User modeling

User modeling is the subdivision of human–computer interaction which describes the process of building up and modifying a conceptual understanding of the user. The main goal of user modeling is customization and adaptation of systems to the user's specific needs. The system needs to "say the 'right' thing at the 'right' time in the 'right' way". To do so it needs an internal representation of the user. Another common purpose is modeling specific kinds of users, including modeling of their skills and declarative knowledge, for use in automatic software-tests. User-models can thus serve as a cheaper alternative to user testing but should not replace user testing. == Background == A user model is the collection and categorization of personal data associated with a specific user. A user model is a (data) structure that is used to capture certain characteristics about an individual user, and a user profile is the actual representation in a given user model. The process of obtaining the user profile is called user modeling. Therefore, it is the basis for any adaptive changes to the system's behavior. Which data is included in the model depends on the purpose of the application. It can include personal information such as users' names and ages, their interests, their skills and knowledge, their goals and plans, their preferences and their dislikes or data about their behavior and their interactions with the system. There are different design patterns for user models, though often a mixture of them is used. Static user models Static user models are the most basic kinds of user models. Once the main data is gathered they are normally not changed again, they are static. Shifts in users' preferences are not registered and no learning algorithms are used to alter the model. Dynamic user models Dynamic user models allow a more up to date representation of users. Changes in their interests, their learning progress or interactions with the system are noticed and influence the user models. The models can thus be updated and take the current needs and goals of the users into account. Stereotype based user models Stereotype based user models are based on demographic statistics. Based on the gathered information users are classified into common stereotypes. The system then adapts to this stereotype. The application therefore can make assumptions about a user even though there might be no data about that specific area, because demographic studies have shown that other users in this stereotype have the same characteristics. Thus, stereotype based user models mainly rely on statistics and do not take into account that personal attributes might not match the stereotype. However, they allow predictions about a user even if there is rather little information about him or her. Highly adaptive user models Highly adaptive user models try to represent one particular user and therefore allow a very high adaptivity of the system. In contrast to stereotype based user models they do not rely on demographic statistics but aim to find a specific solution for each user. Although users can take great benefit from this high adaptivity, this kind of model needs to gather a lot of information first. == Data gathering == Information about users can be gathered in several ways. There are three main methods: Asking for specific facts while (first) interacting with the system Mostly this kind of data gathering is linked with the registration process. While registering users are asked for specific facts, their likes and dislikes and their needs. Often the given answers can be altered afterwards. Learning users' preferences by observing and interpreting their interactions with the system In this case users are not asked directly for their personal data and preferences, but this information is derived from their behavior while interacting with the system. The ways they choose to accomplish a tasks, the combination of things they takes interest in, these observations allow inferences about a specific user. The application dynamically learns from observing these interactions. Different machine learning algorithms may be used to accomplish this task. A hybrid approach which asks for explicit feedback and alters the user model by adaptive learning This approach is a mixture of the ones above. Users have to answer specific questions and give explicit feedback. Furthermore, their interactions with the system are observed and the derived information are used to automatically adjust the user models. Though the first method is a good way to quickly collect main data it lacks the ability to automatically adapt to shifts in users' interests. It depends on the users' readiness to give information and it is unlikely that they are going to edit their answers once the registration process is finished. Therefore, there is a high likelihood that the user models are not up to date. However, this first method allows the users to have full control over the collected data about them. It is their decision which information they are willing to provide. This possibility is missing in the second method. Adaptive changes in a system that learns users' preferences and needs only by interpreting their behavior might appear a bit opaque to the users, because they cannot fully understand and reconstruct why the system behaves the way it does. Moreover, the system is forced to collect a certain amount of data before it is able to predict the users' needs with the required accuracy. Therefore, it takes a certain learning time before a user can benefit from adaptive changes. However, afterwards these automatically adjusted user models allow a quite accurate adaptivity of the system. The hybrid approach tries to combine the advantages of both methods. Through collecting data by directly asking its users it gathers a first stock of information which can be used for adaptive changes. By learning from the users' interactions it can adjust the user models and reach more accuracy. Yet, the designer of the system has to decide, which of these information should have which amount of influence and what to do with learned data that contradicts some of the information given by a user. == System adaptation == Once a system has gathered information about a user it can evaluate that data by preset analytical algorithm and then start to adapt to the user's needs. These adaptations may concern every aspect of the system's behavior and depend on the system's purpose. Information and functions can be presented according to the user's interests, knowledge or goals by displaying only relevant features, hiding information the user does not need, making proposals what to do next and so on. One has to distinguish between adaptive and adaptable systems. In an adaptable system the user can manually change the system's appearance, behavior or functionality by actively selecting the corresponding options. Afterwards the system will stick to these choices. In an adaptive system a dynamic adaption to the user is automatically performed by the system itself, based on the built user model. Thus, an adaptive system needs ways to interpret information about the user in order to make these adaptations. One way to accomplish this task is implementing rule-based filtering. In this case a set of IF... THEN... rules is established that covers the knowledge base of the system. The IF-conditions can check for specific user-information and if they match the THEN-branch is performed which is responsible for the adaptive changes. Another approach is based on collaborative filtering. In this case information about a user is compared to that of other users of the same systems. Thus, if characteristics of the current user match those of another, the system can make assumptions about the current user by presuming that he or she is likely to have similar characteristics in areas where the model of the current user is lacking data. Based on these assumption the system then can perform adaptive changes. == Usages == Adaptive hypermedia: In an adaptive hypermedia system the displayed content and the offered hyperlinks are chosen on basis of users' specific characteristics, taking their goals, interests, knowledge and abilities into account. Thus, an adaptive hypermedia system aims to reduce the "lost in hyperspace" syndrome by presenting only relevant information. Adaptive educational hypermedia: Being a subdivision of adaptive hypermedia the main focus of adaptive educational hypermedia lies on education, displaying content and hyperlinks corresponding to the user's knowledge on the field of study. Intelligent tutoring system: Unlike adaptive educational hypermedia systems intelligent tutoring systems are stand-alone systems. Their aim is to help students in a specific field of study. To do so, they build up a user model where they store information about abilities, knowledge and needs of the user. The system can now adapt to this user by presenting approp

Event condition action

Event condition action (ECA) is a short-cut for referring to the structure of active rules in event-driven architecture and active database systems. Such a rule traditionally consisted of three parts: The event part specifies the signal that triggers the invocation of the rule The condition part is a logical test that, if satisfied or evaluates to true, causes the action to be carried out The action part consists of updates or invocations on the local data This structure was used by the early research in active databases which started to use the term ECA. Current state of the art ECA rule engines use many variations on rule structure. Also other features not considered by the early research is introduced, such as strategies for event selection into the event part. In a memory-based rule engine, the condition could be some tests on local data and actions could be updates to object attributes. In a database system, the condition could simply be a query to the database, with the result set (if not null) being passed to the action part for changes to the database. In either case, actions could also be calls to external programs or remote procedures. Note that for database usage, updates to the database are regarded as internal events. As a consequence, the execution of the action part of an active rule can match the event part of the same or another active rule, thus triggering it. The equivalent in a memory-based rule engine would be to invoke an external method that caused an external event to trigger another ECA rule. ECA rules can also be used in rule engines that use variants of the Rete algorithm for rule processing. == ECA rule engines == Rulecore Concurrent Rules Apart Database Detect Invocation Rules ConceptBase ECArules

JAX (software)

JAX is a Python library for accelerator-oriented array computation and program transformation, designed for high-performance numerical computing and large-scale machine learning. It is developed by Google with contributions from Nvidia and other community contributors. It is described as bringing together a modified version of the automatic differentiation system autograd and OpenXLA's XLA (Accelerated Linear Algebra). It is designed to follow the structure and workflow of NumPy as closely as possible and works with various existing frameworks such as TensorFlow and PyTorch. The primary features of JAX are: Providing a unified NumPy-like interface to computations that run on CPU, GPU, or TPU, in local or distributed settings. Built-in Just-In-Time (JIT) compilation via OpenXLA, an open-source machine learning compiler ecosystem. Efficient evaluation of gradients via its automatic differentiation transformations. Automatic vectorization to efficiently map functions over arrays representing batches of inputs. == Libraries using Jax == Flax Equinox Optax

Conditional random field

Conditional random fields (CRFs) are a class of statistical modeling methods often applied in pattern recognition and machine learning and used for structured prediction. Whereas a classifier predicts a label for a single sample without considering "neighbouring" samples, a CRF can take context into account. To do so, the predictions are modelled as a graphical model, which represents the presence of dependencies between the predictions. The kind of graph used depends on the application. For example, in natural language processing, "linear chain" CRFs are popular, for which each prediction is dependent only on its immediate neighbours. In image processing, the graph typically connects locations to nearby and/or similar locations to enforce that they receive similar predictions. Other examples where CRFs are used are: labeling or parsing of sequential data for natural language processing or biological sequences, part-of-speech tagging, shallow parsing, named entity recognition, gene finding, peptide critical functional region finding, and object recognition and image segmentation in computer vision. == Description == CRFs are a type of discriminative undirected probabilistic graphical model. Lafferty, McCallum and Pereira define a CRF on observations X {\displaystyle {\boldsymbol {X}}} and random variables Y {\displaystyle {\boldsymbol {Y}}} as follows: Let G = ( V , E ) {\displaystyle G=(V,E)} be a graph such that Y = ( Y v ) v ∈ V {\displaystyle {\boldsymbol {Y}}=({\boldsymbol {Y}}_{v})_{v\in V}} , so that Y {\displaystyle {\boldsymbol {Y}}} is indexed by the vertices of G {\displaystyle G} . Then ( X , Y ) {\displaystyle ({\boldsymbol {X}},{\boldsymbol {Y}})} is a conditional random field when each random variable Y v {\displaystyle {\boldsymbol {Y}}_{v}} , conditioned on X {\displaystyle {\boldsymbol {X}}} , obeys the Markov property with respect to the graph; that is, its probability is dependent only on its neighbours in G and not its past states: P ( Y v | X , { Y w : w ≠ v } ) = P ( Y v | X , { Y w : w ∼ v } ) {\displaystyle P({\boldsymbol {Y}}_{v}|{\boldsymbol {X}},\{{\boldsymbol {Y}}_{w}:w\neq v\})=P({\boldsymbol {Y}}_{v}|{\boldsymbol {X}},\{{\boldsymbol {Y}}_{w}:w\sim v\})} , where w ∼ v {\displaystyle {\mathit {w}}\sim v} means that w {\displaystyle w} and v {\displaystyle v} are neighbors in G {\displaystyle G} . What this means is that a CRF is an undirected graphical model whose nodes can be divided into exactly two disjoint sets X {\displaystyle {\boldsymbol {X}}} and Y {\displaystyle {\boldsymbol {Y}}} , the observed and output variables, respectively; the conditional distribution p ( Y | X ) {\displaystyle p({\boldsymbol {Y}}|{\boldsymbol {X}})} is then modeled. === Inference === For general graphs, the problem of exact inference in CRFs is intractable. The inference problem for a CRF is basically the same as for an MRF and the same arguments hold. However, there exist special cases for which exact inference is feasible: If the graph is a chain or a tree, message passing algorithms yield exact solutions. The algorithms used in these cases are analogous to the forward-backward and Viterbi algorithm for the case of HMMs. If the CRF only contains pair-wise potentials and the energy is submodular, combinatorial min cut/max flow algorithms yield exact solutions. If exact inference is impossible, several algorithms can be used to obtain approximate solutions. These include: Loopy belief propagation Alpha expansion Mean field inference Linear programming relaxations === Parameter learning === Learning the parameters θ {\displaystyle \theta } is usually done by maximum likelihood learning for p ( Y i | X i ; θ ) {\displaystyle p(Y_{i}|X_{i};\theta )} . If all nodes have exponential family distributions and all nodes are observed during training, this optimization is convex. It can be solved for example using gradient descent algorithms, or Quasi-Newton methods such as the L-BFGS algorithm. On the other hand, if some variables are unobserved, the inference problem has to be solved for these variables. Exact inference is intractable in general graphs, so approximations have to be used. === Examples === In sequence modeling, the graph of interest is usually a chain graph. An input sequence of observed variables X {\displaystyle X} represents a sequence of observations and Y {\displaystyle Y} represents a hidden (or unknown) state variable that needs to be inferred given the observations. The Y i {\displaystyle Y_{i}} are structured to form a chain, with an edge between each Y i − 1 {\displaystyle Y_{i-1}} and Y i {\displaystyle Y_{i}} . As well as having a simple interpretation of the Y i {\displaystyle Y_{i}} as "labels" for each element in the input sequence, this layout admits efficient algorithms for: model training, learning the conditional distributions between the Y i {\displaystyle Y_{i}} and feature functions from some corpus of training data. decoding, determining the probability of a given label sequence Y {\displaystyle Y} given X {\displaystyle X} . inference, determining the most likely label sequence Y {\displaystyle Y} given X {\displaystyle X} . The conditional dependency of each Y i {\displaystyle Y_{i}} on X {\displaystyle X} is defined through a fixed set of feature functions of the form f ( i , Y i − 1 , Y i , X ) {\displaystyle f(i,Y_{i-1},Y_{i},X)} , which can be thought of as measurements on the input sequence that partially determine the likelihood of each possible value for Y i {\displaystyle Y_{i}} . The model assigns each feature a numerical weight and combines them to determine the probability of a certain value for Y i {\displaystyle Y_{i}} . Linear-chain CRFs have many of the same applications as conceptually simpler hidden Markov models (HMMs), but relax certain assumptions about the input and output sequence distributions. An HMM can loosely be understood as a CRF with very specific feature functions that use constant probabilities to model state transitions and emissions. Conversely, a CRF can loosely be understood as a generalization of an HMM that makes the constant transition probabilities into arbitrary functions that vary across the positions in the sequence of hidden states, depending on the input sequence. Notably, in contrast to HMMs, CRFs can contain any number of feature functions, the feature functions can inspect the entire input sequence X {\displaystyle X} at any point during inference, and the range of the feature functions need not have a probabilistic interpretation. == Variants == === Higher-order CRFs and semi-Markov CRFs === CRFs can be extended into higher order models by making each Y i {\displaystyle Y_{i}} dependent on a fixed number k {\displaystyle k} of previous variables Y i − k , . . . , Y i − 1 {\displaystyle Y_{i-k},...,Y_{i-1}} . In conventional formulations of higher order CRFs, training and inference are only practical for small values of k {\displaystyle k} (such as k ≤ 5), since their computational cost increases exponentially with k {\displaystyle k} . However, another recent advance has managed to ameliorate these issues by leveraging concepts and tools from the field of Bayesian nonparametrics. Specifically, the CRF-infinity approach constitutes a CRF-type model that is capable of learning infinitely-long temporal dynamics in a scalable fashion. This is effected by introducing a novel potential function for CRFs that is based on the Sequence Memoizer (SM), a nonparametric Bayesian model for learning infinitely-long dynamics in sequential observations. To render such a model computationally tractable, CRF-infinity employs a mean-field approximation of the postulated novel potential functions (which are driven by an SM). This allows for devising efficient approximate training and inference algorithms for the model, without undermining its capability to capture and model temporal dependencies of arbitrary length. There exists another generalization of CRFs, the semi-Markov conditional random field (semi-CRF), which models variable-length segmentations of the label sequence Y {\displaystyle Y} . This provides much of the power of higher-order CRFs to model long-range dependencies of the Y i {\displaystyle Y_{i}} , at a reasonable computational cost. Finally, large-margin models for structured prediction, such as the structured Support Vector Machine can be seen as an alternative training procedure to CRFs. === Latent-dynamic conditional random field === Latent-dynamic conditional random fields (LDCRF) or discriminative probabilistic latent variable models (DPLVM) are a type of CRFs for sequence tagging tasks. They are latent variable models that are trained discriminatively. In an LDCRF, like in any sequence tagging task, given a sequence of observations x = x 1 , … , x n {\displaystyle x_{1},\dots ,x_{n}} , the main problem the model must solve is how to assign a sequence of labels y = y 1 , … , y n {\displaystyle y_{1},\dots ,y_{n}} from one finite set

Automation in construction

Automation in construction is the combination of methods, processes, and systems that allow for greater machine autonomy in construction activities. Construction automation may have multiple goals, including but not limited to, reducing jobsite injuries, decreasing activity completion times, and assisting with quality control and quality assurance. Some systems may be fielded as a direct response to increasing skilled labor shortages in some countries. Opponents claim that increased automation may lead to less construction jobs and that software leaves heavy equipment vulnerable to hackers. Research insights on this subject are today published in several journals such as Automation in Construction by Elsevier. == Uses of automation in construction == Equipment control and management: Automation can be used to control and monitor construction equipment, such as cranes, excavators, and bulldozers. Material handling: Automated systems can be used to handle, transport, and place materials such as concrete, bricks, and stones. Surveying: Automated survey equipment and drones can be used to collect and analyze data on construction sites. Quality control: Automated systems can be used to monitor and control the quality of materials and construction processes. Safety management: Automated systems can be used to monitor and control safety conditions on construction sites. Scheduling and planning: Automated systems can be used to manage schedules, resources, and costs. Waste management: Automated systems can be used to manage and dispose of waste materials generated during construction. 3D printing: Automated 3D printing can be used to create prototypes, models, and even full-scale building components. == Autonomous heavy equipment == Advances in sensors, machine learning, and autonomous vehicle technology have led to the development of self-operating construction equipment and retrofit systems designed to automate excavators, bulldozers, tracked loaders, skid steer loaders, and haul trucks, allowing them to perform tasks with limited human supervision. Since 2017, tech companies have developed autonomous or semi-autonomous retrofit kits that can be installed on existing construction machinery. Examples include Bedrock Robotics, Built Robotics, and SafeAI, which develop sensor and software systems that enable excavators and other earthmoving machines to operate with varying degrees of autonomy. Major equipment manufacturers have also introduced autonomous capabilities: Caterpillar and John Deere have developed autonomous or semi-autonomous systems for construction and mining equipment, including haul trucks and earthmoving machines. == Transportation сonstruction == Kratos Defense & Security Solutions fielded the world’s first Autonomous Truck-Mounted Attenuator (ATMA) in 2017, in conjunction with Royal Truck & Equipment. == Benefits of automation in construction == The use of automation in construction has become increasingly prevalent in recent years due to its numerous benefits. Automation in construction refers to the use of machinery, software, and other technologies to perform tasks that were previously done manually by workers. One of the most significant benefits of automation in construction is increased productivity. Automation can help speed up construction processes, reduce project completion times, and improve overall efficiency. For example, using automated machinery for tasks such as concrete pouring, bricklaying, and welding can significantly increase the speed and accuracy of these tasks, allowing for more work to be completed in a shorter amount of time. Another benefit of automation in construction is improved safety. By automating tasks that are hazardous to workers, such as demolition or working at height, companies can reduce the risk of accidents and injuries on site. Automation can also help to reduce worker fatigue, which can be a significant factor in accidents and mistakes. Overall, the use of automation in construction can improve productivity, reduce costs, increase safety, and improve the quality of construction projects. As technology continues to advance, the use of automation is likely to become even more prevalent in the construction industry.

Mastodon (social network)

Mastodon is a free and open-source software platform for decentralized social networking with microblogging features similar to Twitter. It operates as a federated network of independently managed servers that communicate using the ActivityPub protocol, allowing users to connect across different instances within the Fediverse. Each Mastodon instance establishes its own moderation policies and content guidelines, distinguishing it from centrally controlled social media platforms. First released in 2016 by Eugen Rochko, Mastodon has positioned itself as an alternative to mainstream social media, particularly for users seeking decentralized, community-driven spaces. The platform has experienced multiple surges in adoption, most notably following the Twitter acquisition by Elon Musk in 2022, as users sought alternatives to Twitter. It is part of a broader shift toward decentralized social networks, including Bluesky and Lemmy. Mastodon emphasizes user privacy and moderation flexibility, offering features such as granular post visibility controls, content warning options, and local community-driven moderation. The software is written in Ruby on Rails and Node.js, with a web interface built using React and Redux. It is interoperable with other ActivityPub-based platforms, such as Threads, and supports various third-party applications on desktop and mobile devices. == Functionality == Users post short-form status messages, historically known as "toots", for others to see and interact with. On a standard Mastodon instance, these messages can include up to 500 text-based characters, greater than Twitter's 280-character limit. Some instances support even longer messages. Images, audio files, videos or polls can also be added to a message. Users join a specific Mastodon server, rather than a single centralized website or application. The servers are connected as nodes in a network, and each server can administer its own rules, account privileges, and whether to share messages to and from other servers. Users can communicate and follow each other across connected Mastodon servers with usernames similar in format to full email addresses. Since version 2.9.0, Mastodon's web user interface has offered a single-column mode for new users by default. In advanced mode, the interface approximates the microblogging interface of TweetDeck. === Privacy === Mastodon includes a number of specific privacy features. Each message has a variety of privacy options available, and users can choose whether the message is public or private. Messages can display public on a global feed, known as a timeline, or can be shared only to the user's followers. Messages can also be marked as unlisted from timelines or direct between users. Users can also mark their accounts as completely private. In the timeline, messages can display with an optional content warning feature, which requires readers to click on the hidden main body of the message to reveal it. Mastodon servers have used this feature to hide spoilers, trigger warnings, and not safe for work (NSFW) content, though some accounts use the feature to hide links and thoughts others might not want to read. Mastodon aggregates messages in local and federated timelines in real time. The local timeline shows messages from users on a singular server, while the federated timeline shows messages across all participating Mastodon servers. === Content moderation === In early 2017, journalists like Sarah Jeong distinguished Mastodon from Twitter for its approach to combating harassment. Mastodon uses community-based moderation, in which each server can limit or filter out undesirable types of content, while Twitter uses a single, global policy on content moderation. Servers can choose to limit or filter out messages with disparaging content. The founder of Mastodon, Eugen Rochko, believes that small, closely related communities deal with unwanted behavior more effectively than a large company's small safety team. In Move Slowly and Build Bridges, Robert W. Gehl argues that predominantly white participation has shaped Mastodon in ways that affect how reports of racism are received and limit its ability to replicate Black Twitter on Twitter. Users can also block and report others to administrators, much like on Twitter. Instance administrators can block other instances from interacting with their own, an action called defederation. By posting toots hashtagged with #fediblock, some instance administrators and users alert others of issues requiring moderation. === Searching === Mastodon by default allows searching for hashtags and mentioned accounts in the Fediverse. Server administrators can optionally enable Elasticsearch to search the full-text of public posts that have opted in to being indexed. == Versions == In September 2018, with the release of version 2.5 with redesigned public profile pages, Mastodon marked its 100th release. Mastodon 2.6 was released in October 2018, introducing the possibilities of verified profiles and live, in-stream link previews for images and videos. Version 2.7, in January 2019, made it possible to search for multiple hashtags at once, instead of searching for just a single hashtag, with more robust moderation capabilities for server administrators and moderators, while accessibility, such as contrast for users with sight issues, was improved. The ability for users to create and vote in polls, as well as a new invitation system to manage registrations was integrated in April 2019. Mastodon 2.8.1, released in May 2019, made images with content warnings blurred instead of completely hidden. In version 2.9 in June 2019, an optional single-column view was added. This view became the default displayed to new users, with a user "preferences" option to switch to a multiple-column-based view. In August 2020, Mastodon 3.2 was released. It included a redesigned audio player with custom thumbnails and the ability to add personal notes to one's profile. In July 2021, an official client for iOS devices was released. According to the project's then CEO, Eugen Rochko, the release was part of an effort to attract new users. Mastodon 4.0 was released in November 2022, including language support for translating posts, editing posts and following hashtags. Mastodon 4.5 was released in November 2025. Among other features it introduced quote posts, which were previously rejected from being implemented due to concerns about toxicity and harassment. To mitigate these issues Mastodon's quote post feature has been designed in a way that lets users decide if and by whom their posts can be quoted. == Software == Mastodon is published as free and open-source software under the Affero GPL license, allowing anyone to use the software or modify it as they wish. Servers can be run by any individual or organization, and users can join these servers as they wish. The server software itself is powered by Ruby on Rails and Node.js, with its web client being written in React.js and Redux. The only database software supported is PostgreSQL, with Redis being used for job processing and various actions that Mastodon needs to process. The service is interoperable with the fediverse, a collection of social networking services which use the ActivityPub protocol for communication between each other, with previous versions containing support for OStatus. Client apps for interacting with the Mastodon API are available for desktop computer operating systems, including Windows, macOS and the Linux family of operating systems, as well as mobile phones running iOS and Android. The API is open for anyone to utilize, allowing clients to be built for any operating system that can connect to the internet. === Integration with Fediverse === Mastodon uses the ActivityPub protocol for federation; this allows users to communicate between independent Mastodon instances and other ActivityPub compatible services. Thus, Mastodon is generally considered to be a part of the Fediverse. Services utilizing the ActivityPub protocol exist which allow for searching all posts on all instances as long as users opt-in. For similar reasons, only hashtags can appear in a Mastodon instance's trending topics, not arbitrary popular words. Trending topics vary between instances, since individual instances are aware of different subsets of posts from the whole fediverse. === Security concerns === While Mastodon's decentralized structure is one of its most distinctive features, it also poses additional security challenges. Since many Mastodon instances are run by volunteers, some security experts are concerned about data security and responsiveness to new threats and vulnerabilities across the network, considering the difficulty of configuring and maintaining an instance as well as uneven skill levels among administrators. Administrators of an instance also have access to the private information of any users that are either registered with that instance or have federated

Empirical dynamic modeling

Empirical dynamic modeling (EDM) is a framework for analysis and prediction of nonlinear dynamical systems. Applications include population dynamics, ecosystem service, medicine, neuroscience, dynamical systems, geophysics, and human-computer interaction. EDM was originally developed by Robert May and George Sugihara. It can be considered a methodology for data modeling, predictive analytics, dynamical system analysis, machine learning and time series analysis. == Description == Mathematical models have tremendous power to describe observations of real-world systems. They are routinely used to test hypothesis, explain mechanisms and predict future outcomes. However, real-world systems are often nonlinear and multidimensional, in some instances rendering explicit equation-based modeling problematic. Empirical models, which infer patterns and associations from the data instead of using hypothesized equations, represent a natural and flexible framework for modeling complex dynamics. Donald DeAngelis and Simeon Yurek illustrated that canonical statistical models are ill-posed when applied to nonlinear dynamical systems. A hallmark of nonlinear dynamics is state-dependence: system states are related to previous states governing transition from one state to another. EDM operates in this space, the multidimensional state-space of system dynamics rather than on one-dimensional observational time series. EDM does not presume relationships among states, for example, a functional dependence, but projects future states from localised, neighboring states. EDM is thus a state-space, nearest-neighbors paradigm where system dynamics are inferred from states derived from observational time series. This provides a model-free representation of the system naturally encompassing nonlinear dynamics. A cornerstone of EDM is recognition that time series observed from a dynamical system can be transformed into higher-dimensional state-spaces by time-delay embedding with Takens's theorem. The state-space models are evaluated based on in-sample fidelity to observations, conventionally with Pearson correlation between predictions and observations. == Methods == Primary EDM algorithms include Simplex projection, Sequential locally weighted global linear maps (S-Map) projection, Multivariate embedding in Simplex or S-Map, Convergent cross mapping (CCM), and Multiview Embeding, described below. Nearest neighbors are found according to: NN ( y , X , k ) = ‖ X N i E − y ‖ ≤ ‖ X N j E − y ‖ if 1 ≤ i ≤ j ≤ k {\displaystyle {\text{NN}}(y,X,k)=\|X_{N_{i}}^{E}-y\|\leq \|X_{N_{j}}^{E}-y\|{\text{ if }}1\leq i\leq j\leq k} === Simplex === Simplex projection is a nearest neighbor projection. It locates the k {\displaystyle k} nearest neighbors to the location in the state-space from which a prediction is desired. To minimize the number of free parameters k {\displaystyle k} is typically set to E + 1 {\displaystyle E+1} defining an E + 1 {\displaystyle E+1} dimensional simplex in the state-space. The prediction is computed as the average of the weighted phase-space simplex projected T p {\displaystyle Tp} points ahead. Each neighbor is weighted proportional to their distance to the projection origin vector in the state-space. Find k {\displaystyle k} nearest neighbor: N k ← NN ( y , X , k ) {\displaystyle N_{k}\gets {\text{NN}}(y,X,k)} Define the distance scale: d ← ‖ X N 1 E − y ‖ {\displaystyle d\gets \|X_{N_{1}}^{E}-y\|} Compute weights: For{ i = 1 , … , k {\displaystyle i=1,\dots ,k} } : w i ← exp ⁡ ( − ‖ X N i E − y ‖ / d ) {\displaystyle w_{i}\gets \exp(-\|X_{N_{i}}^{E}-y\|/d)} Average of state-space simplex: y ^ ← ∑ i = 1 k ( w i X N i + T p ) / ∑ i = 1 k w i {\displaystyle {\hat {y}}\gets \sum _{i=1}^{k}\left(w_{i}X_{N_{i}+T_{p}}\right)/\sum _{i=1}^{k}w_{i}} === S-Map === S-Map extends the state-space prediction in Simplex from an average of the E + 1 {\displaystyle E+1} nearest neighbors to a linear regression fit to all neighbors, but localised with an exponential decay kernel. The exponential localisation function is F ( θ ) = exp ( − θ d / D ) {\displaystyle F(\theta )={\text{exp}}(-\theta d/D)} , where d {\displaystyle d} is the neighbor distance and D {\displaystyle D} the mean distance. In this way, depending on the value of θ {\displaystyle \theta } , neighbors close to the prediction origin point have a higher weight than those further from it, such that a local linear approximation to the nonlinear system is reasonable. This localisation ability allows one to identify an optimal local scale, in-effect quantifying the degree of state dependence, and hence nonlinearity of the system. Another feature of S-Map is that for a properly fit model, the regression coefficients between variables have been shown to approximate the gradient (directional derivative) of variables along the manifold. These Jacobians represent the time-varying interaction strengths between system variables. Find k {\displaystyle k} nearest neighbor: N ← NN ( y , X , k ) {\displaystyle N\gets {\text{NN}}(y,X,k)} Sum of distances: D ← 1 k ∑ i = 1 k ‖ X N i E − y ‖ {\displaystyle D\gets {\frac {1}{k}}\sum _{i=1}^{k}\|X_{N_{i}}^{E}-y\|} Compute weights: For{ i = 1 , … , k {\displaystyle i=1,\dots ,k} } : w i ← exp ⁡ ( − θ ‖ X N i E − y ‖ / D ) {\displaystyle w_{i}\gets \exp(-\theta \|X_{N_{i}}^{E}-y\|/D)} Reweighting matrix: W ← diag ( w i ) {\displaystyle W\gets {\text{diag}}(w_{i})} Design matrix: A ← [ 1 X N 1 X N 1 − 1 … X N 1 − E + 1 1 X N 2 X N 2 − 1 … X N 2 − E + 1 ⋮ ⋮ ⋮ ⋱ ⋮ 1 X N k X N k − 1 … X N k − E + 1 ] {\displaystyle A\gets {\begin{bmatrix}1&X_{N_{1}}&X_{N_{1}-1}&\dots &X_{N_{1}-E+1}\\1&X_{N_{2}}&X_{N_{2}-1}&\dots &X_{N_{2}-E+1}\\\vdots &\vdots &\vdots &\ddots &\vdots \\1&X_{N_{k}}&X_{N_{k}-1}&\dots &X_{N_{k}-E+1}\end{bmatrix}}} Weighted design matrix: A ← W A {\displaystyle A\gets WA} Response vector at T p {\displaystyle Tp} : b ← [ X N 1 + T p X N 2 + T p ⋮ X N k + T p ] {\displaystyle b\gets {\begin{bmatrix}X_{N_{1}+T_{p}}\\X_{N_{2}+T_{p}}\\\vdots \\X_{N_{k}+T_{p}}\end{bmatrix}}} Weighted response vector: b ← W b {\displaystyle b\gets Wb} Least squares solution (SVD): c ^ ← argmin c ‖ A c − b ‖ 2 2 {\displaystyle {\hat {c}}\gets {\text{argmin}}_{c}\|Ac-b\|_{2}^{2}} Local linear model c ^ {\displaystyle {\hat {c}}} is prediction: y ^ ← c ^ 0 + ∑ i = 1 E c ^ i y i {\displaystyle {\hat {y}}\gets {\hat {c}}_{0}+\sum _{i=1}^{E}{\hat {c}}_{i}y_{i}} === Multivariate Embedding === Multivariate Embedding recognizes that time-delay embeddings are not the only valid state-space construction. In Simplex and S-Map one can generate a state-space from observational vectors, or time-delay embeddings of a single observational time series, or both. === Convergent Cross Mapping === Convergent cross mapping (CCM) leverages a corollary to the Generalized Takens Theorem that it should be possible to cross predict or cross map between variables observed from the same system. Suppose that in some dynamical system involving variables X {\displaystyle X} and Y {\displaystyle Y} , X {\displaystyle X} causes Y {\displaystyle Y} . Since X {\displaystyle X} and Y {\displaystyle Y} belong to the same dynamical system, their reconstructions (via embeddings) M x {\displaystyle M_{x}} , and M y {\displaystyle M_{y}} , also map to the same system. The causal variable X {\displaystyle X} leaves a signature on the affected variable Y {\displaystyle Y} , and consequently, the reconstructed states based on Y {\displaystyle Y} can be used to cross predict values of X {\displaystyle X} . CCM leverages this property to infer causality by predicting X {\displaystyle X} using the M y {\displaystyle M_{y}} library of points (or vice versa for the other direction of causality), while assessing improvements in cross map predictability as larger and larger random samplings of M y {\displaystyle M_{y}} are used. If the prediction skill of X {\displaystyle X} increases and saturates as the entire M y {\displaystyle M_{y}} is used, this provides evidence that X {\displaystyle X} is casually influencing Y {\displaystyle Y} . === Multiview Embedding === Multiview Embedding is a Dimensionality reduction technique where a large number of state-space time series vectors are combitorially assessed towards maximal model predictability. == Extensions == Extensions to EDM techniques include: Generalized Theorems for Nonlinear State Space Reconstruction Extended Convergent Cross Mapping Dynamic stability S-Map regularization Visual analytics with EDM Convergent Cross Sorting Expert system with EDM hybrid Sliding windows based on the extended convergent cross-mapping Empirical Mode Modeling Accounting for missing data and variable step sizes Accounting for observation noise Hierarchical Bayesian EDM via Gaussian processes Intelligent and Adaptive Control Optimal control via Empirical dynamic programming Multiview distance regularised S-map