Azure Data Lake is a scalable data storage and analytics service. The service is hosted in Azure, Microsoft's public cloud. == History == Azure Data Lake service was released on November 16, 2016. It is based on COSMOS, which is used to store and process data for applications such as Azure, AdCenter, Bing, MSN, Skype and Windows Live. COSMOS features a SQL-like query engine called SCOPE upon which U-SQL was built. == Storage == Data Lake Storage is a cloud service to store structured, semi-structured or unstructured data produced from applications including social networks, relational data, sensors, videos, web apps, mobile or desktop devices. A single account can store trillions of files where a single file can be greater than a petabyte in size. == Analytics == Data Lake Analytics is a parallel on-demand job service. The parallel processing system is based on Microsoft Dryad. Dryad can represent arbitrary Directed Acyclic Graphs (DAGs) of computation. Data Lake Analytics provides a distributed infrastructure that can dynamically allocate resources so that customers pay for only the services they use. The system uses Apache YARN, the part of Apache Hadoop which governs resource management across clusters. Data Lake Store supports any application that uses the Hadoop Distributed File System (HDFS) interface. == U-SQL == U-SQL is a query language for Data Lake Analytics parallel data transformation and processing programs. It combines SQL and C#: it is and an evolution of the declarative SQL language with native extensibility through user code written in C#. U-SQL uses C# data types and the C# expression language. == Retirement == In 2021, Microsoft announced the 2024 retirement of the original Azure Data Lake Storage, now called "Gen1". The related Azure Data Lake Analytics / U-SQL technologies are also being retired. Azure Data Lake Storage Gen2, an extension of Azure Storage, will continue. The suggested replacement technologies are Azure Synapse Analytics and Apache Spark.
Group of Governmental Experts on Lethal Autonomous Weapons Systems
The Group of Governmental Experts on Lethal Autonomous Weapons Systems, commonly known as the GGE on LAWS, refers to a group of governmental experts established under the framework of the Convention on Certain Conventional Weapons (CCW), a United Nations arms control framework. The group examines legal, ethical, societal and moral questions that arise from the increased use of autonomous robots to carry weapons and to be programmed to engage in combat in various situations that might arise, including battles between countries, or in patrolling border areas or sensitive areas, or other similar roles. As of 18 March 2025, the Convention on Certain Conventional Weapons had 128 High Contracting Parties. In the Geneva Conventions, the term "High Contracting Parties" refers to the states that have joined the conventions and are therefore bound to uphold them. Among the countries that have joined are states with tense relations or ongoing armed conflict with one another, including Russia and Ukraine, Israel and the State of Palestine, and Pakistan and Afghanistan. == Background == In 2013, the Meeting of State Parties to the Convention on Certain Conventional Weapons agreed on a mandate on lethal autonomous weapon systems and tasked its chairperson with convening an informal Meeting of Experts to discuss issues related to emerging technologies in the area of LAWS. Those informal Meetings of Experts were then held in 2014, 2015 and 2016, and their reports fed into subsequent meetings of the High Contracting Parties. At the Fifth CCW Review Conference in 2016, the High Contracting Parties decided to establish an open-ended Group of Governmental Experts on emerging technologies in the area of LAWS, building on the earlier expert meetings. Since then, the group has been reconvened annually. In 2023, the Meeting of the High Contracting Parties to the CCW decided that the GGE on LAWS would continue its work in 2024 and 2025. The group was tasked with developing, by consensus, elements of a possible instrument, without predetermining its form, as well as other measures addressing lethal autonomous weapon systems, drawing on existing CCW protocols, earlier recommendations, state proposals, and legal, military, and technological expertise. == 2024 == In 2024, the GGE met twice, and the group was chaired by Robert in den Bosch, the Netherlands' disarmament ambassador. The 2024 Meeting of the High Contracting Parties decided that the group would meet for 10 days in 2025, in two five-day sessions, and reaffirmed its mandate to continue work by consensus on possible elements of an instrument and other measures addressing lethal autonomous weapon systems. == 2025 == At its first 2025 session, held in Geneva from 3 to 7 March 2025, the Group of Governmental Experts on Lethal Autonomous Weapon Systems discussed revisions to the chair's rolling text. The text was structured into five sections, or "boxes", though delegates held differing views on whether headings were useful or appropriate. Broadly, the discussions covered the characterization of lethal autonomous weapon systems, the application of international humanitarian law, possible prohibitions and regulations, legal review, and questions of accountability and responsibility. At its second session, held from 1 to 5 September 2025, delegations continued work on the chair's rolling text, which set out elements of a possible instrument and was organized into five thematic "boxes". == 2026 == === Developments before the 2026 session === A few weeks before the meeting, autonomous weapons drew renewed attention when the United States pressured Anthropic to revise the terms of use for its AI model Claude. Anthropic prohibited the model's use for mass domestic surveillance and for fully autonomous weapons operating without human oversight, while reports also emerged that OpenAI had reached an agreement with the U.S. Department of War for the use of its AI models, reportedly stipulating that they would not independently direct autonomous weapons where human control was required. The U.S. military nevertheless continued to use Claude during its war on Iran, and there was increasing alarm about the use of AI-assisted semi-autonomous weapons in conflicts including those in Ukraine, Sudan, Gaza, and Iran. Before the start of the sessions, Robert in den Bosch, as chair, warned that progress was urgent because technological developments were moving quickly. At the same time, although states agreed that international humanitarian law applied to LAWS, specific internationally binding standards governing such systems remained largely absent. A key divide before the session was that Russia and the United States opposed new legally binding instruments, while other states argued that new rules were necessary. According to Robert in den Bosch, the talks could lead to new rules, amendments to an existing convention, or a new treaty. === First session === From 2 to 6 March 2026, the group held its penultimate session under the group's three-year mandate. Delegations discussed the chair's rolling draft text, circulated in December 2025, on elements of a possible instrument or other measures concerning lethal autonomous weapon systems. In revised text circulated by the chair on 5 March 2026, a lethal autonomous weapon system was characterized as "a functionally integrated combination of one or more weapons and technological components, that can identify, select, and engage a target, without intervention by a human operator in the execution of these tasks". The text was divided into five boxes to structure discussion. During the session, delegates conducted a first reading of the draft text, and the chair later circulated revised language for several sections. Informal consultations were also held. According to campaign groups and participating observers, support grew during the week for moving to negotiations on the basis of the rolling text, with more than 70 states said to support that step by the end of the session, though some participants warned that attempts to bridge differences risked blurring the group's core purpose. The International Committee of the Red Cross argued that the text should not only restate existing international humanitarian law, but also clarify how those rules apply to autonomous weapons and set out additional measures tailored to the specific challenges such systems raise. Stop Killer Robots likewise emphasized the need to preserve meaningful human judgment and control over increasingly autonomous systems. During the discussions, the U.S. delegation opposed the term "human control" and reportedly proposed the alternative phrase "good faith human judgment and care". Other delegations rejected that wording as too weak, while many states continued to insist that meaningful human control over weapon systems remained essential.
SF8
SF8 (Korean: 에스 에프 에잇) is a South Korean science fiction anthology television series. It is a movie-drama crossover project between MBC, the Directors Guild of Korea, the OTT platform Wavve and the production company Soo Film. The director's cuts of all episodes were released on Wavve on July 10, 2020 while MBC TV aired one episode a week from August 14 to October 9, 2020. The series has been regarded as a Korean equivalent of the British series Black Mirror as they have the same format and similar themes, though Min Kyu-dong believes that SF8 is more diversified since eight different filmmakers were involved in the project. SF8 was screened at the 24th Bucheon International Fantastic Film Festival. == Synopsis == SF8 revolves around people who dream of a perfect society. It tackles the themes of artificial intelligence, augmented reality, virtual reality, robots, games, fantasy, horror, superpowers and disasters. == Episodes == Short summaries adapted from BiFan. == Production == === Development === Min Kyu-dong, creator of the series, said that "sci-fi movies were the driving force behind many movie directors' dreams. Unfortunately, due to the relatively high budget and narrow market limitations, various works were not able to be produced." He had been working on this project for two years before he partnered with Wavve and MBC. He also took charge of casting the actors, which lasted for a year. During a press conference held at CGV Yongsan I'Park Mall in Seoul on July 8, 2020, Min Kyu-dong said that all the episodes were produced with an equal amount of budget and that the overall budget was lower than one of a small commercial film. Roh Deok, who co-wrote and directed the "Manxin" episode, mentioned that "while commercial film productions [...] inevitably limit the directors' freedom as a creator, [they] had more independence in production" and "although there were physical limits, [he] thinks [they] went through the process of discovering what [they] can do inside those boundaries." === Filming === Eight directors from the Directors Guild of Korea (DGK) each directed an episode from the series. Filming began on February 21, 2020 with Jang Cheol-soo's "White Crow" and ended on May 7 with Kim Ui-seok's "Empty Body". Filming was completed within 10 filming sessions for each episode. === Credits === Credits adapted from BiFan. == Release == The director's cut was released on the OTT platform Wavve on July 10, 2020 and the original episodes were aired on MBC TV from August 14 to October 9.
Refik Anadol
Refik Anadol (born November 7, 1985) is a Turkish American media artist and the co-founder of Refik Anadol Studio and Dataland. Recognized as a pioneer in the aesthetics of data visualization and AI arts, his work merges art, technology, science, and architecture. Through media embedded into existing architecture, live audio-visual performances, immersive rooms, exhibitions, AI data paintings and sculptures, and digital collections, Anadol explores collective memories, humanity's relationship to nature, the perception of space and time, and human-machine collaborations. His work has been exhibited in more than seventy cities on six continents. == Early life and education == Anadol was born and raised in Istanbul and grew up in a family of teachers. He taught himself basic programming on a Commodore 64 when he was eight. His connection to machines began with coding and video games. Anadol saw Blade Runner for the first time when he was eight; his mother said the way he perceived his surroundings shifted the day after he saw the film. He was fascinated with its futuristic depiction of downtown Los Angeles, and transfixed by as a scene during which a replicant discovers that her memories are an implanted component of her machine mind, In a 2024 interview with the Financial Times, he said: "Since that moment, one of my inspirations has been that question: 'What can a machine do with someone else's memories?" Anadol attended Istanbul Bilgi University, where he received a BA in photography and video in 2009 and an MFA in visual communication in 2011. In 2014 he earned an MFA in design media arts at UCLA. He was mentored by Casey Reas, Jennifer Steinkamp, and Christian Moeller. == Career and selected works == === 2008–2012: Data painting, Quadrature and Quadrangle, Istanbul Biennial === As an undergraduate, Anadol read a paper by Lev Manovich on augmented space. Manovich's assertion that collaborations between architects and artists could make the "invisible flow of data visible" triggered Anadol's imagination, and in 2008, he altered built space for the first time. Bringing a projector outside, he projected large-scale images onto a concrete to create the illusion of movement. Coining the term "data painting," the piece inspired Anadol to use light as material and data as pigment. In 2010 he created Quadrature with Alican Aktürk, a fellow graduate student, at the SantralIstanbul Art and Culture Center's main gallery building. A live audio-visual performance that examined the relationship between architecture and media, Quadrature used video projection techniques to manipulate footage of quadrilaterals. He followed Quadrature with Quadrangle at SANAA School of Design in Essen, Germany, using the entire 360 degrees of the building as a canvas. In 2011, he was invited to create a media installation at the Istanbul Biennial on the heavily trafficked İstiklal Avenue. He created a site-specific large-scale interpretation of sounds he recorded during different times of day, and used nine projectors to project reinterpreted images. The work was titled Augmented Structures v1.0. Anadol's first solo exhibition, Sceptical Interventions, was held at the Piveneli Gallery in Istanbul in early 2012. Later that year he moved to Los Angeles to attend UCLA's Design Media Arts program. The first place he went after his arrival was downtown Los Angeles. [6] === 2013–2016: Visions of America: Amériques, Infinity Room, Google AMI === In 2013, at Microsoft Research's annual Design Expo, Anadol presented his idea to use the external walls of Walt Disney Concert Hall as a canvas. His presentation brought him to the attention of Gehry Technologies, and with the support of Gehry and his team, Anadol was offered the use of the original 3D model of the concert hall. For his 2014 thesis project, with assistance from architects and UCLA researchers, he created a site-specific architectural video installation inside the concert hall that accompanied a Los Angeles Philharmonic performance of Edgard Varèse's Amérique. Titled Visions of America: Amériques, Anadol used algorithmic sound analysis to listen and respond to the music in real-time. He tracked conductor Esa-Pekka Salonen's heartbeat with a sensor and used a 3-D camera system to integrate Salonen's movements. He created Infinity Room at the Zorlu PSM for the 2015 Istanbul Biennial. Rather than creating an illusion only with mirrors, Anadol used pixel and 3D projection mapping to transform every surface of the room into an abstract infinite moving space. A temporary immersive environment, Infinity Room was also exhibited at events including South by Southwest in Austin, Texas, the New Zealand Festival in Wellington, New Zealand, and Jeffrey Deitch in Los Angeles. In 2016, Anadol was awarded the first Google Artists and Machine Intelligence Artist Residency; it was just after a team at Google opened up the algorithm for DeepDream, a computer vision program that prompted Anadol's realization that if a machine could learn, it could remember, dream, and hallucinate. === 2017–2018: Winds of Boston, Archive Dreaming, Melting Memories, WDCH Dreams === In 2017, he created the data painting Winds of Boston, a 6' x 13' foot video installation in the lobby of a Boston office building, using software he created to read, analyze and visualize wind speed, direction, and gust patterns along with time and temperature at 20-second intervals recorded over a one-year period at Logan International Airport. Later in the year, he used AI to generate infinite new outputs based on a massive dataset for Archive Dreaming, an immersive installation at Salt Research, a contemporary gallery and library in Istanbul. Inspired by his idea of consciousness and its context within AI, as well as Jorge Luis Borges' The Library of Babel, Anadol used AI and machine learning to look at and discover interactions and correlations between 1.7 million items culled from 40,000 publications covering Turkish contemporary and modern art, architecture, and economics from 1997 to 2010. Archive Dreaming, which could be controlled by users with a joystick, dreamed of unexpected correlations among documents when idle. In 2018, after his uncle was diagnosed with Alzheimer's, Anadol created Melting Memories. Working with scientists from the neuroscape laboratory at the University of California, San Francisco, he used academic data from the neuroscience archives and EEG scans of an anonymous Alzheimer's disease dataset to create AI-generated visuals related to memory, health, degeneration, and decay.Melting Memories was projected on the walls of Pilevneli Gallery; visitors to the exhibition could watch as millions of pixels reconstructed people's memories. Anadol won the Lumen Prize Gold Award for Melting Memories. Anadol was commissioned by the Los Angeles Philharmonic to create an installation to celebrate the orchestra's centennial anniversary in 2018. He worked with Google's Kenric MacDowell to create WDCH Dreams, using algorithmic visualizations of data to mimic the process of human dreaming. Projected across the exterior walls of Walt Disney Concert Hall using 42 large-scale projectors with 50K visual resolution, 8-channel sound, and 1.2M luminance, Anadol painted with data points culled from the orchestra's archives, including 587,763 images, 1,880 videos, 1,483 metadata files, and 17,773 audio files. Because Gehry gave him access to the 3D architectural files of Walt Disney Concert Hall, Anadol knew the exact contours of the building. WDCH Dreams debuted in September 2018. A 12-minute performance in three parts staged every 30 minutes over ten nights, "Centennial Memories,” the first piece, used 44.5 terabytes of historical data from the Phil's archives. It was followed by "Consciousness", which processed every note the orchestra has ever recorded, using billions of data points to generate connections; and "Dream," which merged "Centennial Memories" and "Consciousness" to create hallucinations that were described in the New York Times as "a sort of combinatorial Fantasia. === 2019–2021: Machine Hallucinations: NYC, Machine Hallucinations: Nature Dreams, Machine Memories: Space, Quantum Memories === In 2019, Refik Anadol presented Latent History at Fotografiska Stockholm. The site specific installation transformed photographic archives of Stockholm into a large scale, machine generated visual projection displayed in the museum’s main exhibition hall. Drawing on thousands of archival images spanning approximately 150 years, the work used artificial intelligence to reinterpret the city’s historical imagery as a continuously evolving visual narrative.. Anadol began thinking about the work that would become the Machine Hallucinations series while in residence at Google. In 2019, he completed the first work in the series, Machine Hallucinations: NYC, which used 300 million photos of New York City and 113 million additional data points, including subway sounds, ra
Removal of Sam Altman from OpenAI
On November 17, 2023, OpenAI's board of directors ousted co-founder and chief executive Sam Altman. In an official post on the company's website, it was stated that "the board no longer has confidence in his ability to continue leading OpenAI". The removal was predicated by employee concerns about his handling of artificial intelligence safety, and allegations of abusive behavior. Altman was reinstated on November 22 after pressure from employees and investors. The removal and subsequent reinstatement caused widespread reactions, including impacts felt in the financial markets and technology sector. Microsoft, a partner of OpenAI, received little notice of the removal and experienced a drop in the share price of its stock. The removal also promoted interest in investigations from regulatory agencies. == Background == === OpenAI === OpenAI is an artificial intelligence firm founded in December 2015 as a non-profit entity. The for-profit division of the organization released ChatGPT in November 2022, contributing to a resurgence in generative artificial intelligence funding. The board of directors of the controlling non-profit formerly comprised chief scientist Ilya Sutskever, as well as Adam D'Angelo, chief executive of Quora, entrepreneur Tasha McCauley, and Helen Toner, strategy director for the Center for Security and Emerging Technology. As of October 2023, the company is valued at US$80 billion and was set to bring in US$1 billion in revenue. Altman has described OpenAI's relationship with Microsoft as the "best bromance in tech". OpenAI is uniquely structured, an intentional decision to avoid investor control. A board of directors controls the non-profit OpenAI, Inc. The non-profit owns and controls a for-profit company itself controlling a capped-profit company, OpenAI Global, LLC and a holding company owned by employees and other investors. The holding company is the majority owner of OpenAI Global, LLC.; Microsoft owns a minority stake in the capped-profit company. OpenAI's bylaws, enacted in January 2016, allow a majority of its board of directors to remove any director without prior warning or a formal meeting with written consent. === Sam Altman === Sam Altman is a co-founder of OpenAI and its former chief executive; Altman took over the company following co-chair Elon Musk's resignation in 2018. Under Altman, OpenAI has shifted to becoming a for-profit entity. Altman is credited with convincing Microsoft chief executive Satya Nadella with investing US$10 billion in cash and computing credits into OpenAI and leading several tender offer transactions that tripled the company's valuation. Altman testified before the United States Congress speaking critically of artificial intelligence and appeared at the 2023 AI Safety Summit. In the days leading up to his removal, Altman made several public appearances, announcing the GPT-4 Turbo platform at OpenAI's DevDay conference, attending APEC United States 2023, and speaking at an event related to Burning Man. == Events leading up to the removal == The resignation of LinkedIn co-founder Reid Hoffman, venture capitalist Shivon Zilis, and former Republican representative Will Hurd from the board allowed the remaining members to remove Altman. According to Kara Swisher and The Wall Street Journal, Sutskever was instrumental in Altman's removal. Disagreements over the safety of artificial intelligence divided employees prior to Altman's removal. The release of ChatGPT created divisions with OpenAI as a for-profit company without considerations for the safety of artificial intelligence and a non-profit cautious of artificial intelligence's capabilities; in a staff email sent in 2019 and obtained by The Atlantic, Altman referred to these divisions as "tribes". Prior to his removal, Altman was seeking billions from Middle Eastern sovereign wealth funds to develop an artificial intelligence chip to compete with Nvidia and courted SoftBank chairman Masayoshi Son to develop artificial intelligence hardware with former Apple designer Jony Ive. Sutskever and his allies opposed these efforts, viewing them as unjustly using the OpenAI name. Altman reduced Sutskever's role in October 2023, furthering divisions; Sutskever successfully appealed to several members of the board. Swisher and The Verge reporter Alex Heath stated that opposition to Altman's profit-driven strategy culminated in the DevDay conference in which Altman announced custom ChatGPT instances. According to Axios, the removal was driven by growing discontent and distrust with Altman. On November 22, 2023, reports emerged suggesting that Sam Altman's dismissal from OpenAI might be linked to his alleged mishandling of a significant breakthrough in the organization's secretive project codenamed Q. According to sources within OpenAI, Q is aimed at developing AI capabilities in logical and mathematical reasoning, and reportedly involves performing math on the level of grade-school students. Concerns about Altman's response to this development, specifically regarding the potential safety implications of the discovery, were reportedly raised to the company's board shortly before his firing. A report from The Washington Post in December stated that OpenAI's board of directors were concerned over Altman's allegedly abusive behavior; the complaints were purportedly a major factor in his removal. The Post previously reported that Altman's alleged pattern of deception and subversiveness that ostensibly resulted in his removal from Y Combinator ultimately resulted in the board's decision to remove him. In April 2026, an investigative report from The New Yorker found that Sutskever and others, in response to the board's request, had compiled an approximately 70-page-long annotated dossier consisting of internal communications, documents, and photos. The dossier claimed that Altman "exhibits a consistent pattern of [...] Lying", and that Altman misrepresented information to the company's senior management and board, particularly regarding safety issues. == Removal == On November 17, 2023, at approximately noon PST, OpenAI's board of directors ousted Altman effective immediately following a "deliberative review process". The board concluded that Altman was not "consistently candid in his communications". Altman was informed of his removal five to ten minutes before it occurred on a Google Meet while watching the Las Vegas Grand Prix. Within thirty minutes, Sutskever invited OpenAI chairman and president Greg Brockman to a Google Meet to inform him of Altman's removal. According to an internal memo obtained by Axios, the removal was not due to "malfeasance", and OpenAI chief executive Emmett Shear denied accusations that the removal was due to disagreements. The board publicly announced Altman's removal thirty minutes later. Chief Technology Officer Mira Murati was immediately appointed to interim chief executive officer. Hours after Altman's removal, Brockman resigned as chairman, joined by director of research Jakub Pachocki and researchers Aleksander Mądry and Szymon Sidor. During an all-hands meeting, Sutskever defended the ouster and denied accusations of a hostile takeover. An OpenAI representative requested former board member Will Hurd's presence. == Reinstatement == According to The New Yorker, Altman retreated to his San Francisco home and enlisted the help of communications consultant Chris Lehane and Airbnb chief executive Brian Chesky, as well as former staff and a legal team, to plan his reinstatement. Lehane encouraged Altman to engage on social media, while Chesky sent a journalist negative information about the board. Altman told interim CEO Murati that his team was conducting opposition research on her and the individuals responsible for his removal; Altman later stated he did not remember saying this. Altman insisted multiple times that all board members who supported his removal should resign. Tiger Global Management and Sequoia Capital had attempted to reinstate Altman, according to The Information; Bloomberg News reported that Microsoft and Thrive Capital were seeking Altman's reinstatement. On November 18, The Verge reported that OpenAI's board of directors discussed reinstating Altman. The board agreed in principle to resign and to allow Altman to return, but missed the deadline. According to The Verge, Altman was ambivalent about returning and would seek significant changes to the company, including replacing the board. A list of directors had been prepared by investors in the event that the board steps down, and purportedly included former Salesforce executive Bret Taylor. According to chief strategy officer Jason Kwon, OpenAI was optimistic it could return Altman, Brockman, and other employees. On November 19, Altman and Brockman appeared at OpenAI's headquarters to negotiate, mediated by Nadella. According to Bloomberg News, Murati, Kwon, and chief operating officer Brad Lightcap were pushing for a new board of direc
Rendering equation
In computer graphics, the rendering equation is an integral equation that expresses the amount of light leaving a point on a surface as the sum of emitted light and reflected light. It was independently introduced into computer graphics by David Immel et al. and James Kajiya in 1986. The equation is important in the theory of physically based rendering, describing the relationships between the bidirectional reflectance distribution function (BRDF) and the radiometric quantities used in rendering. The rendering equation is defined at every point on every surface in the scene being rendered, including points hidden from the camera. The incoming light quantities on the right side of the equation usually come from the left (outgoing) side at other points in the scene (ray casting can be used to find these other points). The radiosity rendering method solves a discrete approximation of this system of equations. In distributed ray tracing, the integral on the right side of the equation may be evaluated using Monte Carlo integration by randomly sampling possible incoming light directions. Path tracing improves and simplifies this method. The rendering equation can be extended to handle effects such as fluorescence (in which some absorbed energy is re-emitted at different wavelengths) and can support transparent and translucent materials by using a bidirectional scattering distribution function (BSDF) in place of a BRDF. The theory of path tracing sometimes uses a path integral (integral over possible paths from a light source to a point) instead of the integral over possible incoming directions. == Equation form == The rendering equation may be written in the form L o ( x , ω o , λ , t ) = L e ( x , ω o , λ , t ) + L r ( x , ω o , λ , t ) {\displaystyle L_{\text{o}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)=L_{\text{e}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)+L_{\text{r}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)} L r ( x , ω o , λ , t ) = ∫ Ω f r ( x , ω i , ω o , λ , t ) L i ( x , ω i , λ , t ) ( ω i ⋅ n ) d ω i {\displaystyle L_{\text{r}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)=\int _{\Omega }f_{\text{r}}(\mathbf {x} ,\omega _{\text{i}},\omega _{\text{o}},\lambda ,t)L_{\text{i}}(\mathbf {x} ,\omega _{\text{i}},\lambda ,t)(\omega _{\text{i}}\cdot \mathbf {n} )\operatorname {d} \omega _{\text{i}}} where L o ( x , ω o , λ , t ) {\displaystyle L_{\text{o}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)} is the total spectral radiance of wavelength λ {\displaystyle \lambda } directed outward along direction ω o {\displaystyle \omega _{\text{o}}} at time t {\displaystyle t} , from a particular position x {\displaystyle \mathbf {x} } x {\displaystyle \mathbf {x} } is the location in space ω o {\displaystyle \omega _{\text{o}}} is the direction of the outgoing light λ {\displaystyle \lambda } is a particular wavelength of light t {\displaystyle t} is time L e ( x , ω o , λ , t ) {\displaystyle L_{\text{e}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)} is emitted spectral radiance L r ( x , ω o , λ , t ) {\displaystyle L_{\text{r}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)} is reflected spectral radiance ∫ Ω … d ω i {\displaystyle \int _{\Omega }\dots \operatorname {d} \omega _{\text{i}}} is an integral over Ω {\displaystyle \Omega } Ω {\displaystyle \Omega } is the unit hemisphere centered around n {\displaystyle \mathbf {n} } containing all possible values for ω i {\displaystyle \omega _{\text{i}}} where ω i ⋅ n > 0 {\displaystyle \omega _{\text{i}}\cdot \mathbf {n} >0} f r ( x , ω i , ω o , λ , t ) {\displaystyle f_{\text{r}}(\mathbf {x} ,\omega _{\text{i}},\omega _{\text{o}},\lambda ,t)} is the bidirectional reflectance distribution function, the proportion of light reflected from ω i {\displaystyle \omega _{\text{i}}} to ω o {\displaystyle \omega _{\text{o}}} at position x {\displaystyle \mathbf {x} } , time t {\displaystyle t} , and at wavelength λ {\displaystyle \lambda } ω i {\displaystyle \omega _{\text{i}}} is the negative direction of the incoming light L i ( x , ω i , λ , t ) {\displaystyle L_{\text{i}}(\mathbf {x} ,\omega _{\text{i}},\lambda ,t)} is spectral radiance of wavelength λ {\displaystyle \lambda } coming inward toward x {\displaystyle \mathbf {x} } from direction ω i {\displaystyle \omega _{\text{i}}} at time t {\displaystyle t} n {\displaystyle \mathbf {n} } is the surface normal at x {\displaystyle \mathbf {x} } ω i ⋅ n {\displaystyle \omega _{\text{i}}\cdot \mathbf {n} } is the weakening factor of outward irradiance due to incident angle, as the light flux is smeared across a surface whose area is larger than the projected area perpendicular to the ray. This is often written as cos θ i {\displaystyle \cos \theta _{i}} . Two noteworthy features are: its linearity—it is composed only of multiplications and additions, and its spatial homogeneity—it is the same in all positions and orientations. These mean a wide range of factorings and rearrangements of the equation are possible. It is a Fredholm integral equation of the second kind, similar to those that arise in quantum field theory. Note this equation's spectral and time dependence — L o {\displaystyle L_{\text{o}}} may be sampled at or integrated over sections of the visible spectrum to obtain, for example, a trichromatic color sample. A pixel value for a single frame in an animation may be obtained by fixing t ; {\displaystyle t;} motion blur can be produced by averaging L o {\displaystyle L_{\text{o}}} over some given time interval (by integrating over the time interval and dividing by the length of the interval). Note that a solution to the rendering equation is the function L o {\displaystyle L_{\text{o}}} . The function L i {\displaystyle L_{\text{i}}} is related to L o {\displaystyle L_{\text{o}}} via a ray-tracing operation: The incoming radiance from some direction at one point is the outgoing radiance at some other point in the opposite direction. == Applications == Solving the rendering equation for any given scene is the primary challenge in realistic rendering. One approach to solving the equation is based on finite element methods, leading to the radiosity algorithm. Another approach using Monte Carlo methods has led to many different algorithms including path tracing, photon mapping, and Metropolis light transport, among others. == Limitations == Although the equation is very general, it does not capture every aspect of light reflection. Some missing aspects include the following: Transmission, which occurs when light is transmitted through the surface, such as when it hits a glass object or a water surface, Subsurface scattering, where the spatial locations for incoming and departing light are different. Surfaces rendered without accounting for subsurface scattering may appear unnaturally opaque — however, it is not necessary to account for this if transmission is included in the equation, since that will effectively include also light scattered under the surface, Polarization, where different light polarizations will sometimes have different reflection distributions, for example when light bounces at a water surface, Phosphorescence, which occurs when light or other electromagnetic radiation is absorbed at one moment and emitted at a later moment, usually with a longer wavelength (unless the absorbed electromagnetic radiation is very intense), Interference, where the wave properties of light are exhibited, Fluorescence, where the absorbed and emitted light have different wavelengths, Non-linear effects, where very intense light can increase the energy level of an electron with more energy than that of a single photon (this can occur if the electron is hit by two photons at the same time), and emission of light with higher frequency than the frequency of the light that hit the surface suddenly becomes possible, and Doppler effect, where light that bounces off an object moving at a very high speed will get its wavelength changed: if the light bounces off an object that is moving towards it, the light will be blueshifted and the photons will be packed more closely so the photon flux will be increased; if it bounces off an object moving away from it, it will be redshifted and the photon flux will be decreased. This effect becomes apparent only at speeds comparable to the speed of light, which is not the case for most rendering applications. For scenes that are either not composed of simple surfaces in a vacuum or for which the travel time for light is an important factor, researchers have generalized the rendering equation to produce a volume rendering equation suitable for volume rendering and a transient rendering equation for use with data from a time-of-flight camera.
Herbrand Award
The Herbrand Award for Distinguished Contributions to Automated Reasoning is an award given by the Conference on Automated Deduction (CADE), Inc., (although it predates the formal incorporation of CADE) to honour persons or groups for important contributions to the field of automated deduction. The award is named after the French scientist Jacques Herbrand and given at most once per CADE or International Joint Conference on Automated Reasoning (IJCAR). It comes with a prize of US$1,000. Anyone can be nominated, the award is awarded after a vote among CADE trustees and former recipients, usually with input from the CADE/IJCAR programme committee. == Recipients == Past award recipients are: === 1990s === Larry Wos (1992) Woody Bledsoe (1994) John Alan Robinson (1996) Wu Wenjun (1997) Gérard Huet (1998) Robert S. Boyer and J Strother Moore (1999) === 2000s === William W. McCune (2000) Donald W. Loveland (2001) Mark E. Stickel (2002). Peter B. Andrews (2003) Harald Ganzinger (2004) Martin Davis (2005) Wolfgang Bibel (2006) Alan Bundy (2007) Edmund M. Clarke (2008) Deepak Kapur (2009) === 2010s === David Plaisted (2010) Nachum Dershowitz (2011) Melvin Fitting (2012) C. Greg Nelson (2013) Robert L. Constable (2014) Andrei Voronkov (2015) Zohar Manna and Richard Waldinger (2016) Lawrence C. Paulson (2017) Bruno Buchberger (2018) Nikolaj Bjørner and Leonardo de Moura (2019) === 2020s === Franz Baader (2020) Tobias Nipkow (2021) Natarajan Shankar (2022) Moshe Vardi (2023) Armin Biere (2024) Aart Middeldorp (2025)