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Meta-Labeling

Meta-labeling, also known as corrective AI, is a machine learning (ML) technique utilized in quantitative finance to enhance the performance of investment and trading strategies, developed in 2017 by Marcos López de Prado at Guggenheim Partners and Cornell University. The core idea is to separate the decision of trade direction (side) from the decision of trade sizing, addressing the inefficiencies of simultaneously learning both side and size predictions. The side decision involves forecasting market movements (long, short, neutral), while the size decision focuses on risk management and profitability. It serves as a secondary decision-making layer that evaluates the signals generated by a primary predictive model. By assessing the confidence and likely profitability of those signals, meta-labeling allows investors and algorithms to dynamically size positions and suppress false positives. == Motivation == Meta-labeling is designed to improve precision without sacrificing recall. As noted by López de Prado, attempting to model both the direction and the magnitude of a trade using a single algorithm can result in poor generalization. By separating these tasks, meta-labeling enables greater flexibility and robustness: Enhances control over capital allocation. Reduces overfitting by limiting model complexity. Allows the use of interpretability tools and tailored thresholds to manage risk. Enables dynamic trade suppression in unfavorable regimes. == Applications == Meta-labeling has been applied in a variety of financial ML contexts, including: Algorithmic trading: Filtering and sizing trades to reduce false positives. Portfolio optimization: Scaling exposure across multiple signals with differing confidence levels. Risk management: Dynamically disabling strategies in adverse market conditions. Model validation: Interpreting when and why a model may be underperforming due to regime shifts. == General architecture == Meta-labeling decouples two core components of systematic trading strategies: directional prediction and position sizing. The process involves training a primary model to generate trade signals (e.g., buy, sell, or hold) and then training a secondary model to determine whether each signal is likely to lead to a profitable trade. The second model outputs a probability that is interpreted as the confidence in the forecast, which can be used to adjust the position size or to filter out unreliable trades. Meta-labeling is typically implemented as a three-stage process: Primary model (M1): Predicts the direction or label of a financial outcome using features such as market prices, returns, or volatility indicators. A typical output is directional, e.g., Y ∈ {−1,0,1}, representing short, neutral, or long positions. Secondary model (M2): A binary classifier trained to predict whether the primary model's prediction will be profitable. The target variable is a binary meta-label F ∈ { 0 , 1 } {\displaystyle F\in \{0,1\}} . Inputs can include features used in the primary model, performance diagnostics, or market regime data. Position sizing algorithm (M3): Translates the output probability of the secondary model into a position size. Higher confidence scores result in larger allocations, while lower confidence leads to reduced or zero exposure. === Stage 1: Forecasting side === Primary model architecture Figure 1 Figure 1 presents the architecture of a primary model. It focuses on forecasting the side of the trade. Following the example, this model (M1) takes in input data – such as open-high-low-close data and determines the side of the position to take: a negative number is a short position, and positive number is a long position, the range is set between −1 and 1 (the closer it is to −1 or 1, the stronger the models conviction is). When training the model, the labels are −1 and 1, based on the direction of forward returns for some predefined investment horizon. The researcher may decide to apply a recall check (τ: "Tau") by setting a minimum threshold that the initial output needs to be to qualify of a short or long position (if the threshold is not met, no side forecast is predicted, leading to closing of any open positions), this leads to the primary model output which is one of three possible side forecasts: −1, 0, or 1. The primary model also generates evaluation data which can be used by the secondary model, to improve performance of size forecasts. Some examples of evaluation data include rolling accuracy, F1, recall, precision, and AUC scores. === Stage 2: Filtering out false positives === General meta-labeling architecture Figure 2 Next comes the phase of filtering out false positives, by applying a secondary machine learning model (M2), which is a binary classifier trained to determine if the trade will be profitable or not. The model takes as input four general groupings of data: General input data which is predictive of a false positive. For example the last 30 days rolling volatility of the underlying asset. Evaluation data. Market state and regime data, one may find that macro economic data or clustering the market into regimes may help as specific trading strategies are known to perform better in particular regimes. Example: momentum based strategies perform best in periods with low volatility and strong directional moves. Primary models initial input which is a value between −1 and 1. This highlights the strength of the primary models conviction. The output of the model is a value between −1 and 1 (if using a Tanh function) which will indicate the strength of the conviction that a short or long position is profitable, or it could simply be between 0 and 1 (using a sigmoid function) if one only wanted to know if it made money or not. This output allows filtering out trades that are likely to lead to losses. One could stop at this point or use the outputs of the secondary model as inputs to a position sizing algorithm (M3) which could further enhance strategy performance metrics by translating the output probability of the secondary model into a position size. Higher confidence scores result in larger allocations, while lower confidence leads to reduced or zero exposure. === Stage 3: Optimizing position sizes === ==== Position sizing methods (M3) ==== Various algorithms have been proposed for transforming predicted probabilities into trade sizes: All-or-nothing: Allocate 100% of capital if the probability exceeds a predefined threshold (e.g., 0.5); otherwise, do not trade. Model confidence: Use the probability score directly as the fraction of capital allocated. Linear scaling: Rescale the model's probabilities using min-max normalization based on the training data. Normal CDF (NCDF): Use a normal cumulative distribution function applied to a z-statistic derived from the predicted probability. Empirical CDF (ECDF): Rank probabilities based on their percentile in the training data to ensure relative allocation. Sigmoid Optimal Position Sizing (SOPS): Applies a smooth non-linear sigmoid transformation optimized to maximize risk-adjusted returns (Sharpe ratio). ==== Model calibration ==== Each machine learning algorithm used in meta-labeling tends to produce outputs with different characteristic distributions; for example, some are approximately normally distributed, whereas others exhibit a pronounced U-shape, concentrating probabilities near the extremes. Due to these varying distributions, simply summing the outputs of different models can inadvertently lead to uneven weighting of signals, biasing trade decisions. To address this, model calibration techniques are essential to adjust the predicted probabilities towards frequentist probabilities, ensuring that model outputs reflect true likelihoods more accurately. Two common calibration techniques are: Platt scaling (Sigmoid scaling): Suitable for correcting S-shaped calibration plots typically produced by models such as support vector machines (SVMs). Isotonic regression: Fits a non-decreasing step function to probabilities and is effective particularly with larger datasets, though it can sometimes lead to overfitting. Transforming predictions to frequentist probabilities is crucial as it provides probabilistic outputs that are directly interpretable as the actual likelihood of an event occurring. Such calibration significantly enhances the effectiveness of fixed position sizing methods, reducing maximum drawdowns and increasing risk-adjusted returns. However, calibration has less impact on position sizing methods that directly estimate parameters from the training data, such as ECDF and SOPS, suggesting that calibration is a critical step mainly for fixed methods that rely heavily on raw model outputs. =
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Bigram

A bigram or digram is a sequence of two adjacent elements from a string of tokens, which are typically letters, syllables, or words. A bigram is an n-gram for n=2. The frequency distribution of every bigram in a string is commonly used for simple statistical analysis of text in many applications, including in computational linguistics, cryptography, and speech recognition. Gappy bigrams or skipping bigrams are word pairs which allow gaps (perhaps avoiding connecting words, or allowing some simulation of dependencies, as in a dependency grammar). == Applications == Bigrams, along with other n-grams, are used in most successful language models for speech recognition. Bigram frequency attacks can be used in cryptography to solve cryptograms. See frequency analysis. Bigram frequency is one approach to statistical language identification. Some activities in logology or recreational linguistics involve bigrams. These include attempts to find English words beginning with every possible bigram, or words containing a string of repeated bigrams, such as logogogue. == Bigram frequency in the English language == The frequency of the most common letter bigrams in a large English corpus is: th 3.56% of 1.17% io 0.83% he 3.07% ed 1.17% le 0.83% in 2.43% is 1.13% ve 0.83% er 2.05% it 1.12% co 0.79% an 1.99% al 1.09% me 0.79% re 1.85% ar 1.07% de 0.76% on 1.76% st 1.05% hi 0.76% at 1.49% to 1.05% ri 0.73% en 1.45% nt 1.04% ro 0.73% nd 1.35% ng 0.95% ic 0.70% ti 1.34% se 0.93% ne 0.69% es 1.34% ha 0.93% ea 0.69% or 1.28% as 0.87% ra 0.69% te 1.20% ou 0.87% ce 0.65%
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LIVAC Synchronous Corpus

LIVAC is an uncommon language corpus dynamically maintained since 1995. Different from other existing corpora, LIVAC has adopted a rigorous and regular "Windows" approach in processing and filtering massive media texts from representative Chinese speech communities such as Beijing, Hong Kong, Macau, Taipei, Singapore, Shanghai, as well as Guangzhou, and Shenzhen. The contents are thus deliberately repetitive in most cases, represented by textual samples drawn from editorials, local and international news, cross-Taiwan Strait news, as well as news on finance, sports and entertainment. By 2023, more than 3 billion characters of news media texts have been filtered, of which 700 million characters have been processed and analyzed and have yielded an expanding Pan-Chinese dictionary of 2.5 million words from the Pan-Chinese printed media. Through rigorous analysis based on computational linguistic methodology, LIVAC has at the same time accumulated a large amount of accurate and meaningful statistical data on the Chinese language and on their diverse speech communities in the Pan-Chinese context, and the results show considerable and important long standing as well as evolving variations. The "Windows" approach is the most innovative feature of LIVAC and has enabled Pan-Chinese media texts to be quantitatively analyzed according to various attributes such as locations, time and subject domains. Thus, various types of comparative studies and applications in information technology as well as development of often related innovative applications have been possible. Moreover, LIVAC has allowed longitudinal developments to be taken into account, facilitating Key Word in Context (KWIC) search and comprehensive study of target words and their underlying concepts as well as linguistic structures over the past 25 years, based on the above mentioned variables of location, time and subject. Results from the extensive and accumulative data analysis contained in LIVAC have enabled the cultivation of textual databases of proper names, place names, organization names, new words, and bi-weekly and annual rosters of media figures. Related applications have included the establishment of verb and adjective databases, the formulation of sentiment indices, and related opinion mining, to measure and compare the popularity of global media figures in the Chinese media (LIVAC Annual Pan-Chinese Celebrity Rosters, later renamed as the Pan-Chinese Newsmaker Rosters). Notable among these are the decades long periodic reviews of the 25 years of annual pan-Chinese rosters since 2000 and compilation of new word databases (LIVAC Annual Pan-Chinese New Word Rosters). On this basis, the analysis of the emergence, diffusion and transformation of new words, and the publication of dictionaries of neologisms have been made possible. A recent focus is on the relative balance between disyllabic words and growing trisyllabic words in the Chinese language, and the comparative study of light verbs in three Chinese speech communities. as well as the link between the language use and use of language as a reflection of epochal change in China. A new LIVAC version 3.1 was launched in February 2024. == Corpus data processing == Accessing media texts, manual input, etc. Text unification including conversion from simplified to traditional Chinese characters, stored as Big5 and Unicode versions Automatic word segmentation Automatic alignment of parallel texts Manual verification, part-of-speech tagging Extraction of words and addition to regional sub-corpora Combination of regional sub-corpora to update the LIVAC corpus, and master lexical database == Labeling for data curation == Categories used include general terms and proper names, such as: general names, surnames, semi titles; geographical, organizations and commercial entities, etc.; time, prepositions, locations, etc.; stack-words; loanwords; case-word; numerals, etc. Construction of databases of proper names, place names, and specific terms, etc. Generate rosters: "new word rosters", "celebrity or media personality rosters", "place name rosters", compound words and matched words Other parts of speech tagging for sub-database, such as common nouns, numerals, numeral classifiers, different types of verbs, and of adjectives, pronouns, adverbs, prepositions, conjunctions, particles marking mood, onomatopoeia, interjection, etc. == Applications == Compilation of Pan-Chinese dictionaries or local dictionaries Information technology research, such as predictive Chinese text input for mobile phones, automatic speech to text conversion, opinion mining Comparative studies on linguistic and cultural developments in the Pan-Chinese regions, especially in a critical period of history in modern China. Language teaching and learning research, and speech-to-text conversion Customized service on linguistic research and lexical search for international corporations and government agencies The above applications are provided by the following functions: Word Segmentation Search Phrase Search Example Sentence Selection Multi-word Comparison Word Cloud
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Transfer learning

Transfer learning (TL) is a technique in machine learning (ML) in which knowledge learned from a task is re-used in order to boost performance on a related task. For example, for image classification, knowledge gained while learning to recognize cars could be applied when trying to recognize trucks. This topic is related to the psychological literature on transfer of learning, although practical ties between the two fields are limited. Reusing or transferring information from previously learned tasks to new tasks has the potential to significantly improve learning efficiency. Since transfer learning makes use of training with multiple objective functions it is related to cost-sensitive machine learning and multi-objective optimization. == History == In 1976, Bozinovski and Fulgosi published a paper addressing transfer learning in neural network training. The paper gives a mathematical and geometrical model of the topic. In 1981, a report considered the application of transfer learning to a dataset of images representing letters of computer terminals, experimentally demonstrating positive and negative transfer learning. In 1992, Lorien Pratt formulated the discriminability-based transfer (DBT) algorithm. By 1998, the field had advanced to include multi-task learning, along with more formal theoretical foundations. Influential publications on transfer learning include the book Learning to Learn in 1998, a 2009 survey and a 2019 survey. Ng said in his NIPS 2016 tutorial that TL would become the next driver of machine learning commercial success after supervised learning. In the 2020 paper, "Rethinking Pre-Training and self-training", Zoph et al. reported that pre-training can hurt accuracy, and advocate self-training instead. == Definition == The definition of transfer learning is given in terms of domains and tasks. A domain D {\displaystyle {\mathcal {D}}} consists of: a feature space X {\displaystyle {\mathcal {X}}} and a marginal probability distribution P ( X ) {\displaystyle P(X)} , where X = { x 1 , . . . , x n } ∈ X {\displaystyle X=\{x_{1},...,x_{n}\}\in {\mathcal {X}}} . Given a specific domain, D = { X , P ( X ) } {\displaystyle {\mathcal {D}}=\{{\mathcal {X}},P(X)\}} , a task consists of two components: a label space Y {\displaystyle {\mathcal {Y}}} and an objective predictive function f : X → Y {\displaystyle f:{\mathcal {X}}\rightarrow {\mathcal {Y}}} . The function f {\displaystyle f} is used to predict the corresponding label f ( x ) {\displaystyle f(x)} of a new instance x {\displaystyle x} . This task, denoted by T = { Y , f ( x ) } {\displaystyle {\mathcal {T}}=\{{\mathcal {Y}},f(x)\}} , is learned from the training data consisting of pairs { x i , y i } {\displaystyle \{x_{i},y_{i}\}} , where x i ∈ X {\displaystyle x_{i}\in {\mathcal {X}}} and y i ∈ Y {\displaystyle y_{i}\in {\mathcal {Y}}} . Given a source domain D S {\displaystyle {\mathcal {D}}_{S}} and learning task T S {\displaystyle {\mathcal {T}}_{S}} , a target domain D T {\displaystyle {\mathcal {D}}_{T}} and learning task T T {\displaystyle {\mathcal {T}}_{T}} , where D S ≠ D T {\displaystyle {\mathcal {D}}_{S}\neq {\mathcal {D}}_{T}} , or T S ≠ T T {\displaystyle {\mathcal {T}}_{S}\neq {\mathcal {T}}_{T}} , transfer learning aims to help improve the learning of the target predictive function f T ( ⋅ ) {\displaystyle f_{T}(\cdot )} in D T {\displaystyle {\mathcal {D}}_{T}} using the knowledge in D S {\displaystyle {\mathcal {D}}_{S}} and T S {\displaystyle {\mathcal {T}}_{S}} . == Applications == Algorithms for transfer learning are available in Markov logic networks and Bayesian networks. Transfer learning has been applied to cancer subtype discovery, building utilization, general game playing, text classification, digit recognition, medical imaging and spam filtering. In 2020, it was discovered that, due to their similar physical natures, transfer learning is possible between electromyographic (EMG) signals from the muscles and classifying the behaviors of electroencephalographic (EEG) brainwaves, from the gesture recognition domain to the mental state recognition domain. It was noted that this relationship worked in both directions, showing that electroencephalographic can likewise be used to classify EMG. The experiments noted that the accuracy of neural networks and convolutional neural networks were improved through transfer learning both prior to any learning (compared to standard random weight distribution) and at the end of the learning process (asymptote). That is, results are improved by exposure to another domain. Moreover, the end-user of a pre-trained model can change the structure of fully-connected layers to improve performance.
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Zeuthen strategy

The Zeuthen strategy in cognitive science is a negotiation strategy used by some artificial agents. Its purpose is to measure the willingness to risk conflict. An agent will be more willing to risk conflict if it does not have much to lose in case that the negotiation fails. In contrast, an agent is less willing to risk conflict when it has more to lose. The value of a deal is expressed in its utility. An agent has much to lose when the difference between the utility of its current proposal and the conflict deal is high. When both agents use the monotonic concession protocol, the Zeuthen strategy leads them to agree upon a deal in the negotiation set. This set consists of all conflict free deals, which are individually rational and Pareto optimal, and the conflict deal, which maximizes the Nash product. The strategy was introduced in 1930 by the Danish economist Frederik Zeuthen. == Three key questions == The Zeuthen strategy answers three open questions that arise when using the monotonic concession protocol, namely: Which deal should be proposed at first? On any given round, who should concede? In case of a concession, how much should the agent concede? The answer to the first question is that any agent should start with its most preferred deal, because that deal has the highest utility for that agent. The second answer is that the agent with the smallest value of Risk(i,t) concedes, because the agent with the lowest utility for the conflict deal profits most from avoiding conflict. To the third question, the Zeuthen strategy suggests that the conceding agent should concede just enough raise its value of Risk(i,t) just above that of the other agent. This prevents the conceding agent to have to concede again in the next round. == Risk == Risk ( i , t ) = { 1 U i ( δ ( i , t ) ) = 0 U i ( δ ( i , t ) ) − U i ( δ ( j , t ) ) U i ( δ ( i , t ) ) otherwise {\displaystyle {\text{Risk}}(i,t)={\begin{cases}1&U_{i}(\delta (i,t))=0\\{\frac {U_{i}(\delta (i,t))-U_{i}(\delta (j,t))}{U_{i}(\delta (i,t))}}&{\text{otherwise}}\end{cases}}} Risk(i,t) is a measurement of agent i's willingness to risk conflict. The risk function formalizes the notion that an agent's willingness to risk conflict is the ratio of the utility that agent would lose by accepting the other agent's proposal to the utility that agent would lose by causing a conflict. Agent i is said to be using a rational negotiation strategy if at any step t + 1 that agent i sticks to his last proposal, Risk(i,t) > Risk(j,t). == Sufficient concession == If agent i makes a sufficient concession in the next step, then, assuming that agent j is using a rational negotiation strategy, if agent j does not concede in the next step, he must do so in the step after that. The set of all sufficient concessions of agent i at step t is denoted SC(i, t). == Minimal sufficient concession == δ ′ = arg ⁡ max δ ∈ S C ( A , t ) { U A ( δ ) } {\displaystyle \delta '=\arg \max _{\delta \in {SC(A,t)}}\{U_{A}(\delta )\}} is the minimal sufficient concession of agent A in step t. Agent A begins the negotiation by proposing δ ( A , 0 ) = arg ⁡ max δ ∈ N S U A ( δ ) {\displaystyle \delta (A,0)=\arg \max _{\delta \in {NS}}U_{A}(\delta )} and will make the minimal sufficient concession in step t + 1 if and only if Risk(A,t) ≤ Risk(B,t). Theorem If both agents are using Zeuthen strategies, then they will agree on δ = arg ⁡ max δ ′ ∈ N S { π ( δ ′ ) } , {\displaystyle \delta =\arg \max _{\delta '\in {NS}}\{\pi (\delta ')\},} that is, the deal which maximizes the Nash product. Proof Let δA = δ(A,t). Let δB = δ(B,t). According to the Zeuthen strategy, agent A will concede at step t {\displaystyle t} if and only if R i s k ( A , t ) ≤ R i s k ( B , t ) . {\displaystyle Risk(A,t)\leq Risk(B,t).} That is, if and only if U A ( δ A ) − U A ( δ B ) U A ( δ A ) ≤ U B ( δ B ) − U B ( δ A ) U B ( δ B ) {\displaystyle {\frac {U_{A}(\delta _{A})-U_{A}(\delta _{B})}{U_{A}(\delta _{A})}}\leq {\frac {U_{B}(\delta _{B})-U_{B}(\delta _{A})}{U_{B}(\delta _{B})}}} U B ( δ B ) ( U A ( δ A ) − U A ( δ B ) ) ≤ U A ( δ A ) ( U B ( δ B ) − U B ( δ A ) ) {\displaystyle U_{B}(\delta _{B})(U_{A}(\delta _{A})-U_{A}(\delta _{B}))\leq U_{A}(\delta _{A})(U_{B}(\delta _{B})-U_{B}(\delta _{A}))} U A ( δ A ) U B ( δ B ) − U A ( δ B ) U B ( δ B ) ≤ U A ( δ A ) U B ( δ B ) − U A ( δ A ) U B ( δ A ) {\displaystyle U_{A}(\delta _{A})U_{B}(\delta _{B})-U_{A}(\delta _{B})U_{B}(\delta _{B})\leq U_{A}(\delta _{A})U_{B}(\delta _{B})-U_{A}(\delta _{A})U_{B}(\delta _{A})} − U A ( δ B ) U B ( δ B ) ≤ − U A ( δ A ) U B ( δ A ) {\displaystyle -U_{A}(\delta _{B})U_{B}(\delta _{B})\leq -U_{A}(\delta _{A})U_{B}(\delta _{A})} U A ( δ A ) U B ( δ A ) ≤ U A ( δ B ) U B ( δ B ) {\displaystyle U_{A}(\delta _{A})U_{B}(\delta _{A})\leq U_{A}(\delta _{B})U_{B}(\delta _{B})} π ( δ A ) ≤ π ( δ B ) {\displaystyle \pi (\delta _{A})\leq \pi (\delta _{B})} Thus, Agent A will concede if and only if δ A {\displaystyle \delta _{A}} does not yield the larger product of utilities. Therefore, the Zeuthen strategy guarantees a final agreement that maximizes the Nash Product.
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TipTop Technologies

TipTop Technologies is a real-time web and social search engine with a platform for semantic analysis of natural language. Tip-Top Search provides results capturing individual and group sentiment, opinions, and experiences there from the content of various sorts such as real-time messages from Twitter or consumer product reviews on Amazon.com. TipTop Technologies and ITC Infotech collaborated to create a search interface suitable for both enterprise and consumer applications. Tip-Top's products are part of the "emerging Web 3.0 applications which use semantic technologies to augment the underlying Web system's functionalities." Their main product is 360, an AI tool that incorporates multiple AI applications under one wing. Jonathan AlBright professor at Elon University, found videos generated by TipTop Technologies software on YouTube in his research into artificial intelligence, described it as AI-generated "fake news". Through semantic analysis of large data sets, TipTop gleaned behavioral insights from Tweets around events like Halloween, Thanksgiving, Holiday Gifting, the Super Bowl, and the Oscar Nominees for the Academy Awards coverage. Sentiment analysis, concept trend tracking, and real-time market research are other applications included in the TipTop Search product. TipTop's insight engine solves the problem of real-time data noise, and its ability to "sort the 'good tweets' from the 'bad tweets' when it comes to a product, service, or a region..." In addition, products like TipTop Shopping with customizable search widgets bring together consumer reviews, social search, and sentiment analysis enabling product comparisons across attributes like the overall value and aiding purchasing decisions through user-driven product tips and pits. TipTop Finance adds another complexity to real-time search results by incorporating corporate sentiment, company stock tickers, and social media into TipTop's existing social search platform. Additional success applying semantic technologies has been with polling, "if you compare these Gallup results with TipTop, a sentiment engine based on Twitter, the results are not way off. It does surprise you but it tells me that sentiment analysis in case of public opinion about a burning social issue or a famous personality is relatively easier." With the increasing amount of unstructured, opinion-oriented, and user-generated content available on the Web, TipTop's technology aims to make sense of all this data, and deliver it in a useful way for consumer and enterprise users alike. TipTop Technologies is a privately held company with its headquarters in the San Francisco Bay Area, and team members are located globally.
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Microsoft Teams

Microsoft Teams is a team collaboration platform developed by Microsoft as part of the Microsoft 365 suite. It offers features such as workspace chat, video conferencing, file storage, and integration with both Microsoft and third-party applications and services. Teams gradually replaced earlier Microsoft messaging and collaboration platforms, including Skype for Business, Skype, Flip, and Microsoft Classroom. The platform saw significant growth during the COVID-19 pandemic, alongside competitors such as Zoom, Slack, and Google Meet, as organizations shifted to remote work and virtual meetings. As of January 2023, Microsoft reported approximately 280 million monthly active users. == History == On August 29, 2007, Microsoft acquired Parlano, the developer of the persistent group chat tool MindAlign. Years later, on March 4, 2016, Microsoft considered acquiring Slack for $8 billion. However, the proposal was reportedly opposed by Bill Gates, who advocated for focusing on enhancing Skype for Business instead. Lu Qi, then executive vice president of Applications and Services, had led the initiative to pursue the Slack acquisition. Following Lu's departure later that year, Microsoft announced Microsoft Teams on November 2, 2016, at an event in New York City, positioning it as a direct competitor to Slack. Teams launched worldwide on March 14, 2017. The service was initially led by corporate vice president Brian MacDonald. In response to the launch, Slack published a full-page advertisement in The New York Times welcoming the competition and outlining its product philosophy. Although Slack was used by 28 companies in the Fortune 100, The Verge wrote that executives would question paying for the service if Teams provides a similar function in their company's existing Office 365 subscription. However, ZDNET noted that the platforms initially served different markets, as Teams did not support external users, making it less appealing to small businesses and freelancers, a limitation Microsoft later addressed. In response to Teams' announcement, Slack deepened in-product integration with Google services. In May 2017, Microsoft announced that Teams would replace Microsoft Classroom in Office 365 Education. A free version of Teams was released on July 12, 2018, offering most core features at no cost, albeit with limits on users and storage. In January 2019, Microsoft introduced updates targeting "Firstline Workers" to improve Teams’ performance across shared or limited-access devices. In September 2019, Microsoft announced the retirement of Skype for Business in favor of Teams, which took effect on July 31, 2021. In early 2020, Microsoft introduced a push-to-talk "Walkie Talkie" feature aimed at firstline workers using smartphones and tablets over Wi-Fi or cellular networks. The COVID-19 pandemic significantly boosted usage of Teams. On March 19, 2020, Microsoft reported 44 million daily active users. In April, the platform logged 4.1 billion meeting minutes in a single day. A public preview of Microsoft Teams for Linux was released in December 2019, but the Linux client was discontinued in 2022. In July 2020, Microsoft shut down its video game livestreaming platform Mixer, and announced that some of its technologies would be repurposed for use in Teams. On February 28, 2025, Microsoft announced that Skype would be fully retired on May 5, 2025, with users given options to export their data or transition to Microsoft Teams. In October 2025, together with other Microsoft 365 suite apps, Teams had its logo updated. == Usage == == Underlying software == Microsoft Teams, as part of the Microsoft 365 suite, utilizes SharePoint and Exchange Online. Each Team, Shared Channel, and Private Channel has its own Microsoft 365 Group and SharePoint Site used for file storage. Messages are stored in Cosmos DB and are journaled to Exchange Online mailboxes. Private messages, including messages in Private Channels, are journaled to the sender and recipients' mailboxes. Public Channel messages are journaled to their corresponding Team's group mailbox, whereas, messages from Shared Channels are journaled to their own mailboxes. Contacts and voicemail are stored in Exchange Online. Microsoft Teams client is a web-based desktop app, originally developed on top of the Electron framework which combines the Chromium rendering engine and the Node.js JavaScript platform. Version 2.0 client was rebuilt using the Evergreen version of Microsoft Edge WebView2 in place of Electron. == Features == === Chats === Teams allows users to communicate in two-way persistent chats with one or multiple participants. Participants can message using text, emojis, stickers and gifs, as well as sharing links and files. In August 2022, the chat feature was updated for "chat with yourself"; allowing for the organization of files, notes, comments, images, and videos within a private chat tab. === Teams === Teams allows communities, groups, or teams to contribute in a shared workspace where messages and digital content on a specific topic are shared. Team members can join through an invitation sent by a team administrator or owner or sharing of a specific URL. Teams for Education allows admins and teachers to set up groups for classes, professional learning communities (PLCs), staff members, and everyone. === Channels === Channels allow team members to communicate without the use of email or group SMS (texting). Users can reply to posts with text, images, GIFs, and image macros. Direct messages send private messages to designated users rather than the entire channel. Connectors can be used within a channel to submit information contacted through a third-party service. Connectors include Mailchimp, Facebook Pages, Twitter, Power BI and Bing News. === Group conversations === Ad-hoc groups can be created to share instant messaging, audio calls (VoIP), and video calls inside the client software. === Telephone replacement === A feature on one of the higher cost licencing tiers allows connectivity to the public switched telephone network (PSTN) telephone system. This allows users to use Teams as if it were a telephone, making and receiving calls over the PSTN, including the ability to host "conference calls" with multiple participants. === Meeting === Meetings can be scheduled with multiple participants able to share audio, video, chat and presented content with all participants. Multiple users can connect via a meeting link. Automated minutes are possible using the recording and transcript features. Teams has a plugin for Microsoft Outlook to schedule a Teams Meeting in Outlook for a specific date and time and invite others to attend. If a meeting is scheduled within a channel, users visiting the channel are able to see if a meeting is in progress. ==== Teams Live Events ==== Teams Live Events replaces Skype Meeting Broadcast for users to broadcast to 10,000 participants on Teams, Yammer, or Microsoft Stream. ==== Breakout Rooms ==== Breakout rooms split a meeting into small groups. This is often utilized for collaboration during trainings or any environment where having all participants speak at once could be disruptive or unfeasible. Breakout rooms can be set by the hosts to a certain length of time, after which all participants will automatically rejoin the main meeting room. ==== Front Row ==== Front Row adjusts the layout of the viewer's screen, placing the speaker or content in the center of the gallery with other meeting participant's video feeds reduced in size and located below the speaker. === Education === Microsoft Teams for Education allows teachers to distribute, provide feedback, and grade student assignments turned in via Teams using the Assignments tab through Office 365 for Education subscribers. Quizzes can also be assigned to students through an integration with Office Forms. === Protocols === Microsoft Teams is based on a number of Microsoft-specific protocols. Video conferences are realized over the protocol MNP24, known from the Skype consumer version. VoIP and video conference clients based on SIP and H.323 need special gateways to connect to Microsoft Teams servers. With the help of Interactive Connectivity Establishment (ICE), clients behind Network address translation routers and restrictive firewalls are also able to connect, if peer-to-peer is not possible. === Integrations === Microsoft Teams has integrations through Microsoft AppSource, its integration marketplace. In 2020, Microsoft partnered with KUDO, a cloud-based solution with language interpretation, to allow integrated language meeting controls. In June 2022, an update was released using AI to improve call audio through the elimination of background feedback loops and cancelling non-vocal audio. == Anti-trust controversy == In July 2023, the European Commission opened an anti-trust investigation into the possibility that Microsoft unfairly used its office suite market power to increase sales of Teams and hurt
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Physics-informed neural networks

In machine learning, physics-informed neural networks (PINNs), also referred to as theory-trained neural networks (TTNs), are a type of universal function approximator that can embed the knowledge of any physical laws that govern a given data-set in the learning process, and can be described by partial differential equations (PDEs). Low data availability for some biological and engineering problems limit the robustness of conventional machine learning models used for these applications. The prior knowledge of general physical laws acts in the training of neural networks (NNs) as a regularization agent that limits the space of admissible solutions, increasing the generalizability of the function approximation. This way, embedding this prior information into a neural network results in enhancing the information content of the available data, facilitating the learning algorithm to capture the right solution and to generalize well even with a low amount of training examples. Because they process continuous spatial and time coordinates and output continuous PDE solutions, they can be categorized as neural fields. == Function approximation == Most of the physical laws that govern the dynamics of a system can be described by partial differential equations. For example, the Navier–Stokes equations are a set of partial differential equations derived from the conservation laws (i.e., conservation of mass, momentum, and energy) that govern fluid mechanics. The solution of the Navier–Stokes equations with appropriate initial and boundary conditions allows the quantification of flow dynamics in a precisely defined geometry. However, these equations cannot be solved exactly and therefore numerical methods must be used (such as finite differences, finite elements and finite volumes). In this setting, these governing equations must be solved while accounting for prior assumptions, linearization, and adequate time and space discretization. Recently, solving the governing partial differential equations of physical phenomena using deep learning has emerged as a new field of scientific machine learning (SciML), leveraging the universal approximation theorem and high expressivity of neural networks. In general, deep neural networks could approximate any high-dimensional function given that sufficient training data are supplied. However, such networks do not consider the physical characteristics underlying the problem, and the level of approximation accuracy provided by them is still heavily dependent on careful specifications of the problem geometry as well as the initial and boundary conditions. Without this preliminary information, the solution is not unique and may lose physical correctness. To remedy this, Physics-Informed Neural Networks (PINNs) leverage governing physical equations in neural network training. Namely, PINNs are designed to be trained to satisfy the given training data as well as the imposed governing equations. In this fashion, a neural network can be guided with training datasets that do not necessarily need to be large or complete. An accurate solution of partial differential equations can potentially be found without knowing the boundary conditions. Therefore, with some knowledge about the physical characteristics of the problem and some form of training data (even sparse and incomplete), PINNs may be used for finding an optimal solution with high fidelity. PINNs can be applied to a wide range of problems in computational science, and are a pioneering technology leading to the development of new classes of numerical solvers for PDEs. PINNs can be thought of as a mesh-free alternative to traditional approaches (e.g., CFD for fluid dynamics), and new data-driven approaches for model inversion and system identification. Notably, a trained PINN network can be used to predict values on simulation grids of different resolutions without needing to be retrained. Additionally, the derivatives used in the partial differential equations can be computed using automatic differentiation (AD), which is assessed to be superior to numerical or symbolic differentiation. == Modeling and computation == A general nonlinear partial differential equation can be written as: u t + N [ u ; λ ] = 0 , x ∈ Ω , t ∈ [ 0 , T ] {\displaystyle u_{t}+{\mathcal {N}}[u;\lambda ]=0,\quad x\in \Omega ,\quad t\in [0,T]} where u ( t , x ) {\displaystyle u(t,x)} denotes the solution, N [ ⋅ ; λ ] {\displaystyle {\mathcal {N}}[\cdot ;\lambda ]} is a nonlinear operator parameterized by λ {\displaystyle \lambda } , and Ω {\displaystyle \Omega } is a subset of R D {\displaystyle \mathbb {R} ^{D}} . This general form of governing equations summarizes a wide range of problems in mathematical physics, such as conservative laws, diffusion process, advection-diffusion systems, and kinetic equations. Given noisy measurements of a generic dynamic system described by the equation above, PINNs can be designed to solve two classes of problems: data-driven solutions of partial differential equations data-driven discovery of partial differential equations === Data-driven solution of partial differential equations === The data-driven solution of PDE computes the hidden state u ( t , x ) {\displaystyle u(t,x)} of the system given boundary data and/or measurements z {\displaystyle z} , and fixed model parameters λ {\displaystyle \lambda } . We solve: u t + N [ u ] = 0 , x ∈ Ω , t ∈ [ 0 , T ] {\displaystyle u_{t}+{\mathcal {N}}[u]=0,\quad x\in \Omega ,\quad t\in [0,T]} . by defining the residual f ( t , x ) {\displaystyle f(t,x)} as: f := u t + N [ u ] {\displaystyle f:=u_{t}+{\mathcal {N}}[u]} , and approximating u ( t , x ) {\displaystyle u(t,x)} by a deep neural network. This network can be differentiated using automatic differentiation. The parameters of u ( t , x ) {\displaystyle u(t,x)} and f ( t , x ) {\displaystyle f(t,x)} can be then learned by minimizing the following loss function L tot {\displaystyle L_{\text{tot}}} : L tot = L u + L f {\displaystyle L_{\text{tot}}=L_{u}+L_{f}} where: L u = ‖ u − z ‖ Γ {\displaystyle L_{u}=\Vert u-z\Vert _{\Gamma }} is the error between the PINN u ( t , x ) {\displaystyle u(t,x)} and the set of boundary conditions and measured data on the set of points Γ {\displaystyle \Gamma } where the boundary conditions and data are defined. L f = ‖ f ‖ Γ {\displaystyle L_{f}=\Vert f\Vert _{\Gamma }} is the mean-squared error of the residual function. This second term encourages the PINN to learn the structural information expressed by the PDE during the training process. This approach has been used to yield computationally efficient physics-informed surrogate models with applications in the forecasting of physical processes, model predictive control, multi-physics and multi-scale modeling, and simulation. It has been shown to converge to the solution of the PDE. === Data-driven discovery of partial differential equations === Given noisy and incomplete measurements z {\displaystyle z} of the state of the system, the data-driven discovery of PDEs results in computing the unknown state u ( t , x ) {\displaystyle u(t,x)} and learning model parameters λ {\displaystyle \lambda } that best describe the observed data: u t + N [ u ; λ ] = 0 , x ∈ Ω , t ∈ [ 0 , T ] {\displaystyle u_{t}+{\mathcal {N}}[u;\lambda ]=0,\quad x\in \Omega ,\quad t\in [0,T]} By defining f ( t , x ) {\displaystyle f(t,x)} as: f := u t + N [ u ; λ ] = 0 {\displaystyle f:=u_{t}+{\mathcal {N}}[u;\lambda ]=0} , and approximating u ( t , x ) {\displaystyle u(t,x)} by a deep neural network, f ( t , x ) {\displaystyle f(t,x)} results in a PINN. This network can be derived using automatic differentiation. The parameters of u ( t , x ) {\displaystyle u(t,x)} and f ( t , x ) {\displaystyle f(t,x)} , together with the parameter λ {\displaystyle \lambda } of the differential operator can be then learned by minimizing the following loss function L tot {\displaystyle L_{\text{tot}}} : L tot = L u + L f {\displaystyle L_{\text{tot}}=L_{u}+L_{f}} where: L u = ‖ u − z ‖ Γ {\displaystyle L_{u}=\Vert u-z\Vert _{\Gamma }} , with u {\displaystyle u} and z {\displaystyle z} state solutions and measurements at sparse location Γ {\displaystyle \Gamma } , respectively. L f = ‖ f ‖ Γ {\displaystyle L_{f}=\Vert f\Vert _{\Gamma }} is the residual function. This second term requires the structured information represented by the partial differential equations to be satisfied in the training process. This strategy allows for discovering dynamic models described by nonlinear PDEs assembling computationally efficient and fully differentiable surrogate models that may find application in predictive forecasting, control, and data assimilation. == Extensions and applications == === For piece-wise function approximation === PINNs are unable to approximate PDEs that have strong non-linearity or sharp gradients (such as those that commonly occur in practical fluid flow problems). Piecewise approximation has been an old practic
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CineAsset

CineAsset was a complete mastering software suite by Doremi Labs that could create and playback encrypted (Pro version) and unencrypted DCI compliant packages from virtually any source. CineAsset included a separate "Editor" application for generating Digital Cinema Packages (DCPs). CineAsset Pro added the ability to generate encrypted DCPs and Key Delivery Messages (KDMs) for any encrypted content in the database. It has since been discontinued, along with CineAsset Player. == Features == == Supported formats == === Input === Source: ==== Containers ==== AVI MOV MXF MPG TS WMV M2TS MTS MP4 MKV ==== Video Codecs ==== JPEG2000 ProRes 422 DNxHD® YUV Uncompressed 8-10 bits DIVX® XVID® MPEG4 AVC / H-264 VC-1 MPEG2 ==== Image Sequences ==== BMP TIFF TGA DPX JPG J2C ==== Audio Files ==== WAV MP3 WMA MP2 === Output === Source: ==== JPEG2000 ==== 2D and 3D at up to 4K resolution Bit Rate: 50–250 Mbit/s (500 Mbit/s for frame rates above 30 fps) Speed: Faster than real-time processing when using optional render nodes ==== MPEG2 ==== I-Only or Long GOP 1080p up to 80 Mbit/s ==== H264 ==== 1080p up to 50 Mbit/s ==== VC1 ==== DCP wrapping only (no transcode)
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Superquadrics

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

Connected-component labeling (CCL), connected-component analysis (CCA), blob extraction, region labeling, blob discovery, or region extraction is an algorithmic application of graph theory, where subsets of connected components are uniquely labeled based on a given heuristic. Connected-component labeling is not to be confused with segmentation. Connected-component labeling is used in computer vision to detect connected regions in binary digital images, although color images and data with higher dimensionality can also be processed. When integrated into an image recognition system or human-computer interaction interface, connected component labeling can operate on a variety of information. Blob extraction is generally performed on the resulting binary image from a thresholding step, but it can be applicable to gray-scale and color images as well. Blobs may be counted, filtered, and tracked. Blob extraction is related to but distinct from blob detection. == Overview == A graph, containing vertices and connecting edges, is constructed from relevant input data. The vertices contain information required by the comparison heuristic, while the edges indicate connected 'neighbors'. An algorithm traverses the graph, labeling the vertices based on the connectivity and relative values of their neighbors. Connectivity is determined by the medium; image graphs, for example, can be 4-connected neighborhood or 8-connected neighborhood. Following the labeling stage, the graph may be partitioned into subsets, after which the original information can be recovered and processed . == Definition == The usage of the term connected-component labeling (CCL) and its definition is quite consistent in the academic literature, whereas connected-component analysis (CCA) varies both in terminology and in its definition of the problem. Rosenfeld et al. define connected components labeling as the “[c]reation of a labeled image in which the positions associated with the same connected component of the binary input image have a unique label.” Shapiro et al. define CCL as an operator whose “input is a binary image and [...] output is a symbolic image in which the label assigned to each pixel is an integer uniquely identifying the connected component to which that pixel belongs.” There is no consensus on the definition of CCA in the academic literature. It is often used interchangeably with CCL. A more extensive definition is given by Shapiro et al.: “Connected component analysis consists of connected component labeling of the black pixels followed by property measurement of the component regions and decision making.” The definition for connected-component analysis presented here is more general, taking the thoughts expressed in into account. == Algorithms == The algorithms discussed can be generalised to arbitrary dimensions, albeit with increased time and space complexity. === One component at a time === This is a fast and very simple method to implement and understand. It is based on graph traversal methods in graph theory. In short, once the first pixel of a connected component is found, all the connected pixels of that connected component are labelled before going onto the next pixel in the image. This algorithm is part of Vincent and Soille's watershed segmentation algorithm, other implementations also exist. In order to do that a linked list is formed that will keep the indexes of the pixels that are connected to each other, steps (2) and (3) below. The method of defining the linked list specifies the use of a depth or a breadth first search. For this particular application, there is no difference which strategy to use. The simplest kind of a last in first out queue implemented as a singly linked list will result in a depth first search strategy. It is assumed that the input image is a binary image, with pixels being either background or foreground and that the connected components in the foreground pixels are desired. The algorithm steps can be written as: Start from the first pixel in the image. Set current label to 1. Go to (2). If this pixel is a foreground pixel and it is not already labelled, give it the current label and add it as the first element in a queue, then go to (3). If it is a background pixel or it was already labelled, then repeat (2) for the next pixel in the image. Pop out an element from the queue, and look at its neighbours (based on any type of connectivity). If a neighbour is a foreground pixel and is not already labelled, give it the current label and add it to the queue. Repeat (3) until there are no more elements in the queue. Go to (2) for the next pixel in the image and increment current label by 1. Note that the pixels are labelled before being put into the queue. The queue will only keep a pixel to check its neighbours and add them to the queue if necessary. This algorithm only needs to check the neighbours of each foreground pixel once and doesn't check the neighbours of background pixels. The pseudocode is: algorithm OneComponentAtATime(data) input : imageData[xDim][yDim] initialization : label = 0, labelArray[xDim][yDim] = 0, statusArray[xDim][yDim] = false, queue1, queue2; for i = 0 to xDim do for j = 0 to yDim do if imageData[i][j] has not been processed do if imageData[i][j] is a foreground pixel do check its four neighbors(north, south, east, west) : if neighbor is not processed do if neighbor is a foreground pixel do add it to queue1 else update its status to processed end if labelArray[i][j] = label (give label) statusArray[i][j] = true (update status) while queue1 is not empty do For each pixel in the queue do : check its four neighbors if neighbor is not processed do if neighbor is a foreground pixel do add it to queue2 else update its status to processed end if give it the current label update its status to processed remove the current element from queue1 copy queue2 into queue1 end While increase the label end if else update its status to processed end if end if end if end for end for === Two-pass === Relatively simple to implement and understand, the two-pass algorithm, (also known as the Hoshen–Kopelman algorithm) iterates through 2-dimensional binary data. The algorithm makes two passes over the image: the first pass to assign temporary labels and record equivalences, and the second pass to replace each temporary label by the smallest label of its equivalence class. The input data can be modified in situ (which carries the risk of data corruption), or labeling information can be maintained in an additional data structure. Connectivity checks are carried out by checking neighbor pixels' labels (neighbor elements whose labels are not assigned yet are ignored), or say, the north-east, the north, the north-west and the west of the current pixel (assuming 8-connectivity). 4-connectivity uses only north and west neighbors of the current pixel. The following conditions are checked to determine the value of the label to be assigned to the current pixel (4-connectivity is assumed) Conditions to check: Does the pixel to the left (west) have the same value as the current pixel? Yes – We are in the same region. Assign the same label to the current pixel No – Check next condition Do both pixels to the north and west of the current pixel have the same value as the current pixel but not the same label? Yes – We know that the north and west pixels belong to the same region and must be merged. Assign the current pixel the minimum of the north and west labels, and record their equivalence relationship No – Check next condition Does the pixel to the left (west) have a different value and the one to the north the same value as the current pixel? Yes – Assign the label of the north pixel to the current pixel No – Check next condition Do the pixel's north and west neighbors have different pixel values than current pixel? Yes – Create a new label id and assign it to the current pixel The algorithm continues this way, and creates new region labels whenever necessary. The key to a fast algorithm, however, is how this merging is done. This algorithm uses the union-find data structure which provides excellent performance for keeping track of equivalence relationships. Union-find essentially stores labels which correspond to the same blob in a disjoint-set data structure, making it easy to remember the equivalence of two labels by the use of an interface method E.g.: findSet(l). findSet(l) returns the minimum label value that is equivalent to the function argument 'l'. Once the initial labeling and equivalence recording is completed, the second pass merely replaces each pixel label with its equivalent disjoint-set representative element. A faster-scanning algorithm for connected-region extraction is presented below. On the first pass: Iterate through each element of the data by column, then by row (Raster Scanning) If the element is not the background Get the neighboring elements of the current element If there are no neighbors, uniquely
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Topological deep learning

Topological deep learning (TDL) is a research field that extends deep learning to handle complex, non-Euclidean data structures. Traditional deep learning models, such as convolutional neural networks (CNNs) and recurrent neural networks (RNNs), excel in processing data on regular grids and sequences. However, scientific and real-world data often exhibit more intricate data domains encountered in scientific computations, including point clouds, meshes, time series, scalar fields graphs, or general topological spaces like simplicial complexes and CW complexes. TDL addresses this by incorporating topological concepts to process data with higher-order relationships, such as interactions among multiple entities and complex hierarchies. This approach leverages structures like simplicial complexes and hypergraphs to capture global dependencies and qualitative spatial properties, offering a more nuanced representation of data. TDL also encompasses methods from computational and algebraic topology that permit studying properties of neural networks and their training process, such as their predictive performance or generalization properties. The mathematical foundations of TDL are algebraic topology, differential topology, and geometric topology. Therefore, TDL can be generalized for data on differentiable manifolds, knots, links, tangles, curves, etc. == History and motivation == Traditional techniques from deep learning often operate under the assumption that a dataset is residing in a highly-structured space (like images, where convolutional neural networks exhibit outstanding performance over alternative methods) or a Euclidean space. The prevalence of new types of data, in particular graphs, meshes, and molecules, resulted in the development of new techniques, culminating in the field of geometric deep learning, which originally proposed a signal-processing perspective for treating such data types. While originally confined to graphs, where connectivity is defined based on nodes and edges, follow-up work extended concepts to a larger variety of data types, including simplicial complexes and CW complexes, with recent work proposing a unified perspective of message-passing on general combinatorial complexes. An independent perspective on different types of data originated from topological data analysis, which proposed a new framework for describing structural information of data, i.e., their "shape," that is inherently aware of multiple scales in data, ranging from local information to global information. While at first restricted to smaller datasets, subsequent work developed new descriptors that efficiently summarized topological information of datasets to make them available for traditional machine-learning techniques, such as support vector machines or random forests. Such descriptors ranged from new techniques for feature engineering over new ways of providing suitable coordinates for topological descriptors, or the creation of more efficient dissimilarity measures. Contemporary research in this field is largely concerned with either integrating information about the underlying data topology into existing deep-learning models or obtaining novel ways of training on topological domains. == Learning on topological spaces == One of the core concepts in topological deep learning is considering the domain upon which this data is defined and supported. In case of Euclidean data, such as images, this domain is a grid, upon which the pixel value of the image is supported. In a more general setting this domain might be a topological domain. Studying and developing deep learning models that are supported ln topological domains constitute the essence of topological deep learning. Next, we introduce the most common topological domains that are encountered in a deep learning setting. These domains include, but not limited to, graphs, simplicial complexes, cell complexes, combinatorial complexes and hypergraphs. Given a finite set S of abstract entities, a neighborhood function N {\displaystyle {\mathcal {N}}} on S is an assignment that attach to every point x {\displaystyle x} in S a subset of S or a relation. Such a function can be induced by equipping S with an auxiliary structure. Edges provide one way of defining relations among the entities of S. More specifically, edges in a graph allow one to define the notion of neighborhood using, for instance, the one hop neighborhood notion. Edges however, limited in their modeling capacity as they can only be used to model binary relations among entities of S since every edge is connected typically to two entities. In many applications, it is desirable to permit relations that incorporate more than two entities. The idea of using relations that involve more than two entities is central to topological domains. Such higher-order relations allow for a broader range of neighborhood functions to be defined on S to capture multi-way interactions among entities of S. Next we review the main properties, advantages, and disadvantages of some commonly studied topological domains in the context of deep learning, including (abstract) simplicial complexes, regular cell complexes, hypergraphs, and combinatorial complexes. ==== Comparisons among topological domains ==== Each of the enumerated topological domains has its own characteristics, advantages, and limitations: Simplicial complexes Simplest form of higher-order domains. Extensions of graph-based models. Admit hierarchical structures, making them suitable for various applications. Hodge theory can be naturally defined on simplicial complexes. Require relations to be subsets of larger relations, imposing constraints on the structure. Cell Complexes Generalize simplicial complexes. Provide more flexibility in defining higher-order relations. Each cell in a cell complex is homeomorphic to an open ball, attached together via attaching maps. Boundary cells of each cell in a cell complex are also cells in the complex. Represented combinatorially via incidence matrices. Hypergraphs Allow arbitrary set-type relations among entities. Relations are not imposed by other relations, providing more flexibility. Do not explicitly encode the dimension of cells or relations. Useful when relations in the data do not adhere to constraints imposed by other models like simplicial and cell complexes. Combinatorial Complexes : Generalize and bridge the gaps between simplicial complexes, cell complexes, and hypergraphs. Allow for hierarchical structures and set-type relations. Combine features of other complexes while providing more flexibility in modeling relations. Can be represented combinatorially, similar to cell complexes. ==== Hierarchical structure and set-type relations ==== The properties of simplicial complexes, cell complexes, and hypergraphs give rise to two main features of relations on higher-order domains, namely hierarchies of relations and set-type relations. ===== Rank function ===== A rank function on a higher-order domain X is an order-preserving function rk: X → Z, where rk(x) attaches a non-negative integer value to each relation x in X, preserving set inclusion in X. Cell and simplicial complexes are common examples of higher-order domains equipped with rank functions and therefore with hierarchies of relations. ===== Set-type relations ===== Relations in a higher-order domain are called set-type relations if the existence of a relation is not implied by another relation in the domain. Hypergraphs constitute examples of higher-order domains equipped with set-type relations. Given the modeling limitations of simplicial complexes, cell complexes, and hypergraphs, we develop the combinatorial complex, a higher-order domain that features both hierarchies of relations and set-type relations. The learning tasks in TDL can be broadly classified into three categories: Cell classification: Predict targets for each cell in a complex. Examples include triangular mesh segmentation, where the task is to predict the class of each face or edge in a given mesh. Complex classification: Predict targets for an entire complex. For example, predict the class of each input mesh. Cell prediction: Predict properties of cell-cell interactions in a complex, and in some cases, predict whether a cell exists in the complex. An example is the prediction of linkages among entities in hyperedges of a hypergraph. In practice, to perform the aforementioned tasks, deep learning models designed for specific topological spaces must be constructed and implemented. These models, known as topological neural networks, are tailored to operate effectively within these spaces. === Topological neural networks === Central to TDL are topological neural networks (TNNs), specialized architectures designed to operate on data structured in topological domains. Unlike traditional neural networks tailored for grid-like structures, TNNs are adept at handling more intricate data representations, such as graphs
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Brownout (software engineering)

Brownout in software engineering is a technique that involves disabling certain features of an application. == Description == Brownout is used to increase the robustness of an application to computing capacity shortage. If too many users are simultaneously accessing an application hosted online, the underlying computing infrastructure may become overloaded, rendering the application unresponsive. Users are likely to abandon the application and switch to competing alternatives, hence incurring long-term revenue loss. To better deal with such a situation, the application can be given brownout capabilities: The application will disable certain features – e.g., an online shop will no longer display recommendations of related products – to avoid overload. Although reducing features generally has a negative impact on the short-term revenue of the application owner, long-term revenue loss can be avoided. The technique is inspired by brownouts in power grids, which consists in reducing the power grid's voltage in case electricity demand exceeds production. Some consumers, such as incandescent light bulbs, will dim – hence originating the term – and draw less power, thus helping match demand with production. Similarly, a brownout application helps match its computing capacity requirements to what is available on the target infrastructure. Brownout complements elasticity. The former can help the application withstand short-term capacity shortage, but does so without changing the capacity available to the application. In contrast, elasticity consists of adding (or removing) capacity to the application, preferably in advance, so as to avoid capacity shortage altogether. The two techniques can be combined; e.g., brownout is triggered when the number of users increases unexpectedly until elasticity can be triggered, the latter usually requiring minutes to show an effect. Brownout is relatively non-intrusive for the developer, for example, it can be implemented as an advice in aspect-oriented programming. However, surrounding components, such as load-balancers, need to be made brownout-aware to distinguish between cases where an application is running normally and cases where the application maintains a low response time by triggering brownout. == Usage in phased deprecation == A related use of the brownout concept in software engineering is the deliberate introduction of temporary outages to a system, API or feature that is being phased out. This is sometimes also called a "scream test" when it is used to discover unknown dependents of a system or API. The intention is to allow detection of downstream consumers of an API or service who may otherwise have missed deprecation announcements or to uncover hidden side-effects of the deprecation that may have been overlooked. The intention is that developers of dependent systems will notice their own system failures caused by the upstream brownout. Such brownouts are typically pre-announced scheduled outages or probabilistic in nature (such as artificially failing a percentage of requests). As a brownout is only a temporary or partial outage, it provides downstream consumers of an API or service time to remove any discovered dependencies on the deprecated API before it is fully retired. For consumers that have already prepared for the deprecation, a brownout provides valuable testing that the final removal of the service won't cause any unexpected problems.
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FloodAlerts

FloodAlerts is a software application, developed by software specialists Shoothill, which takes real-time flooding information, and displays the data on an interactive Bing map, updating and warning its users when they, their premises or the routes they need to travel could be at risk of flooding. == History == FloodAlerts was launched in 2012, originally as the world's first Facebook flood warning app. == Operation == FloodAlerts is made available free of charge to individuals. Users are able to set up their own monitored locations and receive alerts via the application or their Facebook wall if the locations they are monitoring are at imminent risk of flooding. Hosted in the Cloud, using the Microsoft Windows Azure platform, the FloodAlerts application processes the data received from the Environment Agency, automatically creates the required map tiles, pins and alerts and displays them on an interactive Bing map, updating the content every 15 minutes. Users are able to see the latest information on the map without having to refresh their browser. FloodAlerts can also be provided as a customised risk management solution to businesses that require infrastructure or asset safety monitoring in areas where water levels are rising or receding. == Awards and recognition == FloodAlerts has received The Guardian and Virgin Media Business's 2012 Innovation Nation Awards and was shortlisted as a finalist for a further two national awards: the UK IT Industry Awards for Innovation and Entrepreneurship and The Institution of Engineering and Technology Innovation Awards for Information Technology. == In the press == The FloodAlerts application was reviewed on the BBC website. It was also reviewed on BBC Click.
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List of chatbots

A chatbot is a software application or web interface that is designed to mimic human conversation through text or voice interactions. Modern chatbots are typically online and use generative artificial intelligence systems that are capable of maintaining a conversation with a user in natural language and simulating the way a human would behave as a conversational partner. Such chatbots often use large language models (LLMs) and natural language processing, but simpler chatbots have existed for decades. == LLM chatbots == == General chatbots == == Historical chatbots ==
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