A time-lock puzzle, or time-released cryptography, encrypts a message that cannot be decrypted until a specified amount of time has passed. The concept was first described by Timothy C. May, and a solution first introduced by Ron Rivest, Adi Shamir, and David A. Wagner in 1996. Time-lock puzzle are useful in cases where confidentiality of information is determined by time, such as a diarist who does not want their views released until 50 years after their death, an auction where bids are sealed until the bidding period is closed, electronic voting, and contract signing. They can additionally be used in creating further cryptographic primitives, such as verifiable delay functions and zero knowledge proofs. Time-released cryptography can be achieved through several different mechanisms. Use mathematical problems requiring sequential calculations to solve, and cannot be solved with parallelization. Thus, adding more computers to a problem will not help solve the problem faster. Use of a trusted agent, or multiple agents who each hold a part of the message and cryptographic keys, who release the message after a specified time period has passed. Distribute public encryption keys to users, and place private cryptographic keys with a trusted agent in an offline location, to be released at a later date.
Path tracing
Path tracing is a rendering algorithm in computer graphics that simulates how light interacts with objects and participating media to generate realistic (physically plausible) images. It is based on earlier, more limited, ray tracing algorithms. Path tracing is used to create photorealistic images for artistic purposes, and for applications such as architectural rendering and product design. It is also used to render frames for animated films, and visual effects for film and television. Because it can be very accurate and unbiased, it is commonly used to generate reference images when testing the quality of other rendering algorithms. The technique uses the Monte Carlo method to compute estimates of global illumination and simulate the ways different materials reflect (or scatter), transmit, absorb, and emit light. It can incorporate simple modeling of the effects of aperture and lens (depth of field, and bokeh) and shutter speed (motion blur), or more realistic simulation of the optical components in a camera. The algorithm works by describing illumination in a scene using the rendering equation, or light transport equation, and finding an approximate solution using Monte Carlo integration. An inefficient (but accurate) version of the algorithm can be very simple, and involves tracing a ray from the camera, allowing this ray to bounce in random directions as it hits different objects in the scene, and computing the amount of light transmitted along the path to the camera whenever the path encounters a light source. This process is repeated many times for each pixel (each repetition, with generated path and transmitted light, is called a sample), and the results are averaged. One main difference between this algorithm and standard ray tracing is that a single unbranching path is traced each time, while "Whitted-style" or "Cook-style" ray tracing recursively samples branching paths (e.g. when light is both reflected and refracted by a glass object). More practical versions incorporate improvements such as quasi-Monte Carlo methods (techniques that distribute samples more evenly), importance sampling (take more samples of paths that are likely to transport more light), and next event estimation (allow a very limited form of branching, and sample additional paths that connect to the lights more directly). Because path tracing uses random samples there is noise in the final image, which decreases as more samples are taken. Images commonly require many thousands of samples per pixel (spp) to reduce noise to an acceptable level, and denoising techniques (e.g. based on neural networks) are often used. Denoising is usually necessary when path tracing is used for real-time rendering in video games, because relatively few samples can be taken. Many alternative algorithms for path tracing have been developed, although they do not always outperform more straightforward implementations. These include bidirectional path tracing (which traces paths forwards from the light source as well as backwards from the camera), Metropolis light transport, and ways of combining path tracing with photon mapping. Video games often use biased versions of path tracing to improve performance (e.g. limiting the number of bounces in each path). A family of techniques called ReSTIR has been developed that can help real-time path tracing by sharing data between nearby pixels and consecutive frames. == History == Like all ray tracing methods, path tracing is based on ray casting, which Arthur Appel used for computer graphics rendering in the late 1960s. In 1980, John Turner Whitted published a recursive ray tracing algorithm that allows rendering images of scenes containing mirrored surfaces and refractive transparent objects. In 1984, Cook et al. described a form of ray tracing called distributed ray tracing, which uses Monte Carlo integration to render effects such as depth of field, motion blur, reflection from rough surfaces, and area lights. The same year, the radiosity method (not a ray tracing method) was published, which was the first physically based method for rendering diffuse global illumination. In 1986, Jim Kajiya published a paper exploring how to use distributed ray tracing to render physically-based global illumination, and this paper also introduced and named the method called "path tracing". Path tracing and other distributed ray tracing techniques were further refined in the late 1980s and early 1990s by researchers such as James Arvo and Peter Shirley, and by Greg Ward in the open source Radiance software. Despite being theoretically able to render any lighting, the original form of path tracing can sometimes be very inefficient (or noisy) for rendering light that is reflected or refracted before illuminating a visible surface, including diffuse global illumination where light enters an area through narrow gaps, because it traces paths only from the camera. To address this, variations of path tracing that trace paths from both the camera and from light sources, called bidirectional path tracing, were published in 1993 by Eric Lafortune and Yves Willems, and in 1997 by Eric Veach and Leonidas Guibas. In 1997 Veach and Guibas also published an alternative method called Metropolis light transport, which combines bidirectional path tracing with the Metropolis method. Veach's lengthy Ph.D. dissertation described both techniques, along with the theoretical background of path tracing; later, the book Physically Based Rendering (which won an Academy Award for Technical Achievement in 2014) helped to make information about path tracing more widely available. Path tracing requires tracing a large number of paths of light in order to produce an image with a visually acceptable amount of noise. This made path tracing very slow on computers available in the 1980s and 1990s, and noise remained a problem when trying to reproduce the style of earlier computer graphics animated films. Most animated films produced until around 2010, by studios such as Pixar, used rasterization-based rendering, with ray tracing used selectively for reflections (and later for precomputed or cached global illumination). However the speed of computers rapidly increased during the 1990s. Blue Sky Studios pioneered using Monte Carlo ray tracing for global illumination in animation, including in the 1998 short film "Bunny", but they did not disclose the precise techniques used. Path tracing gradually become more practical for film production in the early 2000s. The Arnold renderer, developed by Marcos Fajardo, was used by Sony Pictures Imageworks to produce the feature-length film Monster House, released in 2006. Pixar rewrote their RenderMan software to use path tracing, and released their first feature-length path-traced film Finding Dory in 2016. Although path tracing still had a large computational cost, animation studios discovered that less human labor was required when using it, for example because global illumination no longer needed to be faked by manually placing lights. The amount of noise present in path traced images still caused difficulties, particularly when rendering motion blur (which was used extensively by earlier animated films) but denoising techniques were developed to address this. New techniques were also needed for rendering hair and fur, and to handle the extremely large scenes sometimes required by films. Renderers such as Arnold, and Disney's Hyperion, originally only used CPUs for rendering, but as GPUs became more capable (and APIs such as CUDA, OpenCL, and OptiX were released) researchers and developers began adapting algorithms and implementations to use GPUs. GPUs can dramatically reduce rendering time: for example using a high-end GPU to accelerate portions of the rendering code can make it over 30 times faster than using only a high-end CPU. == Description == Kajiya's 1986 paper defined a recursive integral equation called the rendering equation, which describes a simplified form of light transport. Using Monte Carlo integration for the integral on the right side of the equation leads fairly directly to the path tracing algorithm: I ( x , x ′ ) = g ( x , x ′ ) [ ϵ ( x , x ′ ) + ∫ S ρ ( x , x ′ , x ″ ) I ( x ′ , x ″ ) d x ″ ] {\displaystyle I(x,x')=g(x,x')\left[\epsilon (x,x')+\int _{S}\rho (x,x',x'')I(x',x'')dx''\right]} This expresses I(x,x'), the light arriving at point x from point x', as the product of a geometry term, g(x,x'), which is 0 if there is something blocking the light between the two points and 1 otherwise, and the amount of light leaving point x' and traveling towards x. The light leaving point x' is the sum of the light emitted by the surface at x', and the integral of the light arriving at x' from all other points in the scene (the integration domain S) and being reflected towards x. The factor ρ(x,x',x''), which calculates how much light is reflected, must take into account the angles at which the light is arriving and leaving, and
Logical Machine Corporation
Logical Machine Corporation (LOMAC) was an American computer company active from the mid-1970s to the 1980s and based in the San Francisco Bay Area. It was founded as John Peers and Company by the British entrepreneur John Peers in 1974. LOMAC developed the ADAM, a minicomputer which ran a specialized compiler for the company's natural English programming language. Throughout the late 1970s, the company acquired several technology firms, including Byte, Inc., the owner of the Byte Shop retail chain. Despite its unique approach to computing and earning $5 million in revenue in 1977, LOMAC struggled as the industry began to standardize around the IBM Personal Computer (IBM PC). Following Peers's departure in 1980, the company rebranded as Logical Business Machines, Inc. (LBM, or simply Logical), and attempted to pivot toward IBM PC–compatible hardware. However, financial difficulties led to the company filing for Chapter 11 bankruptcy in 1984. After emerging from bankruptcy in 1985 with new investment, Logical ceased hardware manufacturing to focus exclusively on software development and value-added reselling. == History == John Peers (born 1942) founded Logical Machine Corporation as John Peers and Company in September 1974. The company originally occupied a 4,500-square-foot office in Burlingame, California. The company was Peers' fourth; he had recently sold off Allied Business Systems of London to Trafalgar House in 1974. Peers sought to set up manufacturing in an agricultural zone in Ukiah, California. Following a delay, caused in part by concerned residents, a 30,000-square-foot plant was raised in Burke Hill, three miles south of Ukiah. The Ukiah plant was built to mass manufacture the company's ADAM minicomputer. The ADAM computer ran a specialized compiler for the company's natural English programming language; that is to say, the programming language attempted to closely emulate English syntax. Prototypes of the ADAM were built in May 1974, based on specifications devised in October 1973. Peers had yet to patent the technology as of June 1975. The ADAM's central processing unit was bolted onto an 7-by-6-foot L-shaped desk, on which rested its terminal. Twenty units of the ADAM were installed between April 1975 and February 1976, out of a backlog of orders for 3,500 from 500 clients, manufactured out of the company's Burlingame headquarters. It cost US$40,000. A controversial print advertisement featuring a naked woman seated at an ADAM terminal—as a pastiche of Adam and Eve—was recalled in early 1976 as a result of outcry from the National Organization for Women. The company changed its name to Logical Machine Corporation (LOMAC) in October 1976 and moved its headquarters to a 26,000-square-foot building in Sunnyvale, California, in anticipation of a ramping up of orders for the ADAM. The company originally occupied half of the building; they later purchased the other half from the tenant in July 1977 to double its manufacturing output. For fiscal year 1977, the company earned $5 million in revenue. In December 1977, LOMAC acquired Byte, Inc.—the proprietor of The Byte Shop, the first computer retail chain—from Paul Terrell and Boyd Wilson for an unspecified amount. The Byte Shop had 65 locations in the San Francisco Bay Area in 1978; it catered mainly to hobbyists with low cost microcomputer kits, in contrast to the high cost of LOMAC's ADAM. By July 1978, however, LOMAC were able to reduce the price of the ADAM down to $15,000. The company by that point had shipped their 50th ADAM and expanded to 14 countries. Also in 1978, LOMAC acquired Mass Memory—a high-tech optical storage company based in Phoenix, Arizona, whose products had storage capacities on the order gigabytes and terabytes—and Centigram, makers of the Mike—a computer with speech recognition. Later that year, the company introduced Tina, a low-cost version of the ADAM. LOMAC suffered losses that year and appointed Jerry Brandt to the board of directions, naming him chief operating officer, in August 1978. Brandt had Logical absorb Mass Memory and Centigram into the parent operations, shutting down their respective plants in the process, converted 10 Byte Shops to franchises and opened 25 more franchised Byte locations, and stopped direct sales of LOMAC's business computer products. By the beginning of 1979, LOMAC was profitable once more, and Brandt was let go from LOMAC. Peers left LOMAC in 1980, following a slump in the company's sales. He became an executive director of the United States Robotics Society, a consortium for industrial automation companies, that year. Following Peers' departure, LOMAC changed its name to Logical Business Machines, adopting the name of its European subsidiary. In 1983, the company announced a 16-bit clone of the IBM PC, called the Logical L-XT, which featured a 10-MB hard drive, 320-KB floppy drive and 192 KB of RAM, and a real-time clock, and came shipped with various software (including MS-DOS, a word processor, and a spreadsheet application) and an amber CRT monitor. The following year, the company introduced L-NET, a local area network system based on the L-XT that could link up to 64 computers. L-NET came shipped with a natural programming language, Diplomat—a descendant of the programming language used on the ADAM. In June 1983, Logical sued Coleco Industries over trademark infringement with the latter's to-be-released Adam microcomputer. Logical cited confusion from their existing ADAM customer base caused by the announcement of the Coleco Adam as the basis for the suit. Coleco challenged Logical in the press, writing that Logical's rights to the Adam trademark for use in computers had lapsed earlier in the year. The two settled out of court, with Coleco agreeing to license the Adam name from Logical in exchange for unlimited rights to the Adam trademark. Logical halted development of the L-XT when they filed for Chapter 11 bankruptcy in July 1984. The company had been $4 million in debt. They emerged from bankruptcy in September 1985, after being infused with $2 million from Carat Ltd. The latter immediately received a little less than 50 percent ownership in Logical—this stake set to grow to over 50 percent over the next six months. As part of the terms of exiting bankruptcy, Logical stopped manufacturing hardware and strictly became a software development company and value-added reseller of computer systems.
Semantic interpretation
Semantic interpretation is an important component in dialog systems. It is related to natural language understanding, but mostly it refers to the last stage of understanding. The goal of interpretation is binding the user utterance to concept, or something the system can understand. Typically it is creating a database query based on user utterance.
Huawei Mobile Services
Huawei Mobile Services (HMS) is a collection of proprietary services and high level application programming interfaces (APIs) developed by Huawei Technologies Co., Ltd. Its hub known as HMS Core serves as a toolkit for app development on Huawei devices. HMS is typically installed on Huawei devices on top of running HarmonyOS 4.x and earlier operating system on its earlier devices running the Android operating system with EMUI including devices already distributed with Google Mobile Services. Alongside, HMS Core Wear Engine for Android phones with lightweight based LiteOS wearable middleware app framework integration connectivity like notifications, status etc. HMS consists of seven key services and the HMS Core. The key services are Huawei ID, Huawei Cloud, AppGallery, Themes, Huawei Video, Browser, and Assistant. The web browser is based on Chromium. Huawei Quick Apps is the alternative to Google Instant Apps. By January 2020, over 50,000 apps had been integrated with HMS Core. Its rival, Google Mobile Services has 3 million apps on Google's Play Store. The AppGallery claimed 180 billion downloads in 2019. In March 2020, HMS was used by 650 million monthly active users across 170 countries. A Chinese phone manufacturer, LeTV, hosted a smartphone business communication meeting in Beijing on September 27, 2021, to demonstrate its phone, the LeTV S1. This was the first smartphone from a third-party manufacturer to include Huawei Mobile Services (HMS). == HMS on Android and HarmonyOS == Huawei Mobile Services on Android goes all the way back to August 2016 as Huawei ID services for phones, basic functionalities for Huawei P9 series. However, in May 2019 proved to be a significant change to HMS when Google was prohibited from working with Huawei on any new devices extending ecosystem for AppGallery store front launched in April 2018, year prior. This also included bundling Google's Apps, including Gmail, Maps and YouTube. Any new Huawei devices launched after 16 May 2019 were unable to receive updates from Google services and would be considered 'uncertified' meaning Huawei's only solution at the time was to turn HMS into a genuine competitor to Google and incentivize app developers to utilize the platform. Huawei officially launched Huawei Mobile Services in China on December 24, 2019, as a beta. Huawei expanded Huawei Mobile Services in Europe in February 2020 and other markets in Asia, Latin America, Middle East & Africa, Canada, Mexico followed outside banned US market. HMS is available on the Honor 9X Pro, View 30 Pro, Huawei Mate XS. HMS is also available, alongside GMS, on many other Huawei models launched before the ban. Huawei promised developers it would take, “less than 10 minutes", to port their app over to HMS - to illustrate the ease of portability between Google's Play Store and the HMS AppGallery. On January 15, 2020, HMS Core 4.0 (Huawei Mobile Services Core 4.0) was officially launched. Huawei announced that at this time, there were already 1.3 million developers and 55,000 applications on board. The next day, Huawei held a developer day event in London and invested £20 million to encourage developers in the United Kingdom and Ireland to use HMS. On July 15, 2021, Huawei expanded HMS with classic HarmonyOS dual-framework that provided Java support and eventually with JavaScript and ArkTS (eTS) language support with HMS Core 6.0 for app development with primarily Android apps, alongside limited HAP imperative developed based apps that shares AOSP file system libraries in all types of devices from smartphones, tablets, smart screens, smartwatches, and car machines. Including various third-party development frameworks, such as React Native, Cordova, etc. At HDC 2023, Huawei unveiled HarmonyOS 5, marking a total break from the hybrid Android derived platform. This shift replaced the legacy Android and classic HarmonyOS-based HMS SDK with a full native API developer kit SDK built solely on OpenHarmony. The architecture moved from middleware services to vertical integration path. In this new model, HMS Core libraries are no longer external add-ons but are bundled directly into the system and DevEco Studio as native HarmonyOS Kits. == HMS Core == HMS Core is a hub for Huawei Mobile Services and serves as a toolkit for app development on Huawei devices. The core comprises Development, Growth and Monetizing and was created as a replacement for Google Mobile Services (GMS) Core. HMS core services were available in more than 55,000 apps in June 2020; HMS Core 5.0 debuted in September 2020. HMS Core 6.0 was launched in June 2021 with extended support for Huawei Cloud services. In June 2021, the number of registered developers within the HMS ecosystem was 4 million, and the number of apps integrated with the HMS Core had reached 134,000. As of July 2022, registered developers within HMS ecosystem had grown to 5 million, and the number of apps integrated with the HMS Core reached 203,000. The number of apps had grown to 220,000 by 30 September 2022. == AppGallery == The AppGallery has a key rival, Google's Play Store on Android. The AppGallery is available in 170 countries, across 78 languages. == Reception == The reception of HMS is mixed, with the majority of discussion based around the key Google/Android apps which are not yet present on the AppGallery and whether or not this presents a significant problem to users. The open development of HMS Core has been regarded by some as benefiting the Android project as a whole, "If Huawei continues to invest in a holistically open approach ... the result could be that we could all end up a bit less beholden to Google".
Collision detection
Collision detection is the computational problem of detecting an intersection of two or more objects in virtual space. More precisely, it deals with the questions of if, when, and where two or more objects intersect. Collision detection is a classic problem of computational geometry with applications in computer graphics, physical simulation, video games, robotics (including autonomous driving), and computational physics. Collision detection algorithms can be divided into operating on 2D or 3D spatial objects. == Overview == Collision detection is closely linked to calculating the distance between objects, as objects collide when the distance between them is less than or equal to zero. Negative distances indicate that one object has penetrated another. Performing collision detection requires more context than just the distance between the objects. Accurately identifying the points of contact on both objects' surfaces is also essential for computing a physically accurate collision response. The complexity of this task increases with the level of detail in the objects' representations: the more intricate the model, the greater the computational cost. Collision detection frequently involves dynamic objects, adding a temporal dimension to distance calculations. Instead of simply measuring distance between static objects, collision detection algorithms often aim to determine whether the objects' motion will bring them to a point in time when their distance is zero—an operation that adds significant computational overhead. In collision detection involving multiple objects, a naive approach would require detecting collisions for all pairwise combinations of objects. As the number of objects increases, the number of required comparisons grows rapidly: for n {\displaystyle n} objects, n ( n − 1 ) / 2 {n(n-1)}/{2} intersection tests are needed with a naive approach. This quadratic growth makes such an approach computationally expensive as n {\displaystyle n} increases. Due to the complexity mentioned above, collision detection is a computationally intensive process. Nevertheless, it is essential for interactive applications like video games, robotics, and real-time physics engines. To manage these computational demands, extensive efforts have gone into optimizing collision detection algorithms. A commonly used approach towards accelerating the required computations is to divide the process into two phases: the broad phase and the narrow phase. The broad phase aims to answer the question of whether objects might collide, using a conservative but efficient approach to rule out pairs that clearly do not intersect, thus avoiding unnecessary calculations. Objects that cannot be definitively separated in the broad phase are passed to the narrow phase. Here, more precise algorithms determine whether these objects actually intersect. If they do, the narrow phase often calculates the exact time and location of the intersection. == Broad phase == This phase aims at quickly finding objects or parts of objects for which it can be quickly determined that no further collision test is needed. A useful property of such approach is that it is output sensitive. In the context of collision detection this means that the time complexity of the collision detection is proportional to the number of objects that are close to each other. An early example of that is the I-COLLIDE where the number of required narrow phase collision tests was O ( n + m ) {\displaystyle O(n+m)} where n {\displaystyle n} is the number of objects and m {\displaystyle m} is the number of objects at close proximity. This is a significant improvement over the quadratic complexity of the naive approach. === Spatial partitioning === Several approaches can be grouped under the spatial partitioning umbrella, which includes octrees (for 3D), quadtrees (for 2D), binary space partitioning (or BSP trees) and other, similar approaches. If one splits space into a number of simple cells, and if two objects can be shown not to be in the same cell, then they need not be checked for intersection. Dynamic scenes and deformable objects require updating the partitioning which can add overhead. === Bounding volume hierarchy === Bounding Volume Hierarchy (BVH) is a tree structure over a set of bounding volumes. Collision is determined by doing a tree traversal starting from the root. If the bounding volume of the root doesn't intersect with the object of interest, the traversal can be stopped. If, however there is an intersection, the traversal proceeds and checks the branches for each there is an intersection. Branches for which there is no intersection with the bounding volume can be culled from further intersection test. Therefore, multiple objects can be determined to not intersect at once. BVH can be used with deformable objects such as cloth or soft-bodies but the volume hierarchy has to be adjusted as the shape deforms. For deformable objects we need to be concerned about self-collisions or self intersections. BVH can be used for that end as well. Collision between two objects is computed by computing intersection between the bounding volumes of the root of the tree as there are collision we dive into the sub-trees that intersect. Exact collisions between the actual objects, or its parts (often triangles of a triangle mesh) need to be computed only between intersecting leaves. The same approach works for pair wise collision and self-collisions. === Exploiting temporal coherence === During the broad-phase, when the objects in the world move or deform, the data-structures used to cull collisions have to be updated. In cases where the changes between two frames or time-steps are small and the objects can be approximated well with axis-aligned bounding boxes, the sweep and prune algorithm can be a suitable approach. Several key observation make the implementation efficient: Two bounding-boxes intersect if, and only if, there is overlap along all three axes; overlap can be determined, for each axis separately, by sorting the intervals for all the boxes; and lastly, between two frames updates are typically small (making sorting algorithms optimized for almost-sorted lists suitable for this application). The algorithm keeps track of currently intersecting boxes, and as objects move, re-sorting the intervals helps keep track of the status. === Pairwise pruning === Once a pair of physical bodies has been selected for further investigation, collisions need to be checked more carefully. However, in many applications, individual objects (if they are not too deformable) are described by a set of smaller primitives, mainly triangles. So there are two sets of triangles, S = S 1 , S 2 , … , S n {\displaystyle S={S_{1},S_{2},\dots ,S_{n}}} and T = T 1 , T 2 , … , T n {\displaystyle T={T_{1},T_{2},\dots ,T_{n}}} (for simplicity, each set has the same number of triangles.) The obvious thing to do is to check all triangles S j {\displaystyle S_{j}} against all triangles T k {\displaystyle T_{k}} for collisions, but this involves n 2 {\displaystyle n^{2}} comparisons, which is highly inefficient. If possible, it is desirable to use a pruning algorithm to reduce the number of pairs of triangles that need to be checked. The most widely used family of algorithms is known as the hierarchical bounding volumes method. As a preprocessing step, for each object (e.g., S {\displaystyle S} and T {\displaystyle T} ) calculates a hierarchy of bounding volumes. Then, at each time step, when collisions need to be checked between S {\displaystyle S} and T {\displaystyle T} , the hierarchical bounding volumes are used to reduce the number of pairs of triangles under consideration. For simplicity, provide an example using bounding spheres, although it has been noted that spheres are undesirable in many cases. If E {\displaystyle E} is a set of triangles, a bounding sphere is pre-calculated. B ( E ) {\displaystyle B(E)} . There are many ways of choosing B ( E ) {\displaystyle B(E)} , B ( E ) {\displaystyle B(E)} is a sphere that completely contains E {\displaystyle E} and is as small as possible. Ahead of time, B ( S ) {\displaystyle B(S)} and B ( T ) {\displaystyle B(T)} can be computed. Clearly, if these two spheres do not intersect (and that is very easy to test), then neither do S {\displaystyle S} and T {\displaystyle T} . This is not much better than an n-body pruning algorithm, however. If E = E 1 , E 2 , … , E m {\displaystyle E={E_{1},E_{2},\dots ,E_{m}}} is a set of triangles, then split it into two halves L ( E ) := E 1 , E 2 , … , E m / 2 {\displaystyle L(E):={E_{1},E_{2},\dots ,E_{m/2}}} and R ( E ) := E m / 2 + 1 , … , E m − 1 , E m {\displaystyle R(E):={E_{m/2+1},\dots ,E_{m-1},E_{m}}} . Apply this to S {\displaystyle S} and T {\displaystyle T} , and calculate (ahead of time) the bounding spheres B ( L ( S ) ) , B ( R ( S ) ) {\displaystyle B(L(S)),B(R(S))} and B ( L ( T ) ) , B ( R ( T ) ) {\displaystyle B(L(T)),B(R(T))} . T
Knowledge assessment methodology
The knowledge assessment methodology (KAM) is "an interactive benchmarking tool created by the World Bank's Knowledge for Development Program to help countries identify the challenges and opportunities they face in making the transition to the knowledge-based economy." KAM does so by providing information on knowledge economy indicators for 146 countries. Its products include the Knowledge Economy Index and the Knowledge Index.