Symbolic regression (SR) is a type of regression analysis that searches the space of mathematical expressions to find the model that best fits a given dataset, both in terms of accuracy and simplicity. No particular model is provided as a starting point for symbolic regression. Instead, initial expressions are formed by randomly combining mathematical building blocks such as mathematical operators, analytic functions, constants, and state variables. Usually, a subset of these primitives will be specified by the person operating it, but that's not a requirement of the technique. The symbolic regression problem for mathematical functions has been tackled with a variety of methods, including recombining equations most commonly using genetic programming, as well as more recent methods utilizing Bayesian methods and neural networks. Another non-classical alternative method to SR is called Universal Functions Originator (UFO), which has a different mechanism, search-space, and building strategy. Further methods such as Exact Learning attempt to transform the fitting problem into a moments problem in a natural function space, usually built around generalizations of the Meijer-G function. By not requiring a priori specification of a model, symbolic regression isn't affected by human bias, or unknown gaps in domain knowledge. It attempts to uncover the intrinsic relationships of the dataset, by letting the patterns in the data itself reveal the appropriate models, rather than imposing a model structure that is deemed mathematically tractable from a human perspective. The fitness function that drives the evolution of the models takes into account not only error metrics (to ensure the models accurately predict the data), but also special complexity measures, thus ensuring that the resulting models reveal the data's underlying structure in a way that's understandable from a human perspective. This facilitates reasoning and favors the odds of getting insights about the data-generating system, as well as improving generalisability and extrapolation behaviour by preventing overfitting. Accuracy and simplicity may be left as two separate objectives of the regression—in which case the optimum solutions form a Pareto front—or they may be combined into a single objective by means of a model selection principle such as minimum description length. It has been proven that symbolic regression is an NP-hard problem. Nevertheless, if the sought-for equation is not too complex it is possible to solve the symbolic regression problem exactly by generating every possible function (built from some predefined set of operators) and evaluating them on the dataset in question. == Difference from classical regression == While conventional regression techniques seek to optimize the parameters for a pre-specified model structure, symbolic regression avoids imposing prior assumptions, and instead infers the model from the data. In other words, it attempts to discover both model structures and model parameters. This approach has the disadvantage of having a much larger space to search, because not only the search space in symbolic regression is infinite, but there are an infinite number of models which will perfectly fit a finite data set (provided that the model complexity isn't artificially limited). This means that it will possibly take a symbolic regression algorithm longer to find an appropriate model and parametrization, than traditional regression techniques. This can be attenuated by limiting the set of building blocks provided to the algorithm, based on existing knowledge of the system that produced the data; but in the end, using symbolic regression is a decision that has to be balanced with how much is known about the underlying system. Nevertheless, this characteristic of symbolic regression also has advantages: because the evolutionary algorithm requires diversity in order to effectively explore the search space, the result is likely to be a selection of high-scoring models (and their corresponding set of parameters). Examining this collection could provide better insight into the underlying process, and allows the user to identify an approximation that better fits their needs in terms of accuracy and simplicity. == Benchmarking == === SRBench === In 2021, SRBench was proposed as a large benchmark for symbolic regression. In its inception, SRBench featured 14 symbolic regression methods, 7 other ML methods, and 252 datasets from PMLB. The benchmark intends to be a living project: it encourages the submission of improvements, new datasets, and new methods, to keep track of the state of the art in SR. === SRBench Competition 2022 === In 2022, SRBench announced the competition Interpretable Symbolic Regression for Data Science, which was held at the GECCO conference in Boston, MA. The competition pitted nine leading symbolic regression algorithms against each other on a novel set of data problems and considered different evaluation criteria. The competition was organized in two tracks, a synthetic track and a real-world data track. ==== Synthetic Track ==== In the synthetic track, methods were compared according to five properties: re-discovery of exact expressions; feature selection; resistance to local optima; extrapolation; and sensitivity to noise. Rankings of the methods were: QLattice PySR (Python Symbolic Regression) uDSR (Deep Symbolic Optimization) ==== Real-world Track ==== In the real-world track, methods were trained to build interpretable predictive models for 14-day forecast counts of COVID-19 cases, hospitalizations, and deaths in New York State. These models were reviewed by a subject expert and assigned trust ratings and evaluated for accuracy and simplicity. The ranking of the methods was: uDSR (Deep Symbolic Optimization) QLattice geneticengine (Genetic Engine) == Non-standard methods == Most symbolic regression algorithms prevent combinatorial explosion by implementing evolutionary algorithms that iteratively improve the best-fit expression over many generations. Recently, researchers have proposed algorithms utilizing other tactics in AI. Silviu-Marian Udrescu and Max Tegmark developed the "AI Feynman" algorithm, which attempts symbolic regression by training a neural network to represent the mystery function, then runs tests against the neural network to attempt to break up the problem into smaller parts. For example, if f ( x 1 , . . . , x i , x i + 1 , . . . , x n ) = g ( x 1 , . . . , x i ) + h ( x i + 1 , . . . , x n ) {\displaystyle f(x_{1},...,x_{i},x_{i+1},...,x_{n})=g(x_{1},...,x_{i})+h(x_{i+1},...,x_{n})} , tests against the neural network can recognize the separation and proceed to solve for g {\displaystyle g} and h {\displaystyle h} separately and with different variables as inputs. This is an example of divide and conquer, which reduces the size of the problem to be more manageable. AI Feynman also transforms the inputs and outputs of the mystery function in order to produce a new function which can be solved with other techniques, and performs dimensional analysis to reduce the number of independent variables involved. The algorithm was able to "discover" 100 equations from The Feynman Lectures on Physics, while a leading software using evolutionary algorithms, Eureqa, solved only 71. AI Feynman, in contrast to classic symbolic regression methods, requires a very large dataset in order to first train the neural network and is naturally biased towards equations that are common in elementary physics.
Legal information retrieval
Legal information retrieval is the science of information retrieval applied to legal text, including legislation, case law, and scholarly works. Accurate legal information retrieval is important to provide access to the law to laymen and legal professionals. Its importance has increased because of the vast and quickly increasing amount of legal documents available through electronic means. Legal information retrieval is a part of the growing field of legal informatics. In a legal setting, it is frequently important to retrieve all information related to a specific query. However, commonly used boolean search methods (exact matches of specified terms) on full text legal documents have been shown to have an average recall rate as low as 20 percent, meaning that only 1 in 5 relevant documents are actually retrieved. In that case, researchers believed that they had retrieved over 75% of relevant documents. This may result in failing to retrieve important or precedential cases. In some jurisdictions this may be especially problematic, as legal professionals are ethically obligated to be reasonably informed as to relevant legal documents. Legal Information Retrieval attempts to increase the effectiveness of legal searches by increasing the number of relevant documents (providing a high recall rate) and reducing the number of irrelevant documents (a high precision rate). This is a difficult task, as the legal field is prone to jargon, polysemes (words that have different meanings when used in a legal context), and constant change. Techniques used to achieve these goals generally fall into three categories: boolean retrieval, manual classification of legal text, and natural language processing of legal text. == Problems == Application of standard information retrieval techniques to legal text can be more difficult than application in other subjects. One key problem is that the law rarely has an inherent taxonomy. Instead, the law is generally filled with open-ended terms, which may change over time. This can be especially true in common law countries, where each decided case can subtly change the meaning of a certain word or phrase. Legal information systems must also be programmed to deal with law-specific words and phrases. Though this is less problematic in the context of words which exist solely in law, legal texts also frequently use polysemes, words may have different meanings when used in a legal or common-speech manner, potentially both within the same document. The legal meanings may be dependent on the area of law in which it is applied. For example, in the context of European Union legislation, the term "worker" has four different meanings: Any worker as defined in Article 3(a) of Directive 89/391/EEC who habitually uses display screen equipment as a significant part of his normal work. Any person employed by an employer, including trainees and apprentices but excluding domestic servants; Any person carrying out an occupation on board a vessel, including trainees and apprentices, but excluding port pilots and shore personnel carrying out work on board a vessel at the quayside; Any person who, in the Member State concerned, is protected as an employee under national employment law and in accordance with national practice; It also has the common meaning: A person who works at a specific occupation. Though the terms may be similar, correct information retrieval must differentiate between the intended use and irrelevant uses in order to return the correct results. Even if a system overcomes the language problems inherent in law, it must still determine the relevancy of each result. In the context of judicial decisions, this requires determining the precedential value of the case. Case decisions from senior or superior courts may be more relevant than those from lower courts, even where the lower court's decision contains more discussion of the relevant facts. The opposite may be true, however, if the senior court has only a minor discussion of the topic (for example, if it is a secondary consideration in the case). An information retrieval system must also be aware of the authority of the jurisdiction. A case from a binding authority is most likely of more value than one from a non-binding authority. Additionally, the intentions of the user may determine which cases they find valuable. For instance, where a legal professional is attempting to argue a specific interpretation of law, he might find a minor court's decision which supports his position more valuable than a senior courts position which does not. He may also value similar positions from different areas of law, different jurisdictions, or dissenting opinions. Overcoming these problems can be made more difficult because of the large number of cases available. The number of legal cases available via electronic means is constantly increasing (in 2003, US appellate courts handed down approximately 500 new cases per day), meaning that an accurate legal information retrieval system must incorporate methods of both sorting past data and managing new data. == Techniques == === Boolean searches === Boolean searches, where a user may specify terms such as use of specific words or judgments by a specific court, are the most common type of search available via legal information retrieval systems. They are widely implemented but overcome few of the problems discussed above. The recall and precision rates of these searches vary depending on the implementation and searches analyzed. One study found a basic boolean search's recall rate to be roughly 20%, and its precision rate to be roughly 79%. Another study implemented a generic search (that is, not designed for legal uses) and found a recall rate of 56% and a precision rate of 72% among legal professionals. Both numbers increased when searches were run by non-legal professionals, to a 68% recall rate and 77% precision rate. This is likely explained because of the use of complex legal terms by the legal professionals. === Manual classification === In order to overcome the limits of basic boolean searches, information systems have attempted to classify case laws and statutes into more computer friendly structures. Usually, this results in the creation of an ontology to classify the texts, based on the way a legal professional might think about them. These attempt to link texts on the basis of their type, their value, and/or their topic areas. Most major legal search providers now implement some sort of classification search, such as Westlaw's “Natural Language” or LexisNexis' Headnote searches. Additionally, both of these services allow browsing of their classifications, via Westlaw's West Key Numbers or Lexis' Headnotes. Though these two search algorithms are proprietary and secret, it is known that they employ manual classification of text (though this may be computer-assisted). These systems can help overcome the majority of problems inherent in legal information retrieval systems, in that manual classification has the greatest chances of identifying landmark cases and understanding the issues that arise in the text. In one study, ontological searching resulted in a precision rate of 82% and a recall rate of 97% among legal professionals. The legal texts included, however, were carefully controlled to just a few areas of law in a specific jurisdiction. The major drawback to this approach is the requirement of using highly skilled legal professionals and large amounts of time to classify texts. As the amount of text available continues to increase, some have stated their belief that manual classification is unsustainable. === Natural language processing === In order to reduce the reliance on legal professionals and the amount of time needed, efforts have been made to create a system to automatically classify legal text and queries. Adequate translation of both would allow accurate information retrieval without the high cost of human classification. These automatic systems generally employ Natural Language Processing (NLP) techniques that are adapted to the legal domain, and also require the creation of a legal ontology. Though multiple systems have been postulated, few have reported results. One system, “SMILE,” which attempted to automatically extract classifications from case texts, resulted in an f-measure (which is a calculation of both recall rate and precision) of under 0.3 (compared to perfect f-measure of 1.0). This is probably much lower than an acceptable rate for general usage. Despite the limited results, many theorists predict that the evolution of such systems will eventually replace manual classification systems. === Citation-Based ranking === In the mid-90s the Room 5 case law retrieval project used citation mining for summaries and ranked its search results based on citation type and count. This slightly pre-dated the PageRank algorithm at Stanford which was also a citation-based ranking. Ranking of results was based
Image tracing
In computer graphics, image tracing, raster-to-vector conversion or raster vectorization is the conversion of raster graphics into vector graphics. == Background == An image does not have any structure: it is just a collection of marks on paper, grains in film, or pixels in a bitmap. While such an image is useful, it has some limits. If the image is magnified enough, its artifacts appear. The halftone dots, film grains, and pixels become apparent. Images of sharp edges become fuzzy or jagged. See, for example, pixelation. Ideally, a vector image does not have the same problem. Edges and filled areas are represented as mathematical curves or gradients, and they can be magnified arbitrarily (though of course the final image must also be rasterized in to be rendered, and its quality depends on the quality of the rasterization algorithm for the given inputs). The task in vectorization is to convert a two-dimensional image into a two-dimensional vector representation of the image. It is not examining the image and attempting to recognize or extract a three-dimensional model that may be depicted; i.e. it is not a vision system. For most applications, vectorization also does not involve optical character recognition; characters are treated as lines, curves, or filled objects without attaching any significance to them. In vectorization, the shape of the character is preserved, so artistic embellishments remain. Vectorization is the inverse operation corresponding to rasterization, as integration is to differentiation. And, just as with these other operations, while rasterization is fairly straightforward and algorithmic, vectorization involves the reconstruction of lost information and therefore requires heuristic methods. Synthetic images such as maps, cartoons, logos, clip art, and technical drawings are suitable for vectorization. Those images could have been originally made as vector images because they are based on geometric shapes or drawn with simple curves. Continuous tone photographs (such as live portraits) are not good candidates for vectorization. The input to vectorization is an image, but an image may come in many forms such as a photograph, a drawing on paper, or one of several raster file formats. Programs that do raster-to-vector conversion may accept bitmap formats such as TIFF, BMP and PNG. The output is a vector file format. Common vector formats are SVG, DXF, EPS, EMF and AI. Vectorization can be used to update images or recover work. Personal computers often come with a simple paint program that produces a bitmap output file. These programs allow users to make simple illustrations by adding text, drawing outlines, and filling outlines with a specific color. Only the results of these operations (the pixels) are saved in the resulting bitmap; the drawing and filling operations are discarded. Vectorization can be used to recapture some of the information that was lost. Vectorization is also used to recover information that was originally in a vector format but has been lost or has become unavailable. A company may have commissioned a logo from a graphic arts firm. Although the graphics firm used a vector format, the client company may not have received a copy of that format. The company may then acquire a vector format by scanning and vectorizing a paper copy of the logo. == Process == Vectorization starts with an image. === Manual === The image can be vectorized manually. A person could look at the image, make some measurements, and then write the output file by hand. That was the case for the vectorization of a technical illustration about neutrinos. The illustration has a few geometric shapes and a lot of text; it was relatively easy to convert the shapes, and the SVG vector format allows the text (even subscripts and superscripts) to be entered easily. The original image did not have any curves (except for the text), so the conversion is straightforward. Curves make the conversion more complicated. Manual vectorization of complicated shapes can be facilitated by the tracing function built into some vector graphics editing programs. If the image is not yet in machine readable form, then it has to be scanned into a usable file format. Once there is a machine-readable bitmap, the image can be imported into a graphics editing program (such as Adobe Illustrator, CorelDRAW, or Inkscape). Then a person can manually trace the elements of the image using the program's editing features. Curves in the original image can be approximated with lines, arcs, and Bézier curves. An illustration program allows spline knots to be adjusted for a close fit. Manual vectorization is possible, but it can be tedious. Although graphics drawing programs have been around for a long time, artists may find the freehand drawing facilities awkward even when a drawing tablet is used. Instead of using a program, Pepper recommends making an initial sketch on paper. Instead of scanning the sketch and tracing it freehand in the computer, Pepper states: "Those proficient with a graphic tablet and stylus could make the following changes directly in CorelDRAW by using a scan of the sketch as an underlay and drawing over it. I prefer to use pen and ink, and a light table"; most of the final image was traced by hand in ink. Later the line-drawing image was scanned at 600 dpi, cleaned up in a paint program, and then automatically traced with a program. Once the black and white image was in the graphics program, some other elements were added and the figure was colored. Similarly, Ploch recreated a design from a digital photograph. The JPEG was imported and some "basic shapes" were traced by hand and colored in the graphics drawing program; more complex shapes were handled differently. Ploch used a bitmap editor to remove the background and crop the more complex image components. He then printed the image and traced it by hand onto tracing paper to get a clean black and white line drawing. That drawing was scanned and then vectorized with a program. === Automatic === Some programs automate the vectorization process. Example programs are Adobe Illustrator, Inkscape, Corel's PowerTRACE, and Potrace. Some of these programs have a command line interface while others are interactive that allow the user to adjust the conversion settings and view the result. Adobe Streamline is not only an interactive program, but it also allows a user to manually edit the input bitmap and the output curves. Corel's PowerTRACE is accessed through CorelDRAW; CorelDRAW can be used to modify the input bitmap and edit the output curves. Adobe Illustrator has a facility to trace individual curves. Automated programs can have mixed results. A program (PowerTRACE) was used to convert a PNG map to SVG. The program did a good job on the map boundaries (the most tedious task in the tracing) and the settings dropped out all the text (small objects). The text was manually re-inserted. Other conversions may not go as well. The results depend on having high-quality scans, reasonable settings, and good algorithms. Scanned images often have a lot of noise, which can require additional work to clean up. == Options == There are many different image styles and possibilities, and no single vectorization method works well on all images. Consequently, vectorization programs have many options that influence the result. One issue is what the predominant shapes are. If the image is of a fill-in form, then it will probably have just vertical and horizontal lines of a constant width. The program's vectorization should take that into account. On the other hand, a CAD drawing may have lines at any angle, there may be curved lines, and there may be several line weights (thick for objects and thin for dimension lines). Instead of (or in addition to) curves, the image may contain outlines filled with the same color. Adobe Streamline allows users to select a combination of line recognition (horizontal and vertical lines), centerline recognition, or outline recognition. Streamline also allows small outline shapes to be thrown out; the notion is such small shapes are noise. The user may set the noise level between 0 and 1000; an outline that has fewer pixels than that setting is discarded. Another issue is the number of colors in the image. Even images that were created as black on white drawings may end up with many shades of gray. Some line-drawing routines employ anti-aliasing; a pixel completely covered by the line will be black, but a pixel that is only partially covered will be gray. If the original image is on paper and is scanned, there is a similar result: edge pixels will be gray. Sometimes images are compressed (e.g., JPEG images), and the compression will introduce gray levels. Many of the vectorization programs will group same-color pixels into lines, curves, or outlined shapes. If each possible color is grouped into its object, there can be an enormous number of objects. Instead, the user is asked to s
QANDA
QANDA (stands for 'Q and A') is an AI-based learning platform developed by Mathpresso Inc., a South Korea-based education technology company. Its best known feature is a solution search, which uses optical character recognition technology to scan problems and provide step-by-step solutions and learning content. As of March 2024, QANDA solved over 6.3 billion questions. QANDA has 90 million total registered users and has reached 8 million monthly active users (MAU) in 50 countries. 90% of the cumulative users are from overseas such as Vietnam and Indonesia. In January 2024, its MathGPT, a math-specific small large language model set a new world record, surpassed Microsoft's 'ToRA 13B', the previous record holder in benchmarks assessing mathematical performance such as 'MATH' (high school math) and 'GSM8K' (grade school math). 'MathGPT' was co-developed with Upstage and KT. In March 2024, Mathpresso launched 'Cramify' (formerly known as Prep.Pie), an AI-powered study material generator designed to create personalized exam prep materials for U.S. college students. It uses generative AI to create customized study materials uploaded by students. Its features include a range of tools including study summarizer and question solver. == History == Co-founder Jongheun ‘Ray’ Lee first came up with the idea of QANDA during his freshman year in college. While he was tutoring to earn money, Lee realized that the quality of education a student receives is greatly based on their location. Lee saw his K-12 students were regularly asking similar questions and realized that these questions were from a pre-selected number of textbooks currently being used in schools. He decided to team up with his high school friend, Yongjae ‘Jake’ Lee to build a platform whereby, one uses a mobile app to scan and submit questions, and students can ask and receive detailed responses. Lee's school friends, Wonguk Jung and Hojae Jeong, joined the team. In June 2015, Mathpresso, Inc. was founded in Seoul, South Korea. In January 2016, Mathpresso's first product QANDA was launched. It supported a Q&A feature between students and tutors. In October 2017, QANDA introduced an AI-based search capability that permitted users to search for answers in seconds. In April 2020, Jake Yongjae Lee(CEO & co-founder) and Ray Jongheun Lee (co-founder) were selected as Forbes 30 under 30 Asia. In June 2021, QANDA raised $50 million in series C funding. Jake Yongjae Lee was recognized as an Innovator Under 35 by MIT Technology Review. In November 2021, QANDA secured a strategic investment from Google. Since its inception, it has received backing in Series C funding from investors namely Google, Yellowdog, GGV Capital, Goodwater Capital, KDB, and SKS Private Equity with participation from SoftBank Ventures Asia, Legend Capital, Mirae Asset Venture Investment, and Smilegate Investment. In September 2023, Mathpresso has raised $8 million (10 billion KRW) from Korea's telecom giant, KT. The total cumulative investment is about 130 million US dollars. The partnership aims to accelerate the development of an education-specific Large Language Model. The company intends to incorporate the LLM model to fortify its AI tutor, which later will be integrated into the existing services: QANDA App, B2B & B2G Saas, and 1:1 online tutoring (QANDA Tutor). == Features == QANDA features OCR-based solution search, one-on-one Q&A tutoring, a study timer. In 2021, QANDA launched additional features, including the premium subscription model that offers unlimited “byte-sized” micro-video lectures and the community feature that enhances collaborative learning. In 2021, QANDA launched QANDA Tutor, a tablet-based 1:1 tutoring service and QANDA Study, a 1:N online school in Vietnam. In 2022, QANDA launched an exam prep feature that offers past exam materials from school via online. This feature is currently available in South Korea. In August 2023, QANDA launched a beta version of an LLM-powered AI Tutor. == Awards and recognition == Best Hidden Gems of 2017 by Google Playstore 2018 AWS AI Startup Challenge Award National representative for the Google AI for Social Good APAC, 2018 Best Self-Improvement Apps of 2018 by Google Playstore GSV Edtech 150 — the Most Transformational Growth Companies in Digital Learning Speaker at the Google App Summit, 2021 Selected as a prospect unicorn company by Korea Technology Finance Corporation in 2023 Winner of G20-DIA Global Pitching in 2023 2021, 2022, 2023 East Asia EdTech 150 by HolonIQ
Glyph (data visualization)
In the context of data visualization, a glyph is any marker, such as an arrow or similar marking, used to specify part of a visualization. This is a representation to visualize data where the data set is presented as a collection of visual objects. These visual objects are collectively called a glyph. It helps visualizing data relation in data analysis, statistics, etc. by using any custom notation. In the context of data visualization, a glyph is the visual representation of a piece of data where the attributes of a graphical entity are dictated by one or more attributes of a data record. == Constructing glyphs == Glyph construction can be a complex process when there are many dimensions to be represented in the visualization. Maguire et al proposed a taxonomy based approach to glyph-design that uses a tree to guide the visual encodings used to representation various data items. Duffy et al created perhaps one of the most complex glyph representations with their representation of sperm movement.
Percept (artificial intelligence)
A percept is the input that an intelligent agent is perceiving at any given moment. It is essentially the same concept as a percept in psychology, except that it is being perceived not by the brain but by the agent. A percept is detected by a sensor, often a camera, processed accordingly, and acted upon by an actuator. Each percept is added to a "percept sequence", which is a complete history of each percept ever detected. The agent's action at any instant point may depend on the entire percept sequence up to that particular instant point. An intelligent agent chooses how to act not only based on the current percept, but the percept sequence. The next action is chosen by the agent function, which maps every percept to an action. For example, if a camera were to record a gesture, the agent would process the percepts, calculate the corresponding spatial vectors, examine its percept history, and use the agent program (the application of the agent function) to act accordingly. == Examples == Examples of percepts include inputs from touch sensors, cameras, infrared sensors, sonar, microphones, mice, and keyboards. A percept can also be a higher-level feature of the data, such as lines, depth, objects, faces, or gestures.
Once (dating platform)
Once is an online dating platform founded in 2015. The platform offers users one selected match per day for more meaningful connections. == History == Once was established in 2015, the founders included dating industry entrepreneur Jean Meyer, who became a CEO of the company, as well as Guillaume Sempe and Guilhem Duche. It focused on providing a single daily match to its users. On its early stages Once secured a $3.5 million seed round from Partech Ventures and some private investors. The same year, it opened offices in Paris, and London. By 2016, it reached 1 million users. In 2020, the company was acquired by Dating Group for $18 million. Following the acquisition, Once underwent rebranding. Alexandra Beaumont took over leadership of the brand in 2021, driving growth, rebranding, and innovation. == Overview == Once provides an online dating service with a focus on thoughtful connections. Users receive one selected match per day, which encourages meaningful interactions. The platform operates primarily in the United States, the United Kingdom, Canada, France, and Spain. The platform is supported by Android, iOS, and Apple Watch OS.