AI Chatbot You Can Talk To

AI Chatbot You Can Talk To — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

• 

  Continuum robot

  A continuum robot is a type of robot that is characterised by infinite degrees of freedom and number of joints. These characteristics allow continuum manipulators to adjust and modify their shape at any point along their length, granting them the possibility to work in confined spaces and complex environments where standard rigid-link robots cannot operate. In particular, we can define a continuum robot as an actuatable structure whose constitutive material forms curves with continuous tangent vectors. This is a fundamental definition that allows to distinguish between continuum robots and snake-arm robots or hyper-redundant manipulators: the presence of rigid links and joints allows them to only approximately perform curves with continuous tangent vectors. The design of continuum robots is bioinspired, as the intent is to resemble biological trunks, snakes and tentacles. Several concepts of continuum robots have been commercialised and can be found in many different domains of application, ranging from the medical field to undersea exploration. == Classification == Continuum robots can be categorised according to two main criteria: structure and actuation. === Structure === The main characteristic of the design of continuum robots is the presence of a continuously curving core structure, named backbone, whose shape can be actuated. The backbone must also be compliant, meaning that the backbone yields smoothly to external loads. According to the design principles chosen for the continuum manipulator, we can distinguish between: single-backbone: these continuum manipulators have one central elastic backbone through which actuation/transmission elements can run. multi-backbone: the structure of these continuum robots has two or more elastic elements (either rods or tubes) parallel to each other and constrained with one another in some way. concentric-tube: the backbone is made of concentric tubes that are free to rotate and translate between each other, depending on the actuation happening at the base of the robot. === Actuation === The actuation strategy of continuum manipulators can be distinguished between extrinsic or intrinsic actuation, depending on where the actuation happens: extrinsic actuation: the actuation happens outside the main structure of the robot and the forces are transmitted via mechanical transmission; among these techniques, there are cable/tendon driven actuators and multi-backbone strategies. intrinsic actuation: the actuation mechanism operates within the structure of the robot; these strategies include pneumatic or hydraulic chambers and the shape memory effect. The Actuated Flexible Manifold (AFM), introduced by Medina, Shapiro, and Shvalb (2016), models flexible grid-based robots that approximate smooth manifolds using discrete segments, each contributing one degree of freedom. Their work provides forward and inverse kinematics for planar and spatial configurations, bridging hyper-redundant and continuum robotics. == Advantages == The particular design of continuum robots offers several advantages with respect to rigid-link robots. First of all, as already said, continuum robots can more easily operate in environments that require a high level of dexterity, adaptability and flexibility. Moreover, the simplicity of their structure makes continuum robots more prone to miniaturisation. The rise of continuum robots has also paved the way for the development of soft continuum manipulators. These continuum manipulators are made of highly compliant materials that are flexible and can adapt and deform according to the surrounding environment. The "softness" of their material grants higher safety in human-robot interactions. == Disadvantages == The particular design of continuum robots also introduces many challenges. To properly and safely use continuum robots, it is crucial to have an accurate force and shape sensing system. Traditionally, this is done using cameras that are not suitable for some of the applications of continuum robots (e.g. minimally invasive surgery), or using electromagnetic sensors that are however disturbed by the presence of magnetic objects in the environment. To solve this issue, in the last years fiber-Bragg-grating sensors have been proposed as a possible alternative and have shown promising results. It is also necessary to notice that while the mechanical properties of rigid-link robots are fully understood, the comprehension of the behaviour and properties of continuum robots is still subject of study and debate. This poses new challenges in developing accurate models and control algorithms for this kind of robots. == Modelling == Creating an accurate model that can predict the shape of a continuum robot allows to properly control the robot's shape. There are three main approaches to model continuum robots: Cosserat rod theory: this approach is an exact solution to the static of a continuum robot, as it is not subject to any assumption. It solves a set of equilibrium equations between position, orientation, internal force and torque of the robot. This method requires to be solved numerically and it is therefore computationally expensive, due to its high complexity. Constant curvature: this technique assumes the backbone to be made of a series of mutually tangent sections that can be approximated as arcs with constant curvature. This approach is also known as piecewise constant-curvature. This assumption can be applied to the entire segment of the backbone or to its subsegments. This model has shown promising results, however it must be taken into account that the segment/subsegments of the backbone may not comply to the constant curvature assumption and therefore the model's behaviour may not entirely reflect the behaviour of the robot. Rigid-link model: this approach is based on the assumption that the continuum robot can be divided in small segments with rigid links. This is a strong assumption, since if the number of segments is too low, the model hardly behaves like the continuum robot, while increasing the number of segments means increasing the number of variables, and thus complexity. Despite this limitation, rigid-link modelling allows the use of the standard control techniques that are well known for rigid-link robots. It has been proven that this model can be coupled with shape and force sensing to mitigate its inaccuracy and can lead to promising results. == Sensing == To develop accurate control algorithms, it is necessary to complement the presented modelling techniques with real time shape sensing. The following options are currently available: Electromagnetic (EM) sensing: shape is reconstructed thanks to the mutual induction between a magnetic field generator and a magnetic field sensor. The most common external EM tracking system is the commercially available NDI Aurora: small sensors can be placed on the robot and their position is tracked in an external generated magnetic field. The validity of this method has been extensively assessed, however its performance is hindered by the limited workspace, whose dimension depends on the magnetic field. Another alternative is to embed the sensors internally in the continuum robot, combining magnetic sensors with Hall effect sensors: the magnetic field is measured at the level of the Hall effect sensors in order to estimate the deflection of the robot. However, it has been noticed that the higher the bending of the manipulator, the higher is the estimation error, due to crosstalk between sensors and magnets. Optical sensing: fiber Bragg grating sensors incorporated in an optical fiber can be embedded into the backbone of the continuum robot to estimate its shape; these sensors can only reflect a small range of the input light spectrum depending on their strain; therefore, by measuring the strain on each sensor it is possible to obtain the shape of the robot. This type of sensor is however expensive and is more prone to breaking in case of excessive strain, and this can happen in robots that can perform high deflections. == Control strategies == The control strategies can be distinguished in static and dynamic; the first one is based on the steady-state assumption, while the latter also considers the dynamic behaviour of the continuum robot. We can also differentiate between model-based controllers, that depend on a model of the robot, and model-free, that learn the robot's behaviour from data. Model-based static controllers: they rely on one of the modelling approaches presented above; once the model is defined, the kinematics must be inverted to obtain the desired actuator or configuration space variables. There are several ways to do this, like differential inverse kinematics, direct inversion or optimization. Model-free static controllers: these approaches learn directly, via machine learning techniques (e.g. regression methods and neural networks), the inverse kinematic or the direct kinematic representation of the con

  Read more →
• 

  ImageNet

  The ImageNet project is a large visual database designed for use in visual object recognition software research. More than 14 million images have been hand-annotated by the project to indicate what objects are pictured and in at least one million of the images, bounding boxes are also provided. ImageNet contains more than 20,000 categories, with a typical category, such as "balloon" or "strawberry", consisting of several hundred images. The database of annotations of third-party image URLs is freely available directly from ImageNet, though the actual images are not owned by ImageNet. Since 2010, the ImageNet project runs an annual software contest, the ImageNet Large Scale Visual Recognition Challenge (ILSVRC), where software programs compete to correctly classify and detect objects and scenes. The challenge uses a "trimmed" list of one thousand non-overlapping classes. == History == AI researcher Fei-Fei Li began working on the idea for ImageNet in 2006. At a time when most AI research focused on models and algorithms, Li wanted to expand and improve the data available to train AI algorithms. In 2007, Li met with Princeton professor Christiane Fellbaum, one of the creators of WordNet, to discuss the project. As a result of this meeting, Li went on to build ImageNet starting from the roughly 22,000 nouns of WordNet and using many of its features. She was also inspired by a 1987 estimate that the average person recognizes roughly 30,000 different kinds of objects. As an assistant professor at Princeton, Li assembled a team of researchers to work on the ImageNet project. They used Amazon Mechanical Turk to help with the classification of images. Labeling started in July 2008 and ended in April 2010. It took 49K workers from 167 countries filtering and labeling over 160M candidate images. They had enough budget to have each of the 14 million images labelled three times. The original plan called for 10,000 images per category, for 40,000 categories at 400 million images, each verified 3 times. They found that humans can classify at most 2 images/sec. At this rate, it was estimated to take 19 human-years of labor (without rest). They presented their database for the first time as a poster at the 2009 Conference on Computer Vision and Pattern Recognition (CVPR) in Florida, titled "ImageNet: A Preview of a Large-scale Hierarchical Dataset". The poster was reused at Vision Sciences Society 2009. In 2009, Alex Berg suggested adding object localization as a task. Li approached PASCAL Visual Object Classes contest in 2009 for a collaboration. It resulted in the subsequent ImageNet Large Scale Visual Recognition Challenge starting in 2010, which has 1000 classes and object localization, as compared to PASCAL VOC which had just 20 classes and 19,737 images (in 2010). === Significance for deep learning === On 30 September 2012, a convolutional neural network (CNN) called AlexNet achieved a top-5 error of 15.3% in the ImageNet 2012 Challenge, more than 10.8 percentage points lower than that of the runner-up. Using convolutional neural networks was feasible due to the use of graphics processing units (GPUs) during training, an essential ingredient of the deep learning revolution. According to The Economist, "Suddenly people started to pay attention, not just within the AI community but across the technology industry as a whole." In 2015, AlexNet was outperformed by Microsoft's very deep CNN with over 100 layers, which won the ImageNet 2015 contest, having 3.57% error on the test set. Andrej Karpathy estimated in 2014 that with concentrated effort, he could reach 5.1% error rate, and ~10 people from his lab reached ~12-13% with less effort. It was estimated that with maximal effort, a human could reach 2.4%. == Dataset == ImageNet crowdsources its annotation process. Image-level annotations indicate the presence or absence of an object class in an image, such as "there are tigers in this image" or "there are no tigers in this image". Object-level annotations provide a bounding box around the (visible part of the) indicated object. ImageNet uses a variant of the broad WordNet schema to categorize objects, augmented with 120 categories of dog breeds to showcase fine-grained classification. In 2012, ImageNet was the world's largest academic user of Mechanical Turk. The average worker identified 50 images per minute. The original plan of the full ImageNet would have roughly 50M clean, diverse and full resolution images spread over approximately 50K synsets. This was not achieved. The summary statistics given on April 30, 2010: Total number of non-empty synsets: 21841 Total number of images: 14,197,122 Number of images with bounding box annotations: 1,034,908 Number of synsets with SIFT features: 1000 Number of images with SIFT features: 1.2 million === Categories === The categories of ImageNet were filtered from the WordNet concepts. Each concept, since it can contain multiple synonyms (for example, "kitty" and "young cat"), so each concept is called a "synonym set" or "synset". There were more than 100,000 synsets in WordNet 3.0, majority of them are nouns (80,000+). The ImageNet dataset filtered these to 21,841 synsets that are countable nouns that can be visually illustrated. Each synset in WordNet 3.0 has a "WordNet ID" (wnid), which is a concatenation of part of speech and an "offset" (a unique identifying number). Every wnid starts with "n" because ImageNet only includes nouns. For example, the wnid of synset "dog, domestic dog, Canis familiaris" is "n02084071". The categories in ImageNet fall into 9 levels, from level 1 (such as "mammal") to level 9 (such as "German shepherd"). === Image format === The images were scraped from online image search (Google, Picsearch, MSN, Yahoo, Flickr, etc) using synonyms in multiple languages. For example: German shepherd, German police dog, German shepherd dog, Alsatian, ovejero alemán, pastore tedesco, 德国牧羊犬. ImageNet consists of images in RGB format with varying resolutions. For example, in ImageNet 2012, "fish" category, the resolution ranges from 4288 x 2848 to 75 x 56. In machine learning, these are typically preprocessed into a standard constant resolution, and whitened, before further processing by neural networks. For example, in PyTorch, ImageNet images are by default normalized by dividing the pixel values so that they fall between 0 and 1, then subtracting by [0.485, 0.456, 0.406], then dividing by [0.229, 0.224, 0.225]. These are the mean and standard deviations for ImageNet, so this whitens the input data. === Labels and annotations === Each image is labelled with exactly one wnid. Dense SIFT features (raw SIFT descriptors, quantized codewords, and coordinates of each descriptor/codeword) for ImageNet-1K were available for download, designed for bag of visual words. The bounding boxes of objects were available for about 3000 popular synsets with on average 150 images in each synset. Furthermore, some images have attributes. They released 25 attributes for ~400 popular synsets: Color: black, blue, brown, gray, green, orange, pink, red, violet, white, yellow Pattern: spotted, striped Shape: long, round, rectangular, square Texture: furry, smooth, rough, shiny, metallic, vegetation, wooden, wet === ImageNet-21K === The full original dataset is referred to as ImageNet-21K. ImageNet-21k contains 14,197,122 images divided into 21,841 classes. Some papers round this up and name it ImageNet-22k. The full ImageNet-21k was released in Fall of 2011, as fall11_whole.tar. There is no official train-validation-test split for ImageNet-21k. Some classes contain only 1-10 samples, while others contain thousands. === ImageNet-1K === There are various subsets of the ImageNet dataset used in various context, sometimes referred to as "versions". One of the most highly used subsets of ImageNet is the "ImageNet Large Scale Visual Recognition Challenge (ILSVRC) 2012–2017 image classification and localization dataset". This is also referred to in the research literature as ImageNet-1K or ILSVRC2017, reflecting the original ILSVRC challenge that involved 1,000 classes. ImageNet-1K contains 1,281,167 training images, 50,000 validation images and 100,000 test images. Each category in ImageNet-1K is a leaf category, meaning that there are no child nodes below it, unlike ImageNet-21K. For example, in ImageNet-21K, there are some images categorized as simply "mammal", whereas in ImageNet-1K, there are only images categorized as things like "German shepherd", since there are no child-words below "German shepherd". === Later developments === In the WordNet they built ImageNet on, there were 2832 synsets in the "person" subtree. During 2018--2020 period, they removed the download of the ImageNet-21k as they went through extensive filtering in these person synsets. Out of these 2832 synsets, 1593 were deemed "potentially offensive". Out of the remaining 1239, 1081 were deemed not really "visual". The result was that only 158 syn

  Read more →
• 

  Autocommit

  In the context of data management, autocommit is a mode of operation of a database connection. Each individual database interaction (i.e., each SQL statement) submitted through the database connection in autocommit mode will be executed in its own transaction that is implicitly committed. A SQL statement executed in autocommit mode cannot be rolled back. Autocommit mode incurs per-statement transaction overhead and can often lead to undesirable performance or resource utilization impact on the database. Nonetheless, in systems such as Microsoft SQL Server, as well as connection technologies such as ODBC and Microsoft OLE DB, autocommit mode is the default for all statements that change data, in order to ensure that individual statements will conform to the ACID (atomicity-consistency-isolation-durability) properties of transactions. The alternative to autocommit mode (non-autocommit) means that the SQL client application itself is responsible for ending transactions explicitly via the commit or rollback SQL commands. Non-autocommit mode enables grouping of multiple data manipulation SQL commands into a single atomic transaction. Some DBMS (e.g. MariaDB) force autocommit for every DDL statement, even in non-autocommit mode. In this case, before each DDL statement, previous DML statements in transaction are autocommitted. Each DDL statement is executed in its own new autocommit transaction.

  Read more →
• 

  NNDB

  The Notable Names Database (NNDB) is an online database of biographical details of over 40,000 people. Soylent Communications, a sole proprietorship that also hosted the later defunct Rotten.com, describes NNDB as an "intelligence aggregator" of noteworthy persons, highlighting their interpersonal connections. The Rotten.com domain was registered in 1996 by former Apple and Netscape software engineer Thomas E. Dell, who was also known by his internet alias, "Soylent". == Entries == Each entry has an executive summary followed by a brief narrative about their life. It also lists date and cause of death if deceased. Businesspeople and government officials are listed with chronologies of their posts, positions, and board memberships. As of 2022, the site is no longer updated. == NNDB Mapper == The NNDB Mapper, a visual tool for exploring connections between people, was made available in May 2008. It required Adobe Flash 7.

  Read more →
• 

  Sentence extraction

  Sentence extraction is a technique used for automatic summarization of a text. In this shallow approach, statistical heuristics are used to identify the most salient sentences of a text. Sentence extraction is a low-cost approach compared to more knowledge-intensive deeper approaches which require additional knowledge bases such as ontologies or linguistic knowledge. In short, sentence extraction works as a filter that allows only meaningful sentences to pass. The major downside of applying sentence-extraction techniques to the task of summarization is the loss of coherence in the resulting summary. Nevertheless, sentence extraction summaries can give valuable clues to the main points of a document and are frequently sufficiently intelligible to human readers. == Procedure == Usually, a combination of heuristics is used to determine the most important sentences within the document. Each heuristic assigns a (positive or negative) score to the sentence. After all heuristics have been applied, the highest-scoring sentences are included in the summary. The individual heuristics are weighted according to their importance. === Early approaches and some sample heuristics === Seminal papers which laid the foundations for many techniques used today have been published by Hans Peter Luhn in 1958 and H. P Edmundson in 1969. Luhn proposed to assign more weight to sentences at the beginning of the document or a paragraph. Edmundson stressed the importance of title-words for summarization and was the first to employ stop-lists in order to filter uninformative words of low semantic content (e.g. most grammatical words such as of, the, a). He also distinguished between bonus words and stigma words, i.e. words that probably occur together with important (e.g. the word form significant) or unimportant information. His idea of using key-words, i.e. words which occur significantly frequently in the document, is still one of the core heuristics of today's summarizers. With large linguistic corpora available today, the tf–idf value which originated in information retrieval, can be successfully applied to identify the key words of a text: If for example the word cat occurs significantly more often in the text to be summarized (TF = "term frequency") than in the corpus (IDF means "inverse document frequency"; here the corpus is meant by document), then cat is likely to be an important word of the text; the text may in fact be a text about cats.

  Read more →
• 

  Kinematic chain

  In mechanical engineering, a kinematic chain is an assembly of rigid bodies connected by joints to provide constrained motion that is the mathematical model for a mechanical system. As the word chain suggests, the rigid bodies, or links, are constrained by their connections to other links. An example is the simple open chain formed by links connected in series, like the usual chain, which is the kinematic model for a typical robot manipulator. Mathematical models of the connections, or joints, between two links are termed kinematic pairs. Kinematic pairs model the hinged and sliding joints fundamental to robotics, often called lower pairs and the surface contact joints critical to cams and gearing, called higher pairs. These joints are generally modeled as holonomic constraints. A kinematic diagram is a schematic of the mechanical system that shows the kinematic chain. The modern use of kinematic chains includes analysis of Linkages (mechanical), compliance that arises from flexure joints in precision mechanisms, link compliance in compliant mechanisms and micro-electro-mechanical systems, and cable compliance in cable robotic and tensegrity systems. == Mobility formula == The degrees of freedom, or mobility, of a kinematic chain is the number of parameters that define the configuration of the chain. A system of n rigid bodies moving in space has 6n degrees of freedom measured relative to a fixed frame. This frame is included in the count of bodies, so that mobility does not depend on link that forms the fixed frame. This means the degree-of-freedom of this system is M = 6(N − 1), where N = n + 1 is the number of moving bodies plus the fixed body. Joints that connect bodies impose constraints. Specifically, hinges and sliders each impose five constraints and therefore remove five degrees of freedom. It is convenient to define the number of constraints c that a joint imposes in terms of the joint's freedom f, where c = 6 − f. In the case of a hinge or slider, which are one-degree-of-freedom joints, have f = 1 and therefore c = 6 − 1 = 5. The result in general where d {\displaystyle d} is the degrees of freedom for the mobility of a kinematic chain formed from n moving links and j joints each with freedom fi, i = 1, 2, …, j, is given by M = d n − ∑ i = 1 j ( d − f i ) = d ( N − 1 − j ) + ∑ i = 1 j f i {\displaystyle M=dn-\sum _{i=1}^{j}(d-f_{i})=d(N-1-j)+\sum _{i=1}^{j}f_{i}} Where N is the total number of links and includes the fixed link. Spacial linkages used d = 6 {\displaystyle d=6} and planar linkages use d = 3 {\displaystyle d=3} . This result is known as the Chebychev–Grübler–Kutzbach criterion. == Analysis of kinematic chains == The constraint equations of a kinematic chain couple the range of movement allowed at each joint to the dimensions of the links in the chain, and form algebraic equations that are solved to determine the configuration of the chain associated with specific values of input parameters, called degrees of freedom. The constraint equations for a kinematic chain are obtained using rigid transformations [Z] to characterize the relative movement allowed at each joint and separate rigid transformations [X] to define the dimensions of each link. In the case of a serial open chain, the result is a sequence of rigid transformations alternating joint and link transformations from the base of the chain to its end link, which is equated to the specified position for the end link. A chain of n links connected in series has the kinematic equations, [ T ] = [ Z 1 ] [ X 1 ] [ Z 2 ] [ X 2 ] ⋯ [ X n − 1 ] [ Z n ] , {\displaystyle [T]=[Z_{1}][X_{1}][Z_{2}][X_{2}]\cdots [X_{n-1}][Z_{n}],\!} where [T] is the transformation locating the end-link—notice that the chain includes a "zeroth" link consisting of the ground frame to which it is attached. These equations are called the forward kinematics equations of the serial chain. Kinematic chains of a wide range of complexity are analyzed by equating the kinematics equations of serial chains that form loops within the kinematic chain. These equations are often called loop equations. The complexity (in terms of calculating the forward and inverse kinematics) of the chain is determined by the following factors: Its topology: a serial chain, a parallel manipulator, a tree structure, or a graph. Its geometrical form: how are neighbouring joints spatially connected to each other? Explanation Two or more rigid bodies in space are collectively called a rigid body system. We can hinder the motion of these independent rigid bodies with kinematic constraints. Kinematic constraints are constraints between rigid bodies that result in the decrease of the degrees of freedom of rigid body system. == Synthesis of kinematic chains == The constraint equations of a kinematic chain can be used in reverse to determine the dimensions of the links from a specification of the desired movement of the system. This is termed kinematic synthesis. Perhaps the most developed formulation of kinematic synthesis is for four-bar linkages, which is known as Burmester theory. Ferdinand Freudenstein is often called the father of modern kinematics for his contributions to the kinematic synthesis of linkages beginning in the 1950s. His use of the newly developed computer to solve Freudenstein's equation became the prototype of computer-aided design systems. This work has been generalized to the synthesis of spherical and spatial mechanisms.

  Read more →
• 

  Josh (app)

  Josh (stylized as JOSH) was a video-sharing social networking service but it has since evolved into a live call and chat application owned by VerSe Innovation – an Indian technology company based in Bangalore, India. Josh was an Indian short video app that was launched in immediately after the Indian Government banned TikTok and other Chinese apps in June 2020. The founders of the platform have promoted the app as the “Instagram for Bharat” referring to their focus on the Indian audience that speaks its own regional and state languages. Josh was among the top 10 most downloaded apps social and entertainment apps in India of 2021 and had 150 million monthly active users as per April 2022. The word 'Josh' translates to fervour or passion. The app was launched under the aegis of the Atmanirbhar Bharat campaign and to compete with the duopoly of Google and Facebook in India. Josh's parent company VerSe Innovations Pvt. Ltd. owns another startup Dailyhunt, which a content and news aggregator application. Both Dailyhunt and Josh are a part of the VerSe's focus on the "next billion" regional language users of India. Founders Virendra Gupta and Umang Bedi conceptualised Josh as a short-video platform that made content creation accessible to vernacular language users, essentially the non-English speaking audience in India. == Features == Josh is currently available in 12 Indian languages and allows users to upload, share, remix bite-sized videos of up to 120 seconds. There are various categories across the video section including viral, trending, glamour, dance, devotion, yoga and cooking among others. Similar to Instagram and TikTok, it has a video feed which is curated for individuals on the basis of their app behaviour. The app hosts many daily, weekly and monthly social media challenges. == Funding == In December 2020, within 3 months of its launch, Josh's parent app VerSe Innovation raised more than $100 million from investors including Alphabet Inc's Google and Microsoft. In February 2021, VerSe Innovation raised $100 million in Series H funding from Qatar Investment Authority, the sovereign wealth fund of the State of Qatar, and Glade Brook Capital Partners. In August 2021, VerSe raised over $450 million in its Series I financing round with a valuation of $1 billion. Investors included Canada Pension Plan Investment Board (CPPIB), Siguler Guff, Baillie Gifford, Carlyle Asia Partners Growth II affiliates, and others. The startup announced its plan to expand overseas and broaden its ecommerce play for both Dailyhunt and Josh. In April 2022, VerSe announced that it has raised $805 million in funding from investors at a valuation of nearly $5 billion. ByteDance Offloads Stake In Josh Parent VerSe, Exits At 56% Discount == Partnerships == In February 2021, Saregama and Josh signed a music licensing deal, wherein Josh expanded its musical library with 1.3 lakh songs from Saregama in 25 different languages. To improve their user experience, Josh partnered with computer vision company D-ID in August 2021. The company helped Josh introduce photo-to-video features, live portrait technology, animate their photos etc. In order to solidify their efforts in enhancing Josh, VerSe acquired Indian social networking platform GolBol in October 2021. The move came as an effort by the startup to strengthen their discovery initiatives on the platform and classify content at scale and understand the core behaviour of Indian regional audiences. Josh has also announced its plans to include live commerce as a potential revenue stream through its partnership with multiple large e-commerce players. == Notable campaigns == Say No To Dowry – In association with Josh, the Kerala Police partook in the #SayNo2Dowry online social media campaign that was started to highlight and stop the social evil in the state. Salute India – Josh entered the Guinness World Records by creating the largest online video album of people saluting (29,529). It organised an online campaign #SaluteIndia on the app during the 75th Independence Day of India during 10–15 August 2021.

  Read more →
• 

  TikTok

  TikTok is a social media and short-form online video platform. It hosts user-submitted videos, which range in duration from three seconds to 60 minutes. It can be accessed through a mobile app or through its website. Since its launch, TikTok has become one of the world's most popular social media platforms, using recommendation algorithms to connect content creators and influencers with new audiences. In April 2020, TikTok surpassed two billion mobile downloads worldwide. The popularity of TikTok has allowed viral trends in food, fashion, and music to take off and increase the platform's cultural impact worldwide. TikTok has come under scrutiny due to data privacy violations, mental health concerns, misinformation, offensive content, addictive algorithm, its role during the Gaza war, and, following its 2026 divestiture in the U.S., alleged censorship of criticism of Donald Trump and discussions of Jeffrey Epstein. While TikTok remains accessible to users in most countries, a minority of countries (including India and Afghanistan) have implemented full or partial bans. Many other countries limit TikTok's use on government-issued devices for security or privacy reasons. == Corporate structure == TikTok Ltd was incorporated in the Cayman Islands in the Caribbean and is based in both Singapore and Los Angeles. It owns entities which are based respectively in Australia (which also runs the New Zealand business), United Kingdom (also owns subsidiaries in the European Union), and Singapore (owns operations in Southeast Asia and India). A spin-off company, TikTok USDS Joint Venture LLC was formed on 22 January 2026 to handle TikTok and other ByteDance properties in the United States, Oracle Corporation, MGX Fund Management Limited, Silver Lake each holding a 15% stake, ByteDance holds a 19.9% stake and the remaining 35.1% is shared between Dell Technologies founder Michael Dell and Vastmere Strategic Investments. Its parent company, Beijing-based ByteDance, is owned by founders and Chinese investors, other global investors, and employees. One of ByteDance's main domestic subsidiaries is owned by Chinese state funds and entities through a 1% golden share. Employees have reported that multiple overlaps exist between TikTok and ByteDance in terms of personnel management and product development. TikTok says that since 2020, its US-based CEO is responsible for making important decisions, and has downplayed its China connection. == History == === Douyin === Douyin (Chinese: 抖音; pinyin: Dǒuyīn; lit. 'Shaking Sound') was launched on 20 September 2016, by ByteDance, originally under the name A.me, before changing its name to Douyin in December 2016. Douyin was developed in nearly 7 months and within a year had 100 million users, with more than one billion videos viewed every day. While TikTok and Douyin share a similar user interface, the platforms operate separately. Douyin includes an in-video search feature that can search by people's faces for more videos of them, along with other features such as buying, booking hotels, and making geo-tagged reviews. === TikTok === ByteDance planned on Douyin expanding overseas. The founder of ByteDance, Zhang Yiming, stated that "China is home to only one-fifth of Internet users globally. If we don't expand on a global scale, we are bound to lose to peers eyeing the four-fifths. So, going global is a must." ByteDance created TikTok as an overseas version of Douyin. TikTok was launched in the international market in September 2017. On 9 November 2017, ByteDance spent nearly $1 billion to purchase Musical.ly, a startup headquartered in Shanghai with an overseas office in Santa Monica, California. Musical.ly was a social media video platform that allowed users to create short lip-sync and comedy videos, initially released in August 2014. TikTok merged with Musical.ly on 2 August 2018 with existing accounts and data consolidated into one app, keeping the title TikTok. On 23 January 2018, the TikTok app ranked first among free application downloads on app stores in Thailand and other countries. TikTok has been downloaded more than 130 million times in the United States and has reached 2 billion downloads worldwide, according to data from mobile research firm Sensor Tower (those numbers exclude Android users in China). In the United States, Jimmy Fallon, Tony Hawk, and other celebrities began using the app in 2018. Other celebrities like Jennifer Lopez, Jessica Alba, Will Smith, and Justin Bieber joined TikTok. In January 2019, TikTok allowed creators to embed merchandise sale links into their videos. On 3 September 2019, TikTok and the US National Football League (NFL) announced a multi-year partnership. The agreement came just two days before the NFL's 100th season kick-off at Soldier Field in Chicago where TikTok hosted activities for fans in honor of the deal. The partnership entails the launch of an official NFL TikTok account, which is to bring about new marketing opportunities such as sponsored videos and hashtag challenges. In July 2020, TikTok, excluding Douyin, reported close to 800 million monthly active users worldwide after less than four years of existence. In May 2021, TikTok appointed Shou Zi Chew as their new CEO who assumed the position from interim CEO Vanessa Pappas, following the resignation of Kevin A. Mayer on 27 August 2020. In September 2021, TikTok reported that it had reached 1 billion users. In 2021, TikTok earned $4 billion in advertising revenue. In October 2022, TikTok was reported to be planning an expansion into the e-commerce market in the US, following the launch of TikTok Shop in the United Kingdom. The company posted job listings for staff for a series of order fulfillment centers in the US and was reportedly planning to start the new live shopping business before the end of the year. The Financial Times reported that TikTok will launch a video gaming channel, but the report was denied in a statement to Digiday, with TikTok instead aiming to be a social hub for the gaming community. According to data from app analytics group Sensor Tower, advertising on TikTok in the US grew by 11% in March 2023, with companies including Pepsi, DoorDash, Amazon, and Apple among the top spenders. According to estimates from research group Insider Intelligence, TikTok is projected to generate $14.15 billion in revenue in 2023, up from $9.89 billion in 2022. In March 2024, The Wall Street Journal reported that TikTok's growth in the US had stagnated. ==== Plans to sell TikTok's US operations ==== Since at least 2020, following calls to ban TikTok in the country, the Committee on Foreign Investment in the United States (CFIUS) has been investigating the company's 2017 merger with Musical.ly but has not finalized any of its negotiations with TikTok, such as the Project Texas proposal, waiting instead for Congress to act. In January 2025, Chinese officials began preliminary talks about potentially selling TikTok's US operations to Elon Musk if the app faced an impending ban due to national security concerns. While Beijing preferred TikTok remain under ByteDance's control, the sale could happen through a competitive process or with US government involvement. One possibility involved Musk's platform, X, taking over TikTok's US business. The move came ahead of a Supreme Court case that upheld the constitutionality of a law that would force a sale or ban of TikTok in the US by 19 January 2025, due to national security concerns regarding its ties to China. Other potential buyers included Project Liberty's "The People's Bid For TikTok" consortium of Frank McCourt with Kevin O'Leary, Steven Mnuchin, MrBeast and Bobby Kotick, the seriousness of these potential buyers was unclear. The day before the impending ban, California-based conversational search engine company Perplexity AI submitted a bid for a merger with TikTok US. On 14 September 2025, the Wall Street Journal reported the US and China have reached the "framework of a deal" for the US operations of TikTok to be sold to a consortium of investors in the US including close Trump ally Larry Ellison of Oracle. The deal was completed by 22 January 2026, with a consortium of investors—including Oracle, Silver Lake, MGX, and others including the personal investment entity for Michael Dell—owning more than 80% of the new venture. ByteDance retained 19.9% ownership. Under the deal, the app would remain the same, and the algorithm would be adjusted over time to favor American topics for those users. === Expansion in other markets === TikTok was downloaded over 104 million times on Apple's App Store during the first half of 2018, according to data provided to CNBC by Sensor Tower. After merging with musical.ly in August, downloads increased and TikTok subsequently became the most downloaded app in the US in October 2018, which musical.ly had done once before. In February 2019, TikTok, together with Douyin, hit one billion downloads globally, excluding Android

  Read more →
• 

  Image formation

  The study of image formation encompasses the radiometric and geometric processes by which 2D images of 3D objects are formed. In the case of digital images, the image formation process also includes analog to digital conversion and sampling. == Imaging == The imaging process is a mapping of an object to an image plane. Each point on the image corresponds to a point on the object. An illuminated object will scatter light toward a lens and the lens will collect and focus the light to create the image. The ratio of the height of the image to the height of the object is the magnification. The spatial extent of the image surface and the focal length of the lens determines the field of view of the lens. Image formation of mirror these have a center of curvature and its focal length of the mirror is half of the center of curvature. == Illumination == An object may be illuminated by the light from an emitting source such as the sun, a light bulb or a Light Emitting Diode. The light incident on the object is reflected in a manner dependent on the surface properties of the object. For rough surfaces, the reflected light is scattered in a manner described by the Bi-directional Reflectance Distribution Function (BRDF) of the surface. The BRDF of a surface is the ratio of the exiting power per square meter per steradian (radiance) to the incident power per square meter (irradiance). The BRDF typically varies with angle and may vary with wavelength, but a specific important case is a surface that has constant BRDF. This surface type is referred to as Lambertian and the magnitude of the BRDF is R/π, where R is the reflectivity of the surface. The portion of scattered light that propagates toward the lens is collected by the entrance pupil of the imaging lens over the field of view. == Field of view and imagery == The Field of view of a lens is limited by the size of the image plane and the focal length of the lens. The relationship between a location on the image and a location on the object is y = ftan(θ), where y is the max extent of the image plane, f is the focal length of the lens and θ is the field of view. If y is the max radial size of the image then θ is the field of view of the lens. While the image created by a lens is continuous, it can be modeled as a set of discrete field points, each representing a point on the object. The quality of the image is limited by the aberrations in the lens and the diffraction created by the finite aperture stop. == Pupils and stops == The aperture stop of a lens is a mechanical aperture which limits the light collection for each field point. The entrance pupil is the image of the aperture stop created by the optical elements on the object side of the lens. The light scattered by an object is collected by the entrance pupil and focused onto the image plane via a series of refractive elements. The cone of the focused light at the image plane is set by the size of the entrance pupil and the focal length of the lens. This is often referred to as the f-stop or f-number of the lens. f/# = f/D where D is the diameter of the entrance pupil. == Pixelation and color vs. monochrome == In typical digital imaging systems, a sensor is placed at the image plane. The light is focused on to the sensor and the continuous image is pixelated. The light incident on each pixel in the sensor will be integrated within the pixel and a proportional electronic signal will be generated. The angular geometric resolution of a pixel is given by atan(p/f), where p is the pitch of the pixel. This is also called the pixel field of view. The sensor may be monochrome or color. In the case of a monochrome sensor, the light incident on each pixel is integrated and the resulting image is a grayscale like picture. For color images, a mosaic color filter is typically placed over the pixels to create a color image. An example is a Bayer filter. The signal incident on each pixel is then digitized to a bit stream. == Image quality == The quality of an image is dependent upon both geometric and physical items. Geometrically, higher density of pixels across an image will give less blocky pixelation and thus a better geometric image quality. Lens aberrations also contribute to the quality of the image. Physically, diffraction due to the aperture stop will limit the resolvable spatial frequencies as a function of f-number. In the frequency domain, Modulation Transfer Function (MTF) is a measure of the quality of the imaging system. The MTF is a measure of the visibility of a sinusoidal variation in irradiance on the image plane as a function of the frequency of the sinusoid. It includes the effects of diffraction, aberrations and pixelation. For the lens, the MTF is the autocorrelation of the pupil function, so it accounts for the finite pupil extent and the lens aberrations. The sensor MTF is the Fourier Transform of the pixel geometry. For a square pixel, MTF(ξ) = sin(πξp)/πξp where p is the pixel width and ξ is the spatial frequency. The MTF of the combination of the lens and detector is the product of the two component MTFs. == Perception == Color images can be perceived via two means. In the case of computer vision the light incident on the sensor comprises the image. In the case of visual perception, the human eye has a color dependent response to light so this must be accounted for. This is important consideration when converting to grayscale. == Image formation in eye == The principal difference between the lens of the eye and an ordinary optical lens is that the former is flexible. The radius of the curvature of the anterior surface of the lens is greater than the radius of its posterior surface. The shape of the lens is controlled by tension in the fibers of the ciliary body. To focus on distant objects, the controlling muscles cause the lens to be relatively flattened. Similarly, these muscles allow the lens to become thicker in order to focus on objects near the eye. The distance between the center of the lens and the retina (focal length) varies from approximately 17 mm to about 14 mm, as the refractive power of the lens increases from its minimum to its maximum. When the eye focuses on an object farther away than about 3 m, the lens exhibits its lowest refractive power. When the eye focuses on a close object, the lens is most strongly refractive.

  Read more →
• 

  CityEngine

  ArcGIS CityEngine is a commercial 3D modeling program. Developed by Esri R&D Center Zurich (formerly Procedural Inc.), it specializes in the generation of 3D urban environments to support the creation of detailed large-scale 3D city models. Unlike traditional 3D modeling methodology, which uses computer-aided design (CAD) tools and techniques, CityEngine takes a procedural modeling approach which shapes generation via a rules-based system. Due to its integration with the wider ArcGIS platform, CityEngine can also be used with geographic information system (GIS) datasets. CityEngine can be used for urban planning and architecture, graphics visualization, game development, entertainment, and archeology. CityEngine can be used to visualize the building information modeling (BIM) data of buildings in a larger urban context, making for more realistic construction projects. == History and releases == === Software history === ArcGIS CityEngine, originally named Esri CityEngine, was developed at Swiss technology university ETH Zurich by Pascal Mueller, the co-founder and CEO of Procedural Inc. While researching for his PhD at the ETH Computer Vision Lab, Mueller invented a number of techniques for procedural modeling of 3D architecture that make up the foundation of CityEngine. CityEngine publically debuted at the 2001 SIGGRAPH conference; since then, additional research papers have been published that have contributed to CityEngine and its features. The first commercial version of CityEngine was released in 2008. In 2007, Procedural Inc. was founded and separated from ETH Zurich, the top-ranking technology university in Switzerland. In the summer of 2011, Procedural Inc. was acquired by Esri Inc., becoming Esri R&D Center Zurich. Esri CityEngine was renamed to ArcGIS CityEngine in June 2020 to offically make it a part of the ArcGIS software suite. === Releases === === Licensing and pricing === ArcGIS CityEngine is included in the Professional and Professional Plus tiers of ArcGIS Online. Pricing may vary by region and distributors. In the US, the professional tier costs US$2,200 per year; in the UK, it is £4,200 per year (excluding VAT). CityEngine can be purchased elsewhere via a local Esri partner. . Once purchased, users can download and obtain license details from the MyEsri portal. == Features == CGA (computer generated architecture) parametric modeling rules to control mass, geometry assets, proportions, or texturing of buildings or streets on a citywide scale Select a target location and import geo-referenced satellite imagery and 3D terrain of the location to more quickly build accurate urban environments through OpenStreetMap integration Interactively control specific street or building parameters, such as height or age Import/export geo-spatial/vector data with industry-standard formats such as Esri Shapefile, File Geodatabase, and OpenStreetMap, as well as file formats for WebGL, KMZ, Collada, Autodesk FBX, Autodesk Maya, 3DS, Wavefront OBJ, RenderMan RIB, Alembic, e-on software's Vue, Universal Scene Description USD, Khronos Group GLTF, Unreal Engine, and Unreal Datasmith Script and generate rules-based reports to show socioeconomic figures (e.g., Gross Floor Area (GFA) and Floor Area Ratio (FAR)) to analyze their urban design proposals. VR viewing of modeled environments with Samsung Gear VR Use a variety of materials through the Esri materials library == Procedural modeling == ArcGIS CityEngine uses a procedural modeling approach to automatically generate models through a predefined rule set. The rules are defined through a CGA shape grammar system, enabling the creation of complex parametric models. Users can change or add the shape grammar as needed. Urban environments can be modeled within CityEngine by starting with creating a street network (either from the street drawing tool or with data imported from map data). Then, lots may be subdivided as many times as specified, resulting in a map of multiple lots and streets. CityEngine can then be instructed to start generating the buildings using defined procedural modeling rules. At this point, the city model can be re-designed and adjusted by changing the parameters or the shape grammar. === Geodesign === Though CityEngine is not an analytical tool like GIS, discussions about geodesign often mention the use of ArcGIS CityEngine. As it can be used to enhance 3D shape generation in ArcGIS, ArcGIS CityEngine is a critical product to improve the applicability of geodesign by using geospatial information to design or analyze a city. == Applications == === Urban design and planning === Garsdale Design used ArcGIS CityEngine in the creation of city master plans in Iraq before 2013, both to model existing historic areas and also model future plans. Larger companies like Foster+Partners and HOK Architects have also used CityEngine in their urban planning projects. === Urban and environmental studies === Because its primary feature is building informative city models, some urban researchers use CityEngine to compare land-use planning schemes, for example in very dense global cities such as Hong Kong and Seoul. Environmental scientists can also utilize the instant 3D model generation in CityEngine, which can make for more convenient informative research than modeling a city by creating each building individually. === Game development === CityEngine can be used as a tool in the creation of video games that require detailed 3D environments to assign interactive scripts. === Movie industry === Zootopia (also known outside of the US as Zootopolis), which won the 2016 Academy Award for Best Animated Feature Film, used CityEngine to model the city in its movie. multi-scaling city, the designers used CityEngine due to its rule-based system. CityEngine was also used to create Big Hero 6's San-Fransokyo. === Military === Due to its integration with the Esri product suite and its ability to process geospatial data to create 3D scenes/maps, CityEngine can be used within military/defense organizations. == List of movies and TV shows using CityEngine == Studios and companies rarely state what software they use in their pipelines. When CityEngine is mentioned as a tool in production, it's often in a small reference in a larger article. Movies only claimed to use CityEngine by a single Esri employee Presented at FMX 2025 workshop == Ports == ArcGIS CityEngine is built on top of Eclipse IDE, and has therefore able to be used on Windows and Linux operating systems. Support for macOS was stopped in March 2021. == Plugins and extensions == ArcGIS CityEngine currently works with a number of third party 3D modeling, rendering, and analytical software products via its SDK and API; these currently are: ArcGIS CityEngine for ArcGIS Urban: ArcGIS Urban Suite Puma: ArcGIS CityEngine for Rhinoceros 3D Palladio: ArcGIS CityEngine for Houdini Serlio: ArcGIS CityEngine for Maya PyPRT: ArcGIS CityEngine for Python ArcGIS CityEngine provides a Python scripting interface built on Jython (current version 2.7.0) which allows users to create their own tools and functionality. == Publications ==

  Read more →
• 

  SCADA Strangelove

  SCADA Strangelove is an independent group of information security researchers founded in 2012, focused on security assessment of industrial control systems (ICS) and SCADA. == Activities == Main fields of research include: Discovery of 0-day vulnerabilities in cyber physical systems and coordinated vulnerability disclosure; Security assessment of ICS protocols and development suites; Identification of publicly Internet-connected ICS components and secure it with help of proper authorities; Development of security hardening guides for ICS software; Mapping cybersecurity on to functional safety; Awareness control and delivery of information regarding the actual security state of ICS systems. SCADA Strangelove's interests expand further than classic ICS components and covers various embedded systems, however, and encompass smart home components, solar panels, wind turbines, SmartGrid as well as other areas. == Projects == Group members have and continue to develop and publish numerous open source tools for scanning, fingerprinting, security evaluation and password bruteforcing for ICS devices. These devices work over industrial protocols such as modbus, Siemens S7, MMS, ISO EC 60870, ProfiNet. In 2014 Shodan used some of the published tools for building a map of ICS devices which is publicly available on the Internet. Open source security assessment frameworks, such as THC Hydra, Metasploit, and DigitalBond Redpoint have used Shodan-developed tools and techniques. The group has published security-hardening guidelines for industrial solutions based on Siemens SIMATIC WinCC and WinCC Flexible. The guidelines contain detailed security configuration walk-throughs, descriptions of internal security features and appropriate best practices. Among the group’s more noticeable projects is Choo Choo PWN (CCP) also named the Critical Infrastructure Attack (CIA). This is an interactive laboratory built upon ICS software and hardware used in real world. Every system is connected to a toy city infrastructure, which includes factories, railroads and other facilities. The laboratory has been demonstrated at various conferences including PHDays, Power of Community, and 30C3. Primarily the laboratory is used for the discovery of new vulnerabilities and for evaluation of security mechanisms, however it is also used for workshops and other educational activities. At Positive Hack Days IV, contestants found several 0-day vulnerabilities in Indusoft Web Studio 7.1 by Schneider Electric, and in specific ICS hardware RTU PET-7000 during the ICS vulnerability discovery challenge. The group supports Secure Open SmartGrid (SCADASOS) project to find and fix vulnerabilities in intellectual power grid components such as photovoltaic power station, wind turbine, power inverter. More than 80 000 industrial devices were discovered and isolated from the Internet in 2015. == Appearances == Group members are frequently seen presenting at conferences like CCC, SCADA Security Scientific Symposium, Positive Hack Days. Most notable talks are: === 29C3 === An overview of vulnerabilities discovered in the widely distributed Siemens SIMATIC WinCC software and tools that are implemented for searching ICS on the Internet. === PHDays === This talk consisted of an overview of vulnerabilities discovered in various systems produced by ABB, Emerson, Honeywell and Siemens and was presented at PHDays III and PHDays IV. === Confidence 2014 === Implications of security research aimed at realization of various industrial network protocols Profinet, Modbus, DNP3, IEC 61850-8-1 (MMS), IEC (International Electrotechnical Commission) 61870-5-101/104, FTE (Fault Tolerant Ethernet), Siemens S7. === PacSec 2014 === Presentations of security research showing the impact of radio and 3G/4G networks on the security of mobile devices as well as on industrial equipment. === 31C3 === Analysis of security architecture and implementation of the most wide spread platforms for wind and solar energy generation which produce many gigawatts of it. === 32C3 === Cybersecurity assessment of railway signaling systems such as Automatic Train Control (ATC), Computer-based interlocking (CBI) and European Train Control System (ETCS). === China Internet Security Conference 2016 === In "Greater China Cyber Threat Landscape" keynote by Sergey Gordeychik an overview of vulnerabilities, attacks and cyber-security incidents in Greater China region was presented. === Recon 2017 === In talk "Hopeless: Relay Protection for Substation Automation" by Kirill Nesterov and Alexander Tlyapov security analysis results of key Digital Substation component - Relay Protection Terminals was presented. Vulnerabilities, including remote code execution in Siemens SIPROTEC, General Electric Line Distance Relay, NARI and ABB protective relays was presented. == Philosophy == All names, catchwords and graphical elements refer to Stanley Kubrick’s film, Dr. Strangelove. In their talks, group members often refer to Cold War events such as the Caribbean Crisis, and draw parallels between nuclear arms race and the current escalation of cyberwar. Group members follow the approach of “responsible disclosure” and “ready to wait for years, while vendor is patching the vulnerability”. Public exploits for discovered vulnerabilities are not published. This is on account of the longevity of ICS and by implication the long process of patching ICS. However, conflicts still happen, notably in 2012 when the talk at DEF CON was called off due to a dispute of persistent weaknesses in Siemens industrial software.

  Read more →
• 

  Zolostays

  Zolostays is a real-tech co-living focused startup that provides ready-to-move rooms/beds. It was founded in 2015 by Nikhil Sikri, Akhil Sikri and Sneha Choudhry. == Overview == During the pandemic, Zolo provided 75 of rent-free accommodation to those who lost their jobs. Zolo uses bulk inventory in usually residential township and ties up with real estate companies to make the rooms/beds available. Zolostays has both revenue sharing and leased model. == History == Zolostays was founded in 2015 to solve the problem of students and young professionals who would move to temporarily go to other cities to study and work and look for affordable housing. In 2020, it was operating in 10 Indian cities. It has four round of funding, with total $98 million.

  Read more →
• 

  Neural operators

  Neural operators are a class of deep learning architectures designed to learn maps between infinite-dimensional function spaces. Neural operators represent an extension of traditional artificial neural networks, marking a departure from the typical focus on learning mappings between finite-dimensional Euclidean spaces or finite sets. Neural operators directly learn operators between function spaces; they can receive input functions, and the output function can be evaluated at any discretization. The primary application of neural operators is in learning surrogate maps for the solution operators of partial differential equations (PDEs), which are critical tools in modeling the natural environment. Standard PDE solvers can be time-consuming and computationally intensive, especially for complex systems. Neural operators have demonstrated improved performance in solving PDEs compared to existing machine learning methodologies while being significantly faster than numerical solvers. Neural operators have also been applied to various scientific and engineering disciplines such as turbulent flow modeling, computational mechanics, graph-structured data, and the geosciences. In particular, they have been applied to learning stress-strain fields in materials, classifying complex data like spatial transcriptomics, predicting multiphase flow in porous media, and carbon dioxide migration simulations. Finally, the operator learning paradigm allows learning maps between function spaces, and is different from parallel ideas of learning maps from finite-dimensional spaces to function spaces, and subsumes these settings as special cases when limited to a fixed input resolution. == Operator learning == Understanding and mapping relationships between function spaces has many applications in engineering and the sciences. In particular, one can cast the problem of solving partial differential equations as identifying a map between function spaces, such as from an initial condition to a time-evolved state. In other PDEs this map takes an input coefficient function and outputs a solution function. Operator learning is a machine learning paradigm to learn solution operators mapping the input function to the output function . Using traditional machine learning methods, addressing this problem would involve discretizing the infinite-dimensional input and output function spaces into finite-dimensional grids and applying standard learning models, such as neural networks. This approach reduces the operator learning to finite-dimensional function learning and has some limitations, such as generalizing to discretizations beyond the grid used in training. The primary properties of neural operators that differentiate them from traditional neural networks is discretization invariance and discretization convergence. Unlike conventional neural networks, which are fixed on the discretization of training data, neural operators can adapt to various discretizations without re-training. This property improves the robustness and applicability of neural operators in different scenarios, providing consistent performance across different resolutions and grids. == Definition and formulation == Architecturally, neural operators are similar to feed-forward neural networks in the sense that they are composed of alternating linear maps and non-linearities. Since neural operators act on and output functions, neural operators have been instead formulated as a sequence of alternating linear integral operators on function spaces and point-wise non-linearities. Using an analogous architecture to finite-dimensional neural networks, similar universal approximation theorems have been proven for neural operators. In particular, it has been shown that neural operators can approximate any continuous operator on a compact set. Neural operators seek to approximate some operator G : A → U {\displaystyle {\mathcal {G}}:{\mathcal {A}}\to {\mathcal {U}}} between function spaces A {\displaystyle {\mathcal {A}}} and U {\displaystyle {\mathcal {U}}} by building a parametric map G ϕ : A → U {\displaystyle {\mathcal {G}}_{\phi }:{\mathcal {A}}\to {\mathcal {U}}} . Such parametric maps G ϕ {\displaystyle {\mathcal {G}}_{\phi }} can generally be defined in the form G ϕ := Q ∘ σ ( W T + K T + b T ) ∘ ⋯ ∘ σ ( W 1 + K 1 + b 1 ) ∘ P , {\displaystyle {\mathcal {G}}_{\phi }:={\mathcal {Q}}\circ \sigma (W_{T}+{\mathcal {K}}_{T}+b_{T})\circ \cdots \circ \sigma (W_{1}+{\mathcal {K}}_{1}+b_{1})\circ {\mathcal {P}},} where P , Q {\displaystyle {\mathcal {P}},{\mathcal {Q}}} are the lifting (lifting the codomain of the input function to a higher dimensional space) and projection (projecting the codomain of the intermediate function to the output dimension) operators, respectively. These operators act pointwise on functions and are typically parametrized as multilayer perceptrons. σ {\displaystyle \sigma } is a pointwise nonlinearity, such as a rectified linear unit (ReLU), or a Gaussian error linear unit (GeLU). Each layer t = 1 , … , T {\displaystyle t=1,\dots ,T} has a respective local operator W t {\displaystyle W_{t}} (usually parameterized by a pointwise neural network), a kernel integral operator K t {\displaystyle {\mathcal {K}}_{t}} , and a bias function b t {\displaystyle b_{t}} . Given some intermediate functional representation v t {\displaystyle v_{t}} with domain D {\displaystyle D} in the t {\displaystyle t} -th hidden layer, a kernel integral operator K ϕ {\displaystyle {\mathcal {K}}_{\phi }} is defined as ( K ϕ v t ) ( x ) := ∫ D κ ϕ ( x , y , v t ( x ) , v t ( y ) ) v t ( y ) d y , {\displaystyle ({\mathcal {K}}_{\phi }v_{t})(x):=\int _{D}\kappa _{\phi }(x,y,v_{t}(x),v_{t}(y))v_{t}(y)dy,} where the kernel κ ϕ {\displaystyle \kappa _{\phi }} is a learnable implicit neural network, parametrized by ϕ {\displaystyle \phi } . In practice, one is often given the input function to the neural operator at a specific resolution. For instance, consider the setting where one is given the evaluation of v t {\displaystyle v_{t}} at n {\displaystyle n} points { y j } j n {\displaystyle \{y_{j}\}_{j}^{n}} . Borrowing from Nyström integral approximation methods such as Riemann sum integration and Gaussian quadrature, the above integral operation can be computed as follows: ∫ D κ ϕ ( x , y , v t ( x ) , v t ( y ) ) v t ( y ) d y ≈ ∑ j n κ ϕ ( x , y j , v t ( x ) , v t ( y j ) ) v t ( y j ) Δ y j , {\displaystyle \int _{D}\kappa _{\phi }(x,y,v_{t}(x),v_{t}(y))v_{t}(y)dy\approx \sum _{j}^{n}\kappa _{\phi }(x,y_{j},v_{t}(x),v_{t}(y_{j}))v_{t}(y_{j})\Delta _{y_{j}},} where Δ y j {\displaystyle \Delta _{y_{j}}} is the sub-area volume or quadrature weight associated to the point y j {\displaystyle y_{j}} . Thus, a simplified layer can be computed as v t + 1 ( x ) ≈ σ ( ∑ j n κ ϕ ( x , y j , v t ( x ) , v t ( y j ) ) v t ( y j ) Δ y j + W t ( v t ( y j ) ) + b t ( x ) ) . {\displaystyle v_{t+1}(x)\approx \sigma \left(\sum _{j}^{n}\kappa _{\phi }(x,y_{j},v_{t}(x),v_{t}(y_{j}))v_{t}(y_{j})\Delta _{y_{j}}+W_{t}(v_{t}(y_{j}))+b_{t}(x)\right).} The above approximation, along with parametrizing κ ϕ {\displaystyle \kappa _{\phi }} as an implicit neural network, results in the graph neural operator (GNO). There have been various parameterizations of neural operators for different applications. These typically differ in their parameterization of κ {\displaystyle \kappa } . The most popular instantiation is the Fourier neural operator (FNO). FNO takes κ ϕ ( x , y , v t ( x ) , v t ( y ) ) := κ ϕ ( x − y ) {\displaystyle \kappa _{\phi }(x,y,v_{t}(x),v_{t}(y)):=\kappa _{\phi }(x-y)} and by applying the convolution theorem, arrives at the following parameterization of the kernel integral operator: ( K ϕ v t ) ( x ) = F − 1 ( R ϕ ⋅ ( F v t ) ) ( x ) , {\displaystyle ({\mathcal {K}}_{\phi }v_{t})(x)={\mathcal {F}}^{-1}(R_{\phi }\cdot ({\mathcal {F}}v_{t}))(x),} where F {\displaystyle {\mathcal {F}}} represents the Fourier transform and R ϕ {\displaystyle R_{\phi }} represents the Fourier transform of some periodic function κ ϕ {\displaystyle \kappa _{\phi }} . That is, FNO parameterizes the kernel integration directly in Fourier space, using a prescribed number of Fourier modes. When the grid at which the input function is presented is uniform, the Fourier transform can be approximated using the discrete Fourier transform (DFT) with frequencies below some specified threshold. The discrete Fourier transform can be computed using a fast Fourier transform (FFT) implementation. == Training == Training neural operators is similar to the training process for a traditional neural network. Neural operators are typically trained in some Lp norm or Sobolev norm. In particular, for a dataset { ( a i , u i ) } i = 1 N {\displaystyle \{(a_{i},u_{i})\}_{i=1}^{N}} of size N {\displaystyle N} , neural operators minimize (a discretization of) L U ( { ( a i , u i ) } i = 1 N ) := ∑ i = 1 N ‖ u i − G θ ( a i ) ‖ U 2 {\displaystyle {\mathcal {L}}_{\mathca

  Read more →
• 

  DUAL table

  The DUAL table is a special one-row, one-column table present by default in Oracle and other database installations. In Oracle, the table has a single VARCHAR2(1) column called DUMMY that has a value of 'X'. It is suitable for use in selecting a pseudo column such as SYSDATE or USER. == Example use == Oracle's SQL syntax requires the FROM clause but some queries don't require any tables - DUAL can be used in these cases. == History == Charles Weiss explains why he created DUAL: I created the DUAL table as an underlying object in the Oracle Data Dictionary. It was never meant to be seen itself, but instead used inside a view that was expected to be queried. The idea was that you could do a JOIN to the DUAL table and create two rows in the result for every one row in your table. Then, by using GROUP BY, the resulting join could be summarized to show the amount of storage for the DATA extent and for the INDEX extent(s). The name, DUAL, seemed apt for the process of creating a pair of rows from just one. == Optimization == Beginning with 10g Release 1, Oracle no longer performs physical or logical I/O on the DUAL table, though the table still exists. DUAL is readily available for all authorized users in a SQL database. == In other database systems == Several other databases (including Microsoft SQL Server, MySQL, PostgreSQL, SQLite, and Teradata) enable one to omit the FROM clause entirely if no table is needed. This avoids the need for any dummy table. ClickHouse has a one-row system table system.one with a single column named "dummy" of type UInt8 and value 0. This table is implicitly used when no table is specified in the SELECT query. Firebird has a one-row system table RDB$DATABASE that is used in the same way as Oracle's DUAL, although it also has a meaning of its own. IBM Db2 has a view that resolves DUAL when using Oracle Compatibility. It also has a table called sysibm.sysdummy1 that has similar properties to the Oracle DUAL one. Informix: Informix version 11.50 and later has a table named sysmaster:"informix".sysdual with the same functionality but a more verbose name. You can use CREATE PUBLIC SYNONYM dual FOR sysmaster:"informix".sysdual to create a name dual in the current database with the same functionality. Microsoft Access: A table named DUAL may be created and the single-row constraint enforced via ADO (Table-less UNION query in MS Access) Microsoft SQL Server: SQL Server does not require a dummy table. Queries like 'select 1 + 1' can be run without a "from" clause/table name. MySQL allows DUAL to be specified as a table in queries that do not need data from any tables. It is suitable for use in selecting a result function such as SYSDATE() or USER(), although it is not essential. PostgreSQL: A DUAL-view can be added to ease porting from Oracle. Snowflake: DUAL is supported, but not explicitly documented. It appears in sample SQL for other operations in the documentation. SQLite: A VIEW named "dual" that works the same as the Oracle "dual" table can be created as follows: CREATE VIEW dual AS SELECT 'x' AS dummy; SAP HANA has a table called DUMMY that works the same as the Oracle "dual" table. Teradata database does not require a dummy table. Queries like 'select 1 + 1' can be run without a "from" clause/table name. Vertica has support for a DUAL table in their official documentation.

  Read more →
• 

  Color gradient

  In color science, a color gradient (also known as a color ramp or a color progression) specifies a range of position-dependent colors, usually used to fill a region. In assigning colors to a set of values, a gradient is a continuous colormap, a type of color scheme. In computer graphics, the term swatch has come to mean a palette of active colors. == Definitions == Color gradient is a set of colors arranged in a linear order (ordered) A continuous colormap is a curve through a colorspace === Strict definition === A colormap is a function which associate a real value r with point c in color space C {\displaystyle C} f : [ r m i n , r m a x ] ⊂ R → C {\displaystyle f:[r_{min},r_{max}]\subset \mathbf {R} \to C} which is defined by: a colorspace C an increasing sequence of sampling points r 0 < . . . < r m ∈ [ r m i n , r m a x ] {\displaystyle r_{0}<... Read more →