An evolutionary attractor is a point in an evolutionary space where a selection process will always drive trait values towards that point from the region around it. Because of the importance of evolution through natural selection, often such an evolutionary space will be defined by genetic or phenotypic traits, or possibly both. In this case the selection process will be a form of natural selection. The existence of an evolutionary attractor in a biological evolutionary space does not always imply that it can be reached from all points in that evolutionary space, nor does it identify what will happen when the evolutionary attractor is reached. While an evolutionary attractor may represent a point in evolutionary space that is resistant to further selection, such as an evolutionarily stable strategy, other possibilities are available. Because identification of an evolutionary attractor on its own does not describe everything about the evolutionary space in which it lies, this has led to interest in the evolutionary dynamics surrounding evolutionary attractors and in evolutionary spaces in general. (Theoretical biologists and mathematicians working in the area may prefer the terms adaptive dynamics or evolutionary invasion analysis to evolutionary dynamics.) These fields use differential equations which allows a more complete understanding of the dynamics in evolutionary spaces including the existence or otherwise of evolutionary attractors. Advances in the study of molecular evolution have also led to the identification of evolutionary attractors at a molecular level. Because biological evolutionary processes have been studied using evolutionary game theory, a technique inspired by game theory originally derived to address economic problems, not only can evolutionary attractors be found in biology but economists studying evolutionary economic models have also identified evolutionary attractors. Evolution in biology has also inspired evolutionary computation in computer science. Many algorithms in this field use a form of selection inspired by natural selection to generate results through evolutionary algorithms. This is therefore another area in which evolutionary attractors have been identified. == Evolutionary attractors in biology == It is not probably not surprising that biology is the field where most examples of evolutionary attractors have been identified, given the importance of evolution through natural selection. === Evolutionary attractors in adaptive landscapes === An evolutionary attractor is a point in genetic and/or phenotypic trait space, that evolution will always drive trait values towards via a selection process. The concept of an evolutionary attractor arose in population genetics following the origin of the adaptive landscape originally proposed by Sewall Wright in 1932. The height of a point in an adaptive landscape is a measure of evolutionary fitness. If a point in an adaptive landscape is a peak, then selection will always drive traits towards it and it will be an evolutionary attractor. While population genetics deals with discrete genetic traits, quantitative genetics extended such concepts to deal with continuous genetic traits, where the concept of evolutionary attractor is also valid. === Evolutionary attractors in evolutionary game models === Evolutionary game theory introduced into evolutionary biology concepts originally used in economics, with the advantage that evolution could be studied in relation to strategic choices made in animal conflicts. This is of particular interest because of the concept of the evolutionarily stable strategy or ESS, a strategy that once established is resistant to invasion by other strategies. ESSs will not always be evolutionary attractors, but if they are they will persist over evolutionary time. === Dynamics around evolutionary attractors in biology === Evolutionary attractors in biology do not exist in isolation. By definition they must exist in an evolutionary trait space where selection drives all traits towards them from a region immediately around them. That is, they must be convergence stable. Eshel (1983) modified the definition of an ESS by considering individually advantageous reduction from a majority deviation: he created the term continuous stability. A continuously stable ESS can be shown to be convergence stable, therefore it will act as an evolutionary attractor. But the nature of evolutionary trait spaces in biology means that it is not possible to guarantee that the region of convergence to the evolutionary attractor covers the whole of the trait space, nor that there is only one evolutionary attractor in a particular trait space. These issues have led to the emergence of the related fields of evolutionary dynamics, adaptive dynamics and evolutionary invasion analysis, all of which use differential equations to understand the dynamics in evolutionary trait spaces. Hence, if one or more evolutionary attractor exists in an evolutionary trait space, they provide techniques to understand the dynamics in that trait space around the evolutionary attractor. === Evolutionary attractors in an ecological context === Evolution in biology does not take place in single species in isolation. Ecological interaction of species leads to coevolution. Important examples of this are host-parasite or host-pathogen interaction, which can make both the dynamics around evolutionary attractors more complex, and the occurrence and number of evolutionary attractors more diverse. Evolutionary attractors have been identified in the analysis of evolutionary epidemiology of plant pathogens. In the above study working on plant populations the authors were able to identify evolutionary attractors using methods from adaptive dynamics. A model applied to the analysis of a maize (Zea mays L.) virus identified convergence stable equilibria through simulation modelling. A related model identified evolutionary attractors in the interaction of plants with fungal pathogens. === Evolutionary attractors in molecular genetics === As mentioned above much of the consideration of evolutionary attractors in biology has been through investigation of selection at a genetic or phenotypic level or both, in a single species or in coevolving species. Advances in the study of molecular genetics now allow the study of evolutionary attractors to be taken to a molecular genetic level. Wilson et. al (2019) studied the evolution of gene regulatory networks and identified the emergence of evolutionary attractors. == Evolutionary attractors in economics == Evolutionary game theory as applied in biology was inspired by game theory originally devised for applications in economics. Game theory remains an active field of research outside of biology, and thus it is not surprising that researchers in evolutionary economics use evolutionary game theory. Evolutionary attractors have been demonstrated by economists studying the evolutionary dynamics of market entry with market dynamics based on the replicator dynamics of biological evolutionary games. == Evolutionary attractors in computing == Evolutionary computation is a branch of computer science inspired by biological evolution. Many algorithms in evolutionary computation use a form of selection. Thus evolutionary attractors have been identified in computer science as well as in biology and economics. Evolutionary algorithms have generated evolutionary attractors, probably because of the similarity between adaptive hill-climbing in evolutionary heuristics and the adaptive landscape originated to explain evolution through natural selection.
News analytics
In trading strategy, news analysis refers to the measurement of the various qualitative and quantitative attributes of textual (unstructured data) news stories. Some of these attributes are: sentiment, relevance, and novelty. Expressing news stories as numbers and metadata permits the manipulation of everyday information in a mathematical and statistical way. This data is often used in financial markets as part of a trading strategy or by businesses to judge market sentiment and make better business decisions. News analytics are usually derived through automated text analysis and applied to digital texts using elements from natural language processing and machine learning such as latent semantic analysis, support vector machines, "bag of words" among other techniques. == Applications and strategies == The application of sophisticated linguistic analysis to news and social media has grown from an area of research to mature product solutions since 2007. News analytics and news sentiment calculations are now routinely used by both buy-side and sell-side in alpha generation, trading execution, risk management, and market surveillance and compliance. There is however a good deal of variation in the quality, effectiveness and completeness of currently available solutions. A large number of companies use news analysis to help them make better business decisions. Academic researchers have become interested in news analysis especially with regards to predicting stock price movements, volatility and traded volume. Provided a set of values such as sentiment and relevance as well as the frequency of news arrivals, it is possible to construct news sentiment scores for multiple asset classes such as equities, Forex, fixed income, and commodities. Sentiment scores can be constructed at various horizons to meet the different needs and objectives of high and low frequency trading strategies, whilst characteristics such as direction and volatility of asset returns as well as the traded volume may be addressed more directly via the construction of tailor-made sentiment scores. Scores are generally constructed as a range of values. For instance, values may range between 0 and 100, where values above and below 50 convey positive and negative sentiment, respectively. === Absolute return strategies === The objective of absolute return strategies is absolute (positive) returns regardless of the direction of the financial market. To meet this objective, such strategies typically involve opportunistic long and short positions in selected instruments with zero or limited market exposure. In statistical terms, absolute return strategies should have very low correlation with the market return. Typically, hedge funds tend to employ absolute return strategies. Below, a few examples show how news analysis can be applied in the absolute return strategy space with the purpose to identify alpha opportunities applying a market neutral strategy or based on volatility trading. Example 1 Scenario: The gap between the news sentiment scores for direction, S {\displaystyle S} , of Company X {\displaystyle X} and Market Y {\displaystyle Y} has moved beyond + 20 {\displaystyle +20} . That is, S X − S Y {\displaystyle S_{X}-S_{Y}} ≥ 20 {\displaystyle 20} . Action: Buy the stock on Company X {\displaystyle X} and short the future on Market Y {\displaystyle Y} . Exit Strategy: When the gap in the news sentiment scores for direction of Company X {\displaystyle X} and Market Y {\displaystyle Y} has disappeared, S X − S Y {\displaystyle S_{X}-S_{Y}} = 0 {\displaystyle 0} , sell the stock on Company X {\displaystyle X} and go long the future on Market Y {\displaystyle Y} to close the positions. Example 2 Scenario: The news sentiment score for volatility of Company X {\displaystyle X} goes above 70 {\displaystyle 70} out of 100 {\displaystyle 100} indicating an expected volatility above the option implied volatility. Action: Buy a short-dated straddle (the purchase of both a put and a call) on the stock of Company X {\displaystyle X} . Exit Strategy: Keep the straddle on Company X {\displaystyle X} until expiry or until a certain profit target has been reached. === Relative return strategies === The objective of relative return strategies is to either replicate (passive management) or outperform (active management) a theoretical passive reference portfolio or benchmark. To meet these objectives such strategies typically involve long positions in selected instruments. In statistical terms, relative return strategies often have high correlation with the market return. Typically, mutual funds tend to employ relative return strategies. Below, a few examples show how news analysis can be applied in the relative return strategy space with the purpose to outperform the market applying a stock picking strategy and by making tactical tilts to ones asset allocation model. Example 1 Scenario: The news sentiment score for direction of Company X {\displaystyle X} goes above 70 {\displaystyle 70} out of 100 {\displaystyle 100} . Action: Buy the stock on Company X {\displaystyle X} . Exit Strategy: When the news sentiment score for direction of Company X {\displaystyle X} falls below 60 {\displaystyle 60} , sell the stock on Company X {\displaystyle X} to close the position. Example 2 Scenario: The news sentiment score for direction of Sector Z {\displaystyle Z} goes above 70 {\displaystyle 70} out of 100 {\displaystyle 100} . Action: Include Sector Z {\displaystyle Z} as a tactical bet in the asset allocation model. Exit Strategy: When the news sentiment score for direction of Sector Z {\displaystyle Z} falls below 60 {\displaystyle 60} , remove the tactical bet for Sector Z {\displaystyle Z} from the asset allocation model. === Financial risk management === The objective of financial risk management is to create economic value in a firm or to maintain a certain risk profile of an investment portfolio by using financial instruments to manage risk exposures, particularly credit risk and market risk. Other types include Foreign exchange, Shape, Volatility, Sector, Liquidity, Inflation risks, etc. Below, a few examples show how news analysis can be applied in the financial risk management space with the purpose to either arrive at better risk estimates in terms of Value at Risk (VaR) or to manage the risk of a portfolio to meet ones portfolio mandate. Example 1 Scenario: The bank operates a VaR model to manage the overall market risk of its portfolio. Action: Estimate the portfolio covariance matrix taking into account the development of the news sentiment score for volume. Implement the relevant hedges to bring the VaR of the bank in line with the desired levels. Example 2 Scenario: A portfolio manager operates his portfolio towards a certain desired risk profile. Action: Estimate the portfolio covariance matrix taking into account the development of the news sentiment score for volume. Scale the portfolio exposure according to the targeted risk profile. === Computer algorithms using news analytics === Within 0.33 seconds, computer algorithms using news analytics can notify subscribers which company the news is about, if the news article sentiment is positive or negative, if the news is ranked as high or low relative importance … relative relevance. the stock price reaction and the increase in trade volume is concentrated in the first 5 seconds after an news article is released. === Algorithmic order execution === The objective of algorithmic order execution, which is part of the concept of algorithmic trading, is to reduce trading costs by optimizing on the timing of a given order. It is widely used by hedge funds, pension funds, mutual funds, and other institutional traders to divide up large trades into several smaller trades to manage market impact, opportunity cost, and risk more effectively. The example below shows how news analysis can be applied in the algorithmic order execution space with the purpose to arrive at more efficient algorithmic trading systems. Example 1 Scenario: A large order needs to be placed in the market for the stock on Company X {\displaystyle X} . Action: Scale the daily volume distribution for Company X {\displaystyle X} applied in the algorithmic trading system, thus taking into account the news sentiment score for volume. This is followed by the creation of the desired trading distribution forcing greater market participation during the periods of the day when volume is expected to be heaviest. == Effects == Being able to express news stories as numbers permits the manipulation of everyday information in a statistical way that allows computers not only to make decisions once made only by humans, but to do so more efficiently. Since market participants are always looking for an edge, the speed of computer connections and the delivery of news analysis, measured in milliseconds, have become essential.
Yu-Gi-Oh! VRAINS
Yu-Gi-Oh! VRAINS (遊☆戯☆王VRAINS, Yū Gi Ō Vureinzu) is a Japanese anime series created and animated by Nihon Ad Systems (NAS) and Gallop. It is the fifth anime spin-off in the Yu-Gi-Oh! franchise. The series aired in Japan on TV Tokyo from May 10, 2017 to September 25, 2019. It was simulcast outside of Asia by Crunchyroll courtesy of Konami Cross Media NY. It premiered in the United States on November 3, 2020 on Pluto TV. The term 'VRAINS' derives from 'Virtual Reality' (VR), 'Artificial Intelligence' (AI), 'Network System' (NS). The series revolves around the exploits of the protagonist Yusaku within the virtual world named VRAINS. In addition to featuring previous summoning mechanics, VRAINS introduces the new "Link Summon" mechanic. The series was succeeded by Yu-Gi-Oh! Sevens, which premiered in Japan on April 4, 2020. == Plot == In a place known as Den City, thousands of duelists take part in a virtual reality space known as LINK VRAINS, created by SOL Technologies, where users can create unique avatars and participate in games of Duel Monsters with each other. As a mysterious hacker organization known as the Knights of Hanoi, led by Varis, threatens this world, a high-school student and hacking genius named Yusaku Fujiki battles against them under the guise of Playmaker. Both the Knights and SOL Technologies are also after a peculiar self-aware artificial intelligence program, who holds the key to a secret area inside the network named the Cyberse World, which the Knights of Hanoi seek to destroy. As the series begins, Yusaku sees the chance to capture this AI, which he names Ai, who sets off a digital maelstrom in LINK VRAINS known as the Data Storm. As the appearance of this storm gives birth to Speed Duels, in which duellists surf the wind as they duel, Yusaku battles against Hanoi in order to uncover the truth concerning an incident that happened to him 10 years ago. With the help of two Charisma Duellists, Go Onizuka (Japanese) and Skye Zaizen, who uses the alias Blue Angel (season 1), and Blue Maiden (season 2 onwards) online, Playmaker is able to defeat Varis, saving the entire network and part ways with Ai who decides to return to his own world, the Cyberse World. Three months after Hanoi's fall, Ai discovers the Cyberse World destroyed and his friends nowhere to be found, prompting him to return to Yusaku. Meanwhile, Yusaku once again fights as Playmaker after the consciousness of the younger brother of his friend, Cal Kolter, is stolen by a mysterious enemy named Bohman. In pursuit of Bohman, Yusaku and Ai are joined by Theodore Hamilton, a victim of the Lost Incident like Yusaku who uses the alias of Soulburner online and Ai's Fire Ignis friend based on Theodore, Flame. Aqua, the Water Ignis, follows soon after by becoming Skye's partner. At the same time, Varis revives Knights of Hanoi to fight against the new enemies. It's revealed that Bohman is a sentient AI created by the Light Ignis, Lightning, who reveals that he's the one who destroyed the Cyberse World and steals Cal's brother's consciousness. Deeming Ignis superior, he decides to destroy humanity. The Wind Ignis, Windy, also assists Lightning after his program was forcefully rewritten. To defeat Lightning's team, Yusaku and his friends join forces with Knights of Hanoi and enter Lightning's stronghold. Both sides fight until only Playmaker, Ai, and Bohman are left with the latter having absorbed all other Ignis. Before perishing, both Flame and Aqua give Ai the last of their powers, allowing him and Playmaker to defeat Bohman. After the fight against Bohman, LINK VRAINS is shut down and Ai disappear together with Yusaku's robot, Roboppi. Replacing LINK VRAINS, SOL Technology develops a humanoid robot SOLtis, which Ai and Roboppi uses to infiltrate SOL Technology and attack its high executive, Queen. Knowing he'll be the next target, Skye's older brother, Akira, enlists the help of Playmaker and his friends as well as Knights of Hanoi once more to protect him. Ai and Roboppi manage to defeat everyone except Playmaker, Soulburner, and Varis, who are forced to fight decoys. After defeating Akira and taking over SOL Technology, Ai reopens LINK VRAINS and delivers a message for Playmaker that tells the whereabout of his location. Yusaku confronts Ai alone, leading the two of them to duel. Ai explains that Lightning left behind a simulation that shows the world will be destroyed if Ai is the only Ignis left. Fearing that he'll become like Lightning and Bohman, Ai decides to end his life either by Playmaker's hand if he loses or by scattering his free will into the SOLtis if he wins. Despite Playmaker's attempt to dissuade Ai, he still refuses to back down, forcing Playmaker to defeat him. In his last moment, Ai reveals that within the simulations, Yusaku always ends up dying protecting him, which is a future that he wishes to avoid. Three months after the final battle, everyone moves on with their lives and Yusaku goes on a journey. Somewhere within the network, Ai is revealed to be alive. == Production == Yu-Gi-Oh! VRAINS was first announced on December 16, 2016. It began airing on TV Tokyo in Japan on May 10, 2017. The series is being directed by Masahiro Hosoda at Studio Gallop with screenplay by Shin Yoshida and character design by Ken'ichi Hara. It would be the final anime series in the franchise to be animated by Gallop; Bridge would animate future instalments beginning with Yu-Gi-Oh! Sevens. The series ended on September 25, 2019. The series is being simulcast with English subtitles outside of Asia by Crunchyroll. This makes it the first series in the Yu-Gi-Oh! franchise to receive an official simulcast alongside its Japanese broadcast. A localized English adaptation was produced by Konami Cross Media NY. The pilot episode was previewed along with a digitally remastered screening of Yu-Gi-Oh! The Movie: Pyramid of Light on March 11, 2018 and March 12, 2018 in the US, and on June 13, 2018 in the UK. The English dub began airing on Teletoon in Canada on September 1, 2018, and on 9Go! in Australia on April 6, 2019. In November 2020, Cinedigm announced that the streaming service Pluto TV has secured exclusive rights in multiple territories, including the United States and Latin America, to VRAINS. Pluto TV would launch a channel dedicated to the Yu-Gi-Oh! franchise, featuring episodes from the entire Yu-Gi-Oh! Duel Monsters metaseries, including VRAINS, available in English and dubbed in multiple languages. == Trading Card Game == Yu-Gi-Oh! VRAINS introduces new gameplay elements to the Yu-Gi-Oh! Trading Card Game. With the release of the "Link Strike Starter Deck", it introduced the New Master Rules (also known as Master Rule 4 in some countries) to the competitive field of play. Now, only one monster can be summoned directly from each player's Extra Deck at a time, which is placed in one of the two new zones in the middle of the field called the "Extra Monster Zone". Complementing this new gameplay element are the new Link Monsters, honey-comb blue colored monsters that go into your Extra Deck. They do not have "Levels" or "Ranks", but instead have a "Link Rating", which indicates the number of arrows on the card and the required number of monsters required to summon them. A Link Monster's Link Rating can also be used as a number of materials for a Link Summon depending on their rating, subtracted from the Link Monster the player wishes to summon. Link Monsters have a number of Link Arrows equal to their Link Rating that point either vertically, horizontally, and/or diagonally. These Link Arrows that point to an empty Main Monster Zone allow the player to summon monsters from the Extra Deck, which include face-up Pendulum Monsters. The two Pendulum Zones have been moved to the far ends of the Spell & Trap Zones, though they also double as regular Spell & Trap Zones should the player wish not to use them. In 2019, a new format exclusive to the TCG was introduced separate from the main game, known as Speed Duels. The rules are similar to the main game and parallel the formatting used in the mobile game Duel Links. A format meant as a beginner's introduction to the basics, both the field and each player's decks have been drastically simplified to reflect that. Decks contain only 20-30 cards, each player gets only three Main Monster zones, and a turn will immediately end following the Battle Phase. Exclusive to Speed Duels, each player is allowed one Skill Card, which a player places face down during the beginning of a duel and can use anytime. == Reception == The series ranked 52 in Tokyo Anime Award Festival in Best 100 TV Anime 2017 category. The series' rank rose up to 8 in the same award in 2020 with 28,369 votes.
Stanhope Demonstrator
The Stanhope Demonstrator was the first machine to solve problems in logic. It was designed by Charles Stanhope, 3rd Earl Stanhope to demonstrate consequences in logic symbolically. The first model was constructed in 1775. It consisted of two slides coloured red and gray mounted in a square brass frame. This could be used to demonstrate the solution to a syllogistic type of problem in which objects might have two different properties and the question was how many would have both properties. Scales marked zero to ten were used to set the numbers or proportions of objects with the two properties. This form of inference anticipated the numerically definite syllogism which Augustus De Morgan laid out in his book, Formal Logic, in 1847. == Construction == The device was a brass plate about four inches square which was mounted on a piece of mahogany which was three-quarters of an inch thick. There was an opening with a depression in the wood about one and a half inches square and half an inch deep. This opening was called the holon, meaning "whole", and represented the full set of objects under consideration. A slide of red translucent glass could be inserted from the right across the holon. A slide of gray wood could be slid under the red slide. When the device was used for the "Rule for the Logic of Certainty", the gray slider was inserted from the left. When it was used for the "Rule for the Logic of Probability", the gray slider was inserted from above. The red and the gray sliders represented the two affirmative propositions which were being combined. Stanhope called these ho and los. At least four of the devices with this square style were built. In 1879, Robert Harley wrote that he had one which he had been given by Stanhope's great-grandson, Arthur, who had kept one. The other two were owned by Henry Prevost Babbage – the son of Charles Babbage, who continued his work on the Analytical Engine. One of the devices was donated to the Science Museum, London by the last Earl in 1953. Other styles, such as circular models, were constructed, but these were less convenient.
Veo (text-to-video model)
Veo, or Google Veo, is a text-to-video model developed by Google DeepMind and announced in May 2024. As a generative AI model, it creates videos based on user prompts. Veo 3, released in May 2025, can also generate accompanying audio. == Development == In May 2024, a multimodal video generation model called Veo was announced at Google I/O 2024. Google claimed that it could generate 1080p videos over a minute long. In December 2024, Google released Veo 2, available via VideoFX. It supports 4K resolution video generation and has an improved understanding of physics. In April 2025, Google announced that Veo 2 became available for advanced users on the Gemini app. In May 2025, Google released Veo 3, which not only generates videos but also creates synchronized audio — including dialogue, sound effects, and ambient noise — to match the visuals. Google also announced Flow, a video-creation tool powered by Veo and Imagen. Google DeepMind CEO Demis Hassabis described the release as the moment when AI video generation left the era of the silent film. This was rebranded as Google Flow at the 2026 Google I/O keynote, along with the announcement of Google Flow Music. == Capabilities == Google Veo can be purchased at multiple subscription tiers and through Google "AI credits". The software itself can be run by two different consoles, Google Gemini and Google Flow. Gemini being geared towards shorter, quicker, and faster projects, using the Gemini AI chat model, with Google Flow, which is essentially a movie editor allowing users to create longer projects with continuity, using the same characters and actors. Users can create a maximum of eight seconds per clip. According to Gizmodo Veo 3 users were directing the model to generate low-quality content, such as man on the street interviews or haul videos of people unboxing products. 404 Media reported that the tool tended to repeat the same joke in response to different prompts. Commentators speculated that Google had trained the service on YouTube videos or Reddit posts. Google itself had not stated the source of its training content. In July 2025, Media Matters for America reported that racist and antisemitic videos generated using Veo 3 were being uploaded to TikTok. Ryan Whitwam of Ars Technica commented, "In a perfect world, Veo 3 would refuse to create these videos, but vagueness in the prompt and the AI's inability to understand the subtleties of racist tropes (i.e., the use of monkeys instead of humans in some videos) make it easy to skirt the rules."
Line detection
In image processing, line detection is an algorithm that takes a collection of n edge points and finds all the lines on which these edge points lie. The most popular line detectors are the Hough transform and convolution-based techniques. == Hough transform == The Hough transform can be used to detect lines and the output is a parametric description of the lines in an image, for example ρ = r cos(θ) + c sin(θ). If there is a line in a row and column based image space, it can be defined ρ, the distance from the origin to the line along a perpendicular to the line, and θ, the angle of the perpendicular projection from the origin to the line measured in degrees clockwise from the positive row axis. Therefore, a line in the image corresponds to a point in the Hough space. The Hough space for lines has therefore these two dimensions θ and ρ, and a line is represented by a single point corresponding to a unique set of these parameters. The Hough transform can then be implemented by choosing a set of values of ρ and θ to use. For each pixel (r, c) in the image, compute r cos(θ) + c sin(θ) for each values of θ, and place the result in the appropriate position in the (ρ, θ) array. At the end, the values of (ρ, θ) with the highest values in the array will correspond to strongest lines in the image == Convolution-based technique == In a convolution-based technique, the line detector operator consists of a convolution masks tuned to detect the presence of lines of a particular width n and a θ orientation. Here are the four convolution masks to detect horizontal, vertical, oblique (+45 degrees), and oblique (−45 degrees) lines in an image. a) Horizontal mask(R1) (b) Vertical (R3) (C) Oblique (+45 degrees)(R2) (d) Oblique (−45 degrees)(R4) In practice, masks are run over the image and the responses are combined given by the following equation: R(x, y) = max(|R1 (x, y)|, |R2 (x, y)|, |R3 (x, y)|, |R4 (x, y)|) If R(x, y) > T, then discontinuity As can be seen below, if mask is overlay on the image (horizontal line), multiply the coincident values, and sum all these results, the output will be the (convolved image). For example, (−1)(0)+(−1)(0)+(−1)(0) + (2)(1) +(2)(1)+(2)(1) + (−1)(0)+(−1)(0)+(−1)(0) = 6 pixels on the second row, second column in the (convolved image) starting from the upper left corner of the horizontal lines. page 82 == Example == These masks above are tuned for light lines against a dark background, and would give a big negative response to dark lines against a light background. == Code example == The code was used to detect only the vertical lines in an image using Matlab and the result is below. The original image is the one on the top and the result is below it. As can be seen on the picture on the right, only the vertical lines were detected
Probabilistic database
Most real databases contain data whose correctness is uncertain. In order to work with such data, there is a need to quantify the integrity of the data. This is achieved by using probabilistic databases. A probabilistic database is an uncertain database in which the possible worlds have associated probabilities. Probabilistic database management systems are currently an active area of research. "While there are currently no commercial probabilistic database systems, several research prototypes exist..." Probabilistic databases distinguish between the logical data model and the physical representation of the data much like relational databases do in the ANSI-SPARC Architecture. In probabilistic databases this is even more crucial since such databases have to represent very large numbers of possible worlds, often exponential in the size of one world (a classical database), succinctly. == Terminology == In a probabilistic database, each tuple is associated with a probability between 0 and 1, with 0 representing that the data is certainly incorrect, and 1 representing that it is certainly correct. === Possible worlds === A probabilistic database could exist in multiple states. For example, if there is uncertainty about the existence of a tuple in the database, then the database could be in two different states with respect to that tuple—the first state contains the tuple, while the second one does not. Similarly, if an attribute can take one of the values x, y or z, then the database can be in three different states with respect to that attribute. Each of these states is called a possible world. Consider the following database: (Here {b3, b3′, b3′′} denotes that the attribute can take any of the values b3, b3′ or b3′′) Assuming that there is uncertainty about the first tuple, certainty about the second tuple, and uncertainty about the value of attribute B in the third tuple. Then the actual state of the database may or may not contain the first tuple (depending on whether it is correct or not). Similarly, the value of the attribute B may be b3, b3′ or b3′′. Consequently, the possible worlds corresponding to the database are as follows: === Types of Uncertainties === There are essentially two kinds of uncertainties that could exist in a probabilistic database, as described in the table below: By assigning values to random variables associated with the data items, different possible worlds can be represented. == History == The first published use of the term "probabilistic database" was probably in the 1987 VLDB conference paper "The theory of probabilistic databases", by Cavallo and Pittarelli. The title (of the 11 page paper) was intended as a bit of a joke, since David Maier's 600 page monograph, The Theory of Relational Databases, would have been familiar at that time to many of the conference participants and readers of the conference proceedings.