The Level-set method (LSM) is a conceptual framework for using level sets as a tool for numerical analysis of surfaces and shapes. LSM can perform numerical computations involving curves and surfaces on a fixed Cartesian grid without having to parameterize these objects. LSM makes it easier to perform computations on shapes with sharp corners and shapes that change topology (such as by splitting in two or developing holes). These characteristics make LSM effective for modeling objects that vary in time, such as an airbag inflating or a drop of oil floating in water. == Overview == The figure on the right illustrates several ideas about LSM. In the upper left corner is a bounded region with a well-behaved boundary. Below it, the red surface is the graph of a level set function φ {\displaystyle \varphi } determining this shape, and the flat blue region represents the X-Y plane. The boundary of the shape is then the zero-level set of φ {\displaystyle \varphi } , while the shape itself is the set of points in the plane for which φ {\displaystyle \varphi } is positive (interior of the shape) or zero (at the boundary). In the top row, the shape's topology changes as it is split in two. It is challenging to describe this transformation numerically by parameterizing the boundary of the shape and following its evolution. An algorithm can be used to detect the moment the shape splits in two and then construct parameterizations for the two newly obtained curves. On the bottom row, however, the plane at which the level set function is sampled is translated upwards, on which the shape's change in topology is described. It is less challenging to work with a shape through its level-set function rather than with itself directly, in which a method would need to consider all the possible deformations the shape might undergo. Thus, in two dimensions, the level-set method amounts to representing a closed curve Γ {\displaystyle \Gamma } (such as the shape boundary in our example) using an auxiliary function φ {\displaystyle \varphi } , called the level-set function. The curve Γ {\displaystyle \Gamma } is represented as the zero-level set of φ {\displaystyle \varphi } by Γ = { ( x , y ) ∣ φ ( x , y ) = 0 } , {\displaystyle \Gamma =\{(x,y)\mid \varphi (x,y)=0\},} and the level-set method manipulates Γ {\displaystyle \Gamma } implicitly through the function φ {\displaystyle \varphi } . This function φ {\displaystyle \varphi } is assumed to take positive values inside the region delimited by the curve Γ {\displaystyle \Gamma } and negative values outside. == The level-set equation == If the curve Γ {\displaystyle \Gamma } moves in the normal direction with a speed v {\displaystyle v} , then by chain rule and implicit differentiation, it can be determined that the level-set function φ {\displaystyle \varphi } satisfies the level-set equation ∂ φ ∂ t = v | ∇ φ | . {\displaystyle {\frac {\partial \varphi }{\partial t}}=v|\nabla \varphi |.} Here, | ⋅ | {\displaystyle |\cdot |} is the Euclidean norm (denoted customarily by single bars in partial differential equations), and t {\displaystyle t} is time. This is a partial differential equation, in particular a Hamilton–Jacobi equation, and can be solved numerically, for example, by using finite differences on a Cartesian grid. However, the numerical solution of the level set equation may require advanced techniques. Simple finite difference methods fail quickly. Upwinding methods such as the Godunov method are considered better; however, the level set method does not guarantee preservation of the volume and shape of the set level in an advection field that maintains shape and size, for example, a uniform or rotational velocity field. Instead, the shape of the level set may become distorted, and the level set may disappear over a few time steps. Therefore, high-order finite difference schemes, such as high-order essentially non-oscillatory (ENO) schemes, are often required, and even then, the feasibility of long-term simulations is questionable. More advanced methods have been developed to overcome this; for example, combinations of the leveling method with tracking marker particles suggested by the velocity field. == Example == Consider a unit circle in R 2 {\textstyle \mathbb {R} ^{2}} , shrinking in on itself at a constant rate, i.e. each point on the boundary of the circle moves along its inwards pointing normally at some fixed speed. The circle will shrink and eventually collapse down to a point. If an initial distance field is constructed (i.e. a function whose value is the signed Euclidean distance to the boundary, positive interior, negative exterior) on the initial circle, the normalized gradient of this field will be the circle normal. If the field has a constant value subtracted from it in time, the zero level (which was the initial boundary) of the new fields will also be circular and will similarly collapse to a point. This is due to this being effectively the temporal integration of the Eikonal equation with a fixed front velocity. == Applications == In mathematical modeling of combustion, LSM is used to describe the instantaneous flame surface, known as the G equation. Level-set data structures have been developed to facilitate the use of the level-set method in computer applications. Computational fluid dynamics Trajectory planning Optimization Image processing Computational biophysics Discrete complex dynamics (visualization of the parameter plane and the dynamic plane) == History == The level-set method was developed in 1979 by Alain Dervieux, and subsequently popularized by Stanley Osher and James Sethian. It has since become popular in many disciplines, such as image processing, computer graphics, computational geometry, optimization, computational fluid dynamics, and computational biology.
Connection string
In computing, a connection string is a string that specifies information about a data source and the means of connecting to it. It is passed in code to an underlying driver or provider in order to initiate the connection. Whilst commonly used for a database connection, the data source could also be a spreadsheet or text file. The connection string may include attributes such as the name of the driver, server and database, as well as security information such as user name and password. == Examples == This example shows a PostgreSQL connection string for connecting to wikipedia.com with SSL and a connection timeout of 180 seconds: DRIVER={PostgreSQL Unicode};SERVER=www.wikipedia.com;SSL=true;SSLMode=require;DATABASE=wiki;UID=wikiuser;Connect Timeout=180;PWD=ashiknoor Users of Oracle databases can specify connection strings: on the command line (as in: sqlplus scott/tiger@connection_string ) via environment variables ($TWO_TASK in Unix-like environments; %TWO_TASK% in Microsoft Windows environments) in local configuration files (such as the default $ORACLE_HOME/network/admin.tnsnames.ora) in LDAP-capable directory services
SPACEMAP
SPACEMAP (Korean: 스페이스맵) is a South Korean satellite orbit optimization and satellite communications company headquartered in Seoul, South Korea. The company was founded in 2021 by CEO, Douglas Deok-Soo Kim, as an offshoot of Hanyang University. It was funded by the Leader Research grant from the National Research Foundation of Korea with the goal of capitalizing on the growing space industry. == History == Kim initially began research into Voronoi diagrams at the University of Michigan. He met with Dr. Misoon Ma, former director of the Asia Division of the U.S. Air Force Office of Scientific Research (AFOSR) and was recruited to work with the U.S. Air force, using Voronoi diagrams for a satellite collision prevention program. After his work with the U.S. Air Force, Kim founded SPACEMAP Inc in September 2021. In 2023, the company was selected by Korea's Tech Incubator Program for Startups (TIPS) to be funded up to 17 billion KRW (approx. US$13 million) in 3 years. == Technology == The services provided by SPACEMAP are based on using dynamic Voronoi diagrams to predict satellite orbits with the aim of enhancing space mission safety and efficiency. For complex problems involving many moving points, Voronoi diagrams maintain a near-constant computation time regardless of the number of points involved. By utilizing Voronoi diagrams and artificial intelligence, the software can easily determine the number of neighboring satellites surrounding a specific satellite and calculate the distances between them, thereby predicting the probability of a collision. SPACEMAP claims their method to be superior in computational time and memory efficiency, compared to the previously established three-filter method. == Products == SPACEMAP offers satellite products and services including the following: AstroOne, a conjunction assessment, and optimal collision avoidance service for all space vehicles in both orbital and non-orbital motions. AstroOrca, providing data transmission for satellites in multiple orbits, launch optimization, shuttle logistics for space gas stations, and Active Debris Removal (ADR) itinerary. AstroLibrary, a library of RESTful APIs to access the C++ implementation of SPACEMAP's Voronoi diagram algorithms wrapped in a Python interface. It also provides real-time tracking of the North Korean reconnaissance satellite, Malligyong-1.
Vintage computer
A vintage computer is an older computer system that is largely regarded as obsolete. The personal computer has been around since around 1971, and in that time technological advancement means existing models get replaced every few years. Nevertheless, these otherwise useless computers have spawned a sub-culture of vintage computer collectors who often spend large sums for the rarest examples, not only to display but functionally restore. This involves active software development and adaptation to modern uses. This often includes homebrew developers and hackers who add on, update and create hybrid composites from new and old computers for uses they were otherwise never intended. Ethernet interfaces have been designed for many vintage 8-bit machines to allow limited connectivity to the Internet, where users can access discussion groups, bulletin boards, and software databases. Most of this hobby centers on computers made after 1960, though some collectors also specialize in older computers. The Vintage Computer Festival, an event held by the Vintage Computer Federation for the exhibition and celebration of vintage computers, has been held annually since 1997 and has expanded internationally. == By platform == === MITS Inc. === Micro Instrumentation and Telemetry Systems (MITS) produced the Altair 8800 in 1975. According to Harry Garland, the Altair 8800 was the product that catalyzed the microcomputer revolution of the 1970s. === IMSAI === The IMSAI 8080 is a clone of the Altair 8800. It was introduced in 1975, first as a kit, and later as an assembled system. The list price was $591 (equivalent to $3,584 in 2025) for a kit, and $931 (equivalent to $5,570 in 2025) assembled. === Processor Technology === Processor Technology produced the Sol-20. This was one of the first machines to have a case that included a keyboard; a design feature copied by many of later "home computers". === SWTPC === Southwest Technical Products Corporation (SWTPC) produced the 8-bit SWTPC 6800 and later the 16-bit SWTPC 6809 kits that employed the Motorola 68xx series microprocessors. === Apple Inc. === The earliest Apple Inc. personal computers, using the MOS Technology 6502 processors, are among some of the most collectible. They are relatively easy to maintain in an operational state thanks to Apple's use of readily available off-the-shelf parts. Apple I (1976): The Apple-1 was Apple's first product and has brought some of the highest prices ever paid for a microcomputer at auction. Apple II (1977): The Apple II series of computers are some of the easiest to adapt, thanks to the original expansion architecture designed for them. New peripheral cards are still being designed by an avid thriving community, thanks to the longevity of this platform, manufactured from 1977 through 1993. Numerous websites exist to support not only legacy users but new adopters who weren't even born when the Apple II was discontinued by Apple. Macintosh (1984): The original Macintosh used a 32-bit Motorola 68000 processor running at 7.8336 MHz and came with 128 KB of RAM. The list price was $2495 (equivalent to $7,732 in 2025).Perhaps because of its friendly design and first commercially successful graphical user interface as well as its enduring Finder application that persists on the most current Macs, the Macintosh is one of the most collected and used vintage computers. With dozens of websites around the world, old Macintosh hardware and software are input into daily use. The Macintosh had a strong presence in many early computer labs, creating a nostalgia factor for former students who recall their first computing experiences. === RCA === The COSMAC Elf in 1976 was an inexpensive (about $100) single-board computer that was easily built by hobbyists. Many people who could not afford an Altair could afford an ELF, which was based on the RCA 1802 chip. Because the chips are still available from other sources, modern recreations of the ELF are fairly common and there are several fan websites. === IBM === The IBM 1130 (1965) was a desk-sized small computer. It was the often the first computer used by many college students, still has a following of interested users. Most of the remaining 1130 systems in 2023 are in museums, but an emulator is available for users who don't have access to a physical 1130. The 5100 also has an avid collector and fan base. The PC series (5150 PC, 5155 Portable PC, 5160 PC/XT, 5170 PC/AT) has become very popular in recent years, with the earliest models (PC) being considered the most collectible. === Acorn BBC & Archimedes === The Acorn BBC Micro was a very popular British computer in the 1980s with home and educational users and enjoyed near-universal usage in British schools into the mid-1990s. It was possible to use 100K 5+1⁄4-inch disks, and it had many expansion ports. The Archimedes series – the de facto successor to the BBC Micro – has also enjoyed a following in recent years, thanks to its status as the first computer to be based around ARM's RISC microprocessor. === Tandy/Radio Shack === The Tandy/RadioShack Model 100 is still widely collected and used as one of the earliest examples of a truly portable computer. Other Tandy offerings, such as the TRS-80 line, are also very popular, and early systems, like the Model I, in good condition can command premium prices on the vintage computer market. === Sinclair === The Sinclair ZX81 and ZX Spectrum series were the most popular British home computers of the early 1980s, with a wide choice of emulators available for both platforms. The Spectrum in particular enjoys a cult following due to its popularity as a games platform, with new games titles still being developed even today. Original "rubber key" Spectrums fetch the highest prices on the second-hand market, with the later Amstrad-built models attracting less of a following. The earlier ZX81 is not as popular in original hardware form due to its monochrome display and limited abilities next to the Spectrum, but still unassembled ZX81 kits still appear on eBay occasionally. === MSX === Although nearly nonexistent in the United States, the MSX architecture has strong communities of fans and hobbyists worldwide, particularly in Japan (where the standard was conceived and developed), South Korea (the only country that had an MSX-based game console, Zemmix), Netherlands, Spain, Brazil, Argentina, Russia, Chile, the Middle East, and others. New hardware and software are being actively developed to this day as well. One of the latest fundamental (from hardware and software perspectives) revivals of the MSX is the GR8BIT. === Robotron === The Robotron Z1013 was an East German home computer produced by VEB Robotron. It had a U880 processor, 16 KB RAM, and a membrane keyboard. The KC 85 series of computers was a modular 8-bit computer system used in East German schools. === Commodore === VIC-20 Commodore 64 Commodore PET Amiga === Xerox === The Xerox Alto, designed and manufactured by Xerox PARC and released in 1973, was the first personal computer equipped with a graphic user interface. In 1979, Steve Jobs of Apple Inc. arranged for his engineers to visit Xerox in order to see the Alto. The design concepts of the Alto soon appeared in the Apple Lisa and Macintosh systems. The Xerox Star, also known as the 8010/40, was made available in 1981. It followed on the Alto. Like the Alto, this machine was expensive and was only intended for corporate office usage. Therefore, being out of the price range of the average user, this product had little market penetration. === Silicon Graphics === The SGI Indy, built in 1993 for Silicon Graphics has a history of usage in the development of the Nintendo 64 as well as various CGI projects throughout the 1990s and early 2000s. The Indy and other machines in the SGI lineup have remained cult classics.
Content Credentials
Content Credentials (also known as C2PA signatures) are a digital media metadata specification. They aim to provide provenance information about a piece of media (such as an image or a video) and help prove its authenticity. They are described as the equivalent of nutrition labels for digital media. One of the stated goal of this specification is to fight online disinformation. The specification is written and maintained by the Coalition for Content Provenance and Authenticity (C2PA), a group of many media and tech organizations including Adobe, Amazon, the BBC, Google, Meta, Microsoft, OpenAI and Sony. Another organization, the Content Authenticity Initiative (CAI), is responsible for promoting the standard and accelerate its adoption. The standard relies on cryptographic digital signatures. == Adoption == There are two main stakeholders who can implement Content Credentials: Producers (softwares and hardwares that produce or modify digital media) and publishers (softwares that show digital media to users). === Producers === ==== Adobe ==== Adobe is one of the first companies to implement the specification, announcing support in Photoshop in 2021. Content Credentials can be enabled and the complete history of edits is kept. ==== Google ==== Google announced support for Content Credentials on its Pixel 10 phones in August 2025. The Content Credentials are embedded on each picture taken from the Pixel Camera, and modifications done using Google Photos. Information include picture timestamp and a non-identifiable signature that proves it was taken from a Pixel 10. As for Google Photos, a list of AI and non-AI edits are kept. Google is the first company to introduce support for Content Credentials on either phones or consumer-grade devices, and also the first company to make it available for free to all users. ==== Nikon ==== Nikon announced in 2024 that their Z6 III camera would support embedding Content Credentials in its photos. However, in 2025, a vulnerability was discovered in the software of the camera that allowed to combine unauthentic images with authentic photos and still have the resulting image with a valid digital signature. Nikon revoked the certificates. ==== Media organizations ==== CBC/Radio-Canada and the BBC both have started attaching Content Credentials to media they produce or verify. ==== OpenAI ==== OpenAI embeds Content Credentials on the images and videos it generates that includes that the media was created by AI using their platforms. ==== Sony ==== In June 2025, Sony announced the release of its Camera Verify system for press photographers and news editors using C2PA digital signatures. Initially, the system will be limited to still images, high‑end cameras, and selected news agencies. Registration with Sony Creators' Cloud is also required. === Publishers === ==== LinkedIn ==== In 2024, LinkedIn started showing a "CR" icon on images that contain Content Credentials of AI-generated images. In 2025, they announced a partnership with Adobe to allow photographers to prove ownership of images using Content Credentials. ==== TikTok ==== TikTok announced in 2024 that an "AI-generated" label would be applied to videos containing Content Credentials if they were AI-generated. In 2025, they announced that users could control the amount of AI-generated content they see, using self-reported labels, Content Credentials and an invisible, proprietary AI watermark embedded in videos by their AI editor tool. ==== YouTube ==== In 2024, YouTube started showing to users a label that reads "captured with a camera" on videos that show authentic, unedited videos taken by Content Credentials-compatible cameras.
LMArena
Arena (formerly LMArena and Chatbot Arena) is a public, web-based platform that evaluates large language models (LLMs). Users enter prompts for two anonymous models to respond to and vote on the model that gave the better response, after which the models' identities are revealed. Users can also choose models to test themselves via the "Direct" selection. Companies which have supplied the company with their large language models include OpenAI, Google DeepMind, and Anthropic. The website has been used for preview releases of upcoming models. Chinese company DeepSeek tested its prototype models in the Arena months before its R1 model gained attention in Western media. Other notable pre-release models include OpenAI's GPT-5 under the codename "summit" and Google DeepMind's Gemini 2.5 Flash Image (an image-generation and editing model) under the codename "Nano Banana". Research has identified specific limitations in Arena's methodology. == History == Chatbot Arena was released on April 24, 2023. In June 2024, Chatbot Arena added image support. In September 2024, Chatbot Arena moved to its own dedicated domain name, lmarena.ai (or LMArena). In April 2025, Meta released Llama 4. Llama 4 Maverick beat GPT-4o and Gemini 2.0 Flash on LMArena, but the version of Maverick on LMArena unfairly differed from the publicly available version. LMArena updated their policies in response. In April 2025, LMArena incorporated as an independent company. That May, LMArena raised $100 million in a seed funding round, valuing the company at $600 million. Participants in the seed funding round included Andreessen Horowitz, UC Investments, Lightspeed Venture Partners, Felicis Ventures, and Kleiner Perkins. On January 6, 2026, LMArena announced the closing of a $150 million Series A funding round, bringing the company’s post-money valuation to approximately $1.7 billion. The round was led by Felicis and UC Investments (University of California), with participation from Andreessen Horowitz, The House Fund, LDVP, Kleiner Perkins, Lightspeed Venture Partners, and Laude Ventures. In January 2026, LMArena added video support. On January 28, 2026, LMArena rebranded to "Arena".
Rider Spoke
Rider Spoke developed by Blast Theory in collaboration with the Mixed Reality Lab was first staged at the Barbican, London in October 2007. Created for cyclists, it combines elements of theatre, performance, game play and state of the art technology. Rider Spoke was built in the IPerG project on the EQUIP architecture. Rider Spoke has since been presented in Athens (2008), Brighton (2008), Budapest (2008), Sydney (2009, Adelaide (2009) and Liverpool (2010).