {r} _{m}} . Assume that an m-th facet with the normal vector n m {\displaystyle \mathbf {n} _{m}} and area A m {\displaystyle A_{m}} carries a uniform surface charge density ρ m {\displaystyle \rho _{m}} . If a volumetric tetrahedral mesh were present, the charged facets would belong to tetrahedra with different conductivity values. We first compute the electric field E m + {\displaystyle \mathbf {E} _{m}^{+}} at the point r m + δ n m {\displaystyle \mathbf {r} _{m}+\delta \mathbf {n} _{m}} , for δ → 0 + {\displaystyle \delta \rightarrow 0^{+}} i.e., just outside facet 𝑚 at its center. This field contains three contributions: The continuous impressed electric field E i {\displaystyle \mathbf {E} ^{i}} itself; An electric field of the m-th charged facet itself. Very close to the facet, it can be approximated as the electric field of an infinite sheet of uniform surface charge ρ m {\displaystyle \rho _{m}} . By Gauss's law, it is given by + ρ m / 2 ε 0 ⋅ n m {\displaystyle +\rho _{m}/2\varepsilon _{0}\cdot \mathbf {n} _{m}} where ε 0 {\displaystyle \varepsilon _{0}} is a background electrical permittivity; An electric field generated by all other facets t n {\displaystyle t_{n}} , which we approximate as point charges of charge A n ρ n {\displaystyle A_{n}\rho _{n}} at each center r n {\displaystyle \mathbf {r} _{n}} . A similar treatment holds for the electric field E m − {\displaystyle \mathbf {E} _{m}^{-}} just inside facet 𝑚, but the electric field of the flat sheet of charge changes its sign. Using Coulomb's law to calculate the contribution of facets different from t m {\displaystyle t_{m}} , we find From this equation, we see that the normal component of the electric field indeed undergoes a jump through the charged interface. This is equivalent to a jump relation of the potential theory. As a second step, the two expressions for E m ± {\displaystyle \mathbf {E} _{m}^{\pm }} are substituted into the interfacial boundary condition σ − E m − ⋅ n m = σ + E m + ⋅ n m {\displaystyle \sigma ^{-}\mathbf {E} _{m}^{-}\cdot \mathbf {n} _{m}=\sigma ^{+}\mathbf {E} _{m}^{+}\cdot \mathbf {n} _{m}} , applied to every facet 𝑚. This operation leads to a system of linear equations for unknown charge densities ρ m {\displaystyle \rho _{m}} which solves the problem: where K m = σ − − σ + σ − + σ + {\displaystyle K_{m}={\frac {\sigma ^{-}-\sigma ^{+}}{\sigma ^{-}+\sigma ^{+}}}} is the electric conductivity contrast at the m-th facet. The normalization constant ε 0 {\displaystyle \varepsilon _{0}} will cancel out after the solution is substituted in the expression for E s {\displaystyle \mathbf {E} ^{s}} and becomes redundant. == Application of fast multipole method == For modern characterizations of brain topologies with ever-increasing levels of complexity, the above system of equations for ρ m {\displaystyle \rho _{m}} is very large; it is t

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