The Generative AI Copyright Disclosure Act is a piece of legislation introduced by California Representative Adam Schiff in the United States Congress on April 9, 2024. It concerns the transparency of companies regarding their use of copyrighted work to train their generative artificial intelligence (AI) models. The legislation requires the submission of a notice regarding the identity and the uniform resource locator (URL) address of the copyrighted works used in the training data to the Register of Copyrights at least 30 days before the public release of the new or updated version of the AI model; it does not ban the use of copyrighted works for AI training. The bill's requirements would apply retroactively to prior AI models. Violation penalties would start at US$5,000. The legislation does not have a maximum penalty assessment that can be charged. The bill by Schiff was introduced a few days after The New York Times published an article regarding the business activities of major tech firms, including Google and Meta, in the training of their generative AI platforms on April 6, 2024. The legislation is supported by the Professional Photographers of America (PPA), SAG-AFTRA, the Writers Guild of America, the International Alliance of Theatrical Stage Employees (IATSE), the Recording Industry Association of America (RIAA), and others.
Automatic summarization
Automatic summarization is the process of shortening a set of data computationally, to create a subset (a summary) that represents the most important or relevant information within the original content. Artificial intelligence (AI) algorithms are commonly developed and employed to achieve this, specialized for different types of data. Text summarization is usually implemented by natural language processing methods, designed to locate the most informative sentences in a given document. On the other hand, visual content can be summarized using computer vision algorithms. Image summarization is the subject of ongoing research; existing approaches typically attempt to display the most representative images from a given image collection, or generate a video that only includes the most important content from the entire collection. Video summarization algorithms identify and extract from the original video content the most important frames (key-frames), and/or the most important video segments (key-shots), normally in a temporally ordered fashion. Video summaries simply retain a carefully selected subset of the original video frames and, therefore, are not identical to the output of video synopsis algorithms, where new video frames are being synthesized based on the original video content. == Commercial products == In 2022 Google Docs released an automatic summarization feature. == Approaches == There are two general approaches to automatic summarization: extraction and abstraction. === Extraction-based summarization === Here, content is extracted from the original data, but the extracted content is not modified in any way. Examples of extracted content include key-phrases that can be used to "tag" or index a text document, or key sentences (including headings) that collectively comprise an abstract, and representative images or video segments, as stated above. For text, extraction is analogous to the process of skimming, where the summary (if available), headings and subheadings, figures, the first and last paragraphs of a section, and optionally the first and last sentences in a paragraph are read before one chooses to read the entire document in detail. Other examples of extraction that include key sequences of text in terms of clinical relevance (including patient/problem, intervention, and outcome). === Abstractive-based summarization === Abstractive summarization methods generate new text that did not exist in the original text. This has been applied mainly for text. Abstractive methods build an internal semantic representation of the original content (often called a language model), and then use this representation to create a summary that is closer to what a human might express. Abstraction may transform the extracted content by paraphrasing sections of the source document, to condense a text more strongly than extraction. Such transformation, however, is computationally much more challenging than extraction, involving both natural language processing and often a deep understanding of the domain of the original text in cases where the original document relates to a special field of knowledge. "Paraphrasing" is even more difficult to apply to images and videos, which is why most summarization systems are extractive. === Aided summarization === Approaches aimed at higher summarization quality rely on combined software and human effort. In Machine Aided Human Summarization, extractive techniques highlight candidate passages for inclusion (to which the human adds or removes text). In Human Aided Machine Summarization, a human post-processes software output, in the same way that one edits the output of automatic translation by Google Translate. == Applications and systems for summarization == There are broadly two types of extractive summarization tasks depending on what the summarization program focuses on. The first is generic summarization, which focuses on obtaining a generic summary or abstract of the collection (whether documents, or sets of images, or videos, news stories etc.). The second is query relevant summarization, sometimes called query-based summarization, which summarizes objects specific to a query. Summarization systems are able to create both query relevant text summaries and generic machine-generated summaries depending on what the user needs. An example of a summarization problem is document summarization, which attempts to automatically produce an abstract from a given document. Sometimes one might be interested in generating a summary from a single source document, while others can use multiple source documents (for example, a cluster of articles on the same topic). This problem is called multi-document summarization. A related application is summarizing news articles. Imagine a system, which automatically pulls together news articles on a given topic (from the web), and concisely represents the latest news as a summary. Image collection summarization is another application example of automatic summarization. It consists in selecting a representative set of images from a larger set of images. A summary in this context is useful to show the most representative images of results in an image collection exploration system. Video summarization is a related domain, where the system automatically creates a trailer of a long video. This also has applications in consumer or personal videos, where one might want to skip the boring or repetitive actions. Similarly, in surveillance videos, one would want to extract important and suspicious activity, while ignoring all the boring and redundant frames captured. At a very high level, summarization algorithms try to find subsets of objects (like set of sentences, or a set of images), which cover information of the entire set. This is also called the core-set. These algorithms model notions like diversity, coverage, information and representativeness of the summary. Query based summarization techniques, additionally model for relevance of the summary with the query. Some techniques and algorithms which naturally model summarization problems are TextRank and PageRank, Submodular set function, Determinantal point process, maximal marginal relevance (MMR) etc. === Keyphrase extraction === The task is the following. You are given a piece of text, such as a journal article, and you must produce a list of keywords or key[phrase]s that capture the primary topics discussed in the text. In the case of research articles, many authors provide manually assigned keywords, but most text lacks pre-existing keyphrases. For example, news articles rarely have keyphrases attached, but it would be useful to be able to automatically do so for a number of applications discussed below. Consider the example text from a news article: "The Army Corps of Engineers, rushing to meet President Bush's promise to protect New Orleans by the start of the 2006 hurricane season, installed defective flood-control pumps last year despite warnings from its own expert that the equipment would fail during a storm, according to documents obtained by The Associated Press". A keyphrase extractor might select "Army Corps of Engineers", "President Bush", "New Orleans", and "defective flood-control pumps" as keyphrases. These are pulled directly from the text. In contrast, an abstractive keyphrase system would somehow internalize the content and generate keyphrases that do not appear in the text, but more closely resemble what a human might produce, such as "political negligence" or "inadequate protection from floods". Abstraction requires a deep understanding of the text, which makes it difficult for a computer system. Keyphrases have many applications. They can enable document browsing by providing a short summary, improve information retrieval (if documents have keyphrases assigned, a user could search by keyphrase to produce more reliable hits than a full-text search), and be employed in generating index entries for a large text corpus. Depending on the different literature and the definition of key terms, words or phrases, keyword extraction is a highly related theme. ==== Supervised learning approaches ==== Beginning with the work of Turney, many researchers have approached keyphrase extraction as a supervised machine learning problem. Given a document, we construct an example for each unigram, bigram, and trigram found in the text (though other text units are also possible, as discussed below). We then compute various features describing each example (e.g., does the phrase begin with an upper-case letter?). We assume there are known keyphrases available for a set of training documents. Using the known keyphrases, we can assign positive or negative labels to the examples. Then we learn a classifier that can discriminate between positive and negative examples as a function of the features. Some classifiers make a binary classification for a test example, while others assign a probability of being a keyphrase. For ins
Paprika (app)
Paprika is an app and website that helps users organize recipes, produce meal plans, and create grocery lists. The app is available for Android, iOS, macOS, and Windows devices. == Overview == The app allows users to import recipes from various sources, including websites and other apps. The app also allows users to automatically generate meal plans, which are also customizable, in order to achieve specific objectives such as weight loss, muscle gain, adherence to various dietary preferences, or personal taste. The app is also capable of generating grocery lists based on the daily or weekly meal plans chosen by the user. All the recipes, menus, and grocery lists of each user are accessible from smartphones, tablets, and computers. The app is part of a broader category of mobile apps focused on meal planning, recipe management, and shopping list automation, which have grown in popularity with the expansion of smartphone usage and digital cooking tools. == History == Paprika Recipe Manager for iPad version 1.0 was initially released in September 2010 by Hindsight LLC. Paprika 2.0 was released for iPhone and iPad in November 2013, and Paprika 3.0 was released for iOS and macOS in November 2017. == Reception == Paprika has been featured in technology and lifestyle publications as a recipe management and meal planning application. Coverage has noted features such as importing recipes from websites, ingredient scaling, and cross-platform synchronization. The app has also appeared in lists of cooking and meal planning tools published by outlets including The Verge and The Kitchn.
I Am Rich
I Am Rich is a discontinued 2008 mobile app for iPhones which had minimal function and was priced at US$999.99 (equivalent to $1,495 in 2025). The app was pulled from the App Store less than 24 hours after its launch. Receiving negative reviews from critics, only eight copies were sold. In the years since, several similar applications have been released at lower prices. == Overview == I Am Rich was developed as a joke by German software developer, Armin Heinrich, after he saw iPhone users complaining about software priced above $0.99. The app only showed a glowing red gem and an icon that, when pressed, displayed the following mantra in large text: I am richI deserv [sic] itI am good,healthy & successful Heinrich told The New York Times that "I regard it as art. I did not expect many people to buy it and did not expect all the fuss about it." The application is described as "a work of art with no hidden function at all", with its only purpose being to show other people that they were able to afford it. Vox writer Zachary Crockett called it "the ultimate Veblen good in app form". == Release == Heinrich released and distributed I Am Rich through the App Store on 5 August 2008. The app was sold for US$999.99 (equivalent to $1,495 in 2025), €799.99 (equivalent to €1,078 in 2023), and £599.99 (equivalent to £978.12 in 2025)—the highest prices Apple allowed for App Store content. Without explanation, the application was removed from the App Store by Apple less than a day after its release. === Purchases === Eight people bought the application, at least one of whom claimed to have done so accidentally. Six US sales and two European sales netted $5,600 for Heinrich and $2,400 for Apple (respectively equivalent to $8,374 and $3,589 in 2025). In correspondence with the Los Angeles Times, Heinrich told the newspaper that Apple had refunded two purchasers of his app, and that he was happy to not have dissatisfied customers. == Reception == Discussing the app on the website Silicon Alley Insider, Dan Frommer described the program as a "scam", "worthless", and finally "a joke that smells like a scammy rip-off" on August 5, 6, and 8, respectively. Without purchasing the app, Fox News's Paul Wagenseil guessed that the secret mantra was "German for 'Sucker!'" (Heinrich is German). Wired's Brian X. Chen described I Am Rich as a waste of money to "prove you're a jerk", and contrasted the expenditure with donating to cancer foundations and Third World countries. Heinrich told the Los Angeles Times's Mark Milian that he had received correspondence from satisfied customers: "I've got e-mails from customers telling me that they really love the app [... and that they had] no trouble spending the money". In an interview with The New York Times, though, he told of receiving many insulting emails and telephone messages. == Similar applications == The next year, Heinrich released I Am Rich LE. Priced at US$9.99 (equivalent to $14.99 in 2025), the new app has several new features (including a calculator, "help system", and the "famous mantra without the spelling mistakes") to meet Apple's requirement that apps have "definable content". Some customers were disappointed by the new functionality, poorly rating the app due to its ostensible improvements. On 23 February 2009, CNET Asia reported on the "conceptually similar" app, I Am Richer, developed by Mike DG for Google's Android. The app was released on the Android Market for US$200 (equivalent to $300.14 in 2025), a limit imposed by Google, who had no objection to the application. With the same name, the I Am Rich that was released on the Windows Phone Marketplace on 22 December 2010, was developed by DotNetNuzzi. Described by MobileCrunch as equally useless as the original, this app cost US$499.99 (equivalent to $738.2 in 2025), the price cap imposed by Microsoft.
Security information management
Security information management (SIM) is an information security industry term for the collection of data such as log files into a central repository for trend analysis. == Overview == SIM products generally are software agents running on the computer systems that are monitored. The recorded log information is then sent to a centralized server that acts as a "security console". The console typically displays reports, charts, and graphs of that information, often in real time. Some software agents can incorporate local filters to reduce and manipulate the data that they send to the server, although typically from a forensic point of view you would collect all audit and accounting logs to ensure you can recreate a security incident. The security console is monitored by an administrator who reviews the consolidated information and takes action in response to any alerts issued. The data that is sent to the server to be correlated and analyzed are normalized by the software agents into a common form, usually XML. Those data are then aggregated in order to reduce their overall size. == Terminology == The terminology can easily be mistaken as a reference to the whole aspect of protecting one's infrastructure from any computer security breach. Due to historic reasons of terminology evolution; SIM refers to just the part of information security which consists of discovery of 'bad behavior' or policy violations by using data collection techniques. The term commonly used to represent an entire security infrastructure that protects an environment is commonly called information security management (InfoSec). Security information management is also referred to as log management and is different from SEM (security event management), but makes up a portion of a SIEM (security information and event management) solution. == Regulatory compliance == Security information management systems support compliance with regulatory frameworks that require centralized collection and analysis of security data. The Health Insurance Portability and Accountability Act (HIPAA) Security Rule requires covered entities to implement audit controls that record and examine activity in information systems containing electronic protected health information (45 CFR 164.312(b))."45 CFR § 164.312 - Technical safeguards". Legal Information Institute. Retrieved April 1, 2026. SIM platforms aggregate these audit records to support the required regular review of information system activity records (45 CFR 164.308(a)(1)(ii)(D)). The December 2024 HIPAA Security Rule NPRM proposed requiring regulated entities to deploy automated systems capable of monitoring and recording access to ePHI, including the ability to detect unauthorized access attempts in near real-time."HIPAA Security Rule To Strengthen the Cybersecurity of Electronic Protected Health Information". Federal Register. January 6, 2025. Retrieved April 1, 2026. The Payment Card Industry Data Security Standard (PCI DSS) similarly requires centralized log management and daily review of security events (Requirements 10.4 and 10.6)."PCI DSS v4.0" (PDF). PCI Security Standards Council. March 2022. Retrieved April 1, 2026. NIST Special Publication 800-53 addresses security information management through the AU (Audit and Accountability) control family, which specifies requirements for audit event generation, content, storage, and analysis."NIST SP 800-53 Rev. 5: Security and Privacy Controls". National Institute of Standards and Technology. September 2020. Retrieved April 1, 2026.
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.
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.