AI Art Quora

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80 Million Tiny Images

80 Million Tiny Images is a dataset intended for training machine-learning systems constructed by Antonio Torralba, Rob Fergus, and William T. Freeman in a collaboration between MIT and New York University. It was published in 2008. The dataset has size 760 GB. It contains 79,302,017 32×32-pixel color images, scaled down from images scraped from the World Wide Web over 8 months. The images are classified into 75,062 classes. Each class is a non-abstract noun in WordNet. Images may appear in more than one class. The dataset was motivated by non-parametric models of neural activations in the visual cortex upon seeing images. The CIFAR-10 dataset uses a subset of the images in this dataset, but with independently generated labels, as the original labels were not reliable. The CIFAR-10 set has 6000 examples of each of 10 classes, and the CIFAR-100 set has 600 examples of each of 100 non-overlapping classes. == Construction == It was first reported in a technical report in April 2007, during the middle of the construction process, when there were only 73 million images. The full dataset was published in 2008. They began with all 75,846 non-abstract nouns in WordNet, and then for each of these nouns, they scraped 7 image search engines: Altavista, Ask.com, Flickr, Cydral, Google, Picsearch, and Webshots. After 8 months of scraping, they obtained 97,245,098 images. Since they did not have enough storage, they downsized the images to 32×32 as they were scraped. After gathering, they removed images with zero variance and intra-word duplicate images, resulting in the final dataset. Out of the 75,846 nouns, only 75,062 classes had any results, so the other nouns did not appear in the final dataset. The number of images per noun follows a Zipf-like distribution, with 1056 images per noun on average. To prevent a few nouns taking up too many images, they put an upper bound of at most 3000 images per noun. == Retirement == The 80 Million Tiny Images dataset was retired from use by its creators in 2020, after a paper by researchers Abeba Birhane and Vinay Prabhu found that some of the labeling of several publicly available image datasets, including 80 Million Tiny Images, contained racist and misogynistic slurs which were causing models trained on them to exhibit racial and sexual bias. The dataset also contained offensive images. Following the release of the paper, the dataset's creators removed the dataset from distribution, and requested that other researchers not use it for further research and to delete their copies of the dataset.
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Weak stability boundary

Weak stability boundary (WSB), including low-energy transfer, is a concept introduced by Edward Belbruno in 1987. The concept explained how a spacecraft could change orbits using very little fuel. Weak stability boundary is defined for the three-body problem. This problem considers the motion of a particle P of negligible mass moving with respect to two larger bodies, P1, P2, modeled as point masses, where these bodies move in circular or elliptical orbits with respect to each other, and P2 is smaller than P1. The force between the three bodies is the classical Newtonian gravitational force. For example, P1 is the Earth, P2 is the Moon and P is a spacecraft; or P1 is the Sun, P2 is Jupiter and P is a comet, etc. This model is called the restricted three-body problem. The weak stability boundary defines a region about P2 where P is temporarily captured. This region is in position-velocity space. Capture means that the Kepler energy between P and P2 is negative. This is also called weak capture. == Background == This boundary was defined for the first time by Edward Belbruno of Princeton University in 1987. He described a Low-energy transfer which would allow a spacecraft to change orbits using very little fuel. It was for motion about Moon (P2) with P1 = Earth. It is defined algorithmically by monitoring cycling motion of P about the Moon and finding the region where cycling motion transitions between stable and unstable after one cycle. Stable motion means P can completely cycle about the Moon for one cycle relative to a reference section, starting in weak capture. P needs to return to the reference section with negative Kepler energy. Otherwise, the motion is called unstable, where P does not return to the reference section within one cycle or if it returns, it has non-negative Kepler energy. The set of all transition points about the Moon comprises the weak stability boundary, W. The motion of P is sensitive or chaotic as it moves about the Moon within W. A mathematical proof that the motion within W is chaotic was given in 2004. This is accomplished by showing that the set W about an arbitrary body P2 in the restricted three-body problem contains a hyperbolic invariant set of fractional dimension consisting of the infinitely many intersections Hyperbolic manifolds. The weak stability boundary was originally referred to as the fuzzy boundary. This term was used since the transition between capture and escape defined in the algorithm is not well defined and limited by the numerical accuracy. This defines a "fuzzy" location for the transition points. It is also due the inherent chaos in the motion of P near the transition points. It can be thought of as a fuzzy chaos region. As is described in an article in Discover magazine, the WSB can be roughly viewed as the fuzzy edge of a region, referred to as a gravity well, about a body (the Moon), where its force of gravity becomes small enough to be dominated by force of gravity of another body (the Earth) and the motion there is chaotic. A much more general algorithm defining W was given in 2007. It defines W relative to n-cycles, where n = 1,2,3,..., yielding boundaries of order n. This gives a much more complex region consisting of the union of all the weak stability boundaries of order n. This definition was explored further in 2010. The results suggested that W consists, in part, of the hyperbolic network of invariant manifolds associated to the Lyapunov orbits about the L1, L2 Lagrange points near P2. The explicit determination of the set W about P2 = Jupiter, where P1 is the Sun, is described in "Computation of Weak Stability Boundaries: Sun-Jupiter Case". It turns out that a weak stability region can also be defined relative to the larger mass point, P1. A proof of the existence of the weak stability boundary about P1 was given in 2012, but a different definition is used. The chaos of the motion is analytically proven in "Geometry of Weak Stability Boundaries". The boundary is studied in "Applicability and Dynamical Characterization of the Associated Sets of the Algorithmic Weak Stability Boundary in the Lunar Sphere of Influence". == Applications == There are a number of important applications for the weak stability boundary (WSB). Since the WSB defines a region of temporary capture, it can be used, for example, to find transfer trajectories from the Earth to the Moon that arrive at the Moon within the WSB region in weak capture, which is called ballistic capture for a spacecraft. No fuel is required for capture in this case. This was numerically demonstrated in 1987. This is the first reference for ballistic capture for spacecraft and definition of the weak stability boundary. The boundary was operationally demonstrated to exist in 1991 when it was used to find a ballistic capture transfer to the Moon for Japan's Hiten spacecraft. Other missions have used the same transfer type as Hiten, including Grail, Capstone, Danuri, Hakuto-R Mission 1 and SLIM. The WSB for Mars is studied in "Earth-Mars Transfers with Ballistic Capture" and ballistic capture transfers to Mars are computed. The BepiColombo mission of ESA should achieve ballistic capture at the WSB of Mercury in November 2026. The WSB region can be used in the field of Astrophysics. It can be defined for stars within open star clusters. This is done in "Chaotic Exchange of Solid Material Between Planetary Systems: Implications for the Lithopanspermia Hypothesis" to analyze the capture of solid material that may have arrived on the Earth early in the age of the Solar System to study the validity of the lithopanspermia hypothesis. Numerical explorations of trajectories for P starting in the WSB region about P2 show that after the particle P escapes P2 at the end of weak capture, it moves about the primary body, P1, in a near resonant orbit, in resonance with P2 about P1. This property was used to study comets that move in orbits about the Sun in orbital resonance with Jupiter, which change resonance orbits by becoming weakly captured by Jupiter. An example of such a comet is 39P/Oterma. This property of change of resonance of orbits about P1 when P is weakly captured by the WSB of P2 has an interesting application to the field of quantum mechanics to the motion of an electron about the proton in a hydrogen atom. The transition motion of an electron about the proton between different energy states described by the Schrödinger equation is shown to be equivalent to the change of resonance of P about P1 via weak capture by P2 for a family of transitioning resonance orbits. This gives a classical model using chaotic dynamics with Newtonian gravity for the motion of an electron.
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Small Data

Small Data: the Tiny Clues that Uncover Huge Trends is Martin Lindstrom's seventh book. It chronicles his work as a branding expert, working with consumers across the world to better understand their behavior. The theory behind the book is that businesses can better create products and services based on observing consumer behavior in their homes, as opposed to relying solely on big data. == Content == The book is based on a several year period of consumer studies for major corporations across the globe. It features case studies of the author's work interviewing consumers in their homes and using his observations to create hypotheses as to why they use products the way that they do. == Public reception == The book was a New York Times Bestseller upon release and was positively reviewed on several websites, Including Entrepreneur and Forbes. In 2016, it was named a Best Business Book by strategy+business and one of Inc. Magazine's Best Sales and Marketing books.
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TurboQuant

TurboQuant is an online vector quantization algorithm for compressing high-dimensional Euclidean vectors while preserving their geometric structure. It was proposed in 2025 by Amir Zandieh, Majid Daliri, Majid Hadian, and Vahab Mirrokni in the paper TurboQuant: Online Vector Quantization with Near-optimal Distortion Rate. The paper lists Zandieh and Mirrokni as affiliated with Google Research, Daliri with New York University, and Hadian with Google DeepMind. The method was developed for applications including large language model (LLM) inference, key–value (KV) cache compression, vector databases, and nearest neighbor search. TurboQuant consists of two related algorithms: TurboQuantmse, which is optimized for mean squared error (MSE), and TurboQuantprod, which is optimized for unbiased inner product estimation. The algorithm uses a random rotation of input vectors, applies scalar quantizers to the rotated coordinates, and, for inner-product estimation, applies a one-bit Quantized Johnson–Lindenstrauss (QJL) transform to the residual error. == Background == Vector quantization is a compression method that maps high-dimensional vectors to a finite set of codewords. The problem has roots in Shannon's source coding theory and rate–distortion theory. In machine learning and information retrieval, vector quantization is used to reduce the memory required to store embeddings, activation vectors, and other numerical representations. In Transformer-based large language models, the KV cache stores key and value vectors from previous tokens during autoregressive decoding. The size of this cache grows with context length, the number of attention heads, and the number of concurrent requests, making it a major memory bottleneck in LLM serving. Similar compression problems appear in vector search, where large collections of embedding vectors must be stored and searched efficiently. Earlier approaches to vector quantization include product quantization, scalar quantization, and data-dependent k-means codebook construction. The TurboQuant paper argues that many existing methods either require offline preprocessing and calibration or suffer from suboptimal distortion guarantees in online settings. == Algorithm == === TurboQuantmse === TurboQuantmse is the version of the algorithm optimized for mean-squared error. For a unit vector x ∈ S d − 1 {\displaystyle x\in S^{d-1}} , the algorithm first applies a random rotation matrix Π ∈ R d × d {\displaystyle \Pi \in \mathbb {R} ^{d\times d}} and sets z = Π x {\displaystyle z=\Pi x} . Each coordinate of the rotated vector follows a shifted and scaled beta distribution, which converges to a normal distribution in high dimensions. In high dimensions, distinct coordinates also become nearly independent, allowing the algorithm to apply scalar quantizers independently to each coordinate. The scalar quantizer is constructed by solving a one-dimensional continuous k-means or Lloyd–Max quantization problem. If the centroids are c 1 , c 2 , … , c 2 b {\displaystyle c_{1},c_{2},\ldots ,c_{2^{b}}} , the quantization step stores, for each coordinate, i d x j = ⁡ a r g m i n k ∈ [ 2 b ] | z j − c k | . {\displaystyle \mathrm {idx} _{j}=\operatorname {} {arg\,min}_{k\in [2^{b}]}|z_{j}-c_{k}|.} During dequantization, the stored index for each coordinate is replaced by the corresponding centroid, giving a reconstructed rotated vector z ~ {\displaystyle {\tilde {z}}} . The algorithm then rotates back: x ~ = Π ⊤ z ~ . {\displaystyle {\tilde {x}}=\Pi ^{\top }{\tilde {z}}.} The paper gives the following bound for TurboQuantmse: D m s e ≤ 3 π 2 ⋅ 1 4 b . {\displaystyle D_{\mathrm {mse} }\leq {\frac {\sqrt {3\pi }}{2}}\cdot {\frac {1}{4^{b}}}.} It also reports finer-grained MSE values of approximately 0.36, 0.117, 0.03, and 0.009 for bit-widths b = 1 , 2 , 3 , 4 {\displaystyle b=1,2,3,4} , respectively. === TurboQuantprod === TurboQuantprod is optimized for unbiased inner-product estimation. The authors note that an MSE-optimized quantizer may introduce bias when used to estimate inner products. To address this, TurboQuantprod first applies TurboQuantmse with bit-width b − 1 {\displaystyle b-1} , then applies a one-bit Quantized Johnson–Lindenstrauss transform to the remaining residual vector. Let r = x − Q m s e − 1 ( Q m s e ( x ) ) {\displaystyle r=x-Q_{\mathrm {mse} }^{-1}(Q_{\mathrm {mse} }(x))} be the residual after MSE quantization, and let γ = ‖ r ‖ 2 {\displaystyle \gamma =\|r\|_{2}} . The QJL step stores a sign vector for the residual. For γ ≠ 0 {\displaystyle \gamma \neq 0} , this can be written using the normalized residual u = r / γ {\displaystyle u=r/\gamma } : q j l = sign ⁡ ( S u ) , {\displaystyle qjl=\operatorname {sign} (Su),} where S ∈ R d × d {\displaystyle S\in \mathbb {R} ^{d\times d}} is a random projection matrix. Since the sign function is invariant under positive rescaling, this is equivalent to sign ⁡ ( S r ) {\displaystyle \operatorname {sign} (Sr)} when r ≠ 0 {\displaystyle r\neq 0} . If γ = 0 {\displaystyle \gamma =0} , the residual correction is zero. TurboQuantprod stores the MSE quantization, the QJL sign vector, and the residual norm: Q p r o d ( x ) = [ Q m s e ( x ) , q j l , γ ] . {\displaystyle Q_{\mathrm {prod} }(x)=\left[Q_{\mathrm {mse} }(x),qjl,\gamma \right].} The dequantized vector is reconstructed as x ~ = x ~ m s e + π / 2 d γ S ⊤ q j l . {\displaystyle {\tilde {x}}={\tilde {x}}_{\mathrm {mse} }+{\frac {\sqrt {\pi /2}}{d}}\,\gamma S^{\top }qjl.} The paper proves that TurboQuantprod is unbiased for inner-product estimation: E x ~ [ ⟨ y , x ~ ⟩ ] = ⟨ y , x ⟩ . {\displaystyle \mathbb {E} _{\tilde {x}}\left[\langle y,{\tilde {x}}\rangle \right]=\langle y,x\rangle .} It also gives the distortion bound D p r o d ≤ 3 π 2 ⋅ ‖ y ‖ 2 2 d ⋅ 1 4 b . {\displaystyle D_{\mathrm {prod} }\leq {\frac {\sqrt {3\pi }}{2}}\cdot {\frac {\|y\|_{2}^{2}}{d}}\cdot {\frac {1}{4^{b}}}.} == Performance and applications == The TurboQuant paper reports that the algorithm achieves near-optimal distortion rates within a small constant factor of information-theoretic lower bounds. The authors report that, for KV cache quantization, TurboQuant achieved quality neutrality at 3.5 bits per channel and marginal degradation at 2.5 bits per channel. In long-context LLM experiments using Llama 3.1 8B Instruct, the paper evaluated the method on a "needle-in-a-haystack" retrieval task with document lengths from 4,000 to 104,000 tokens. It reported that TurboQuant matched the uncompressed full-precision baseline while using more than 4× compression, and compared the method against PolarQuant, SnapKV, PyramidKV, and KIVI. Google Research stated that TurboQuant was evaluated on long-context benchmarks including LongBench, Needle in a Haystack, ZeroSCROLLS, RULER, and L-Eval using open-source models including Gemma and Mistral. According to a report in Tom's Hardware, Google described the method as reducing KV-cache memory by at least six times and achieving up to an eightfold improvement in attention-logit computation on Nvidia H100 GPUs compared with unquantized 32-bit keys. TurboQuant has also been applied to nearest-neighbor vector search. The original paper reports experiments on DBpedia entity embeddings and GloVe embeddings, comparing TurboQuant with product quantization and other vector-search quantization baselines. == Relationship to other methods == TurboQuant is related to several methods for efficient large language model inference and high-dimensional search: Product quantization – a vector quantization technique widely used for approximate nearest-neighbor search Quantization (machine learning) – reducing the numerical precision of weights, activations, or cached tensors in machine learning models PagedAttention – a memory-management algorithm for LLM serving that reduces fragmentation in the KV cache Johnson–Lindenstrauss lemma – a result in high-dimensional geometry used in random projection methods Lloyd's algorithm – an algorithm for scalar and vector quantization, including k-means-style codebook construction Unlike PagedAttention, which focuses on memory allocation and cache layout, TurboQuant reduces the numerical storage cost of the vectors themselves. Unlike many product-quantization methods, TurboQuant is designed to be data-oblivious and online, avoiding dataset-specific codebook training. == Limitations == The strongest performance claims for TurboQuant come from the original paper and Google Research's own publication. Coverage in technology media has noted that the broader impact of the method will depend on real-world implementation details, workloads, and hardware architectures.
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Framebuffer

A framebuffer (frame buffer, or sometimes framestore) is a portion of random-access memory (RAM) containing a bitmap that drives a video display. It is a memory buffer containing data representing all the pixels in a complete video frame. Modern video cards contain framebuffer circuitry in their cores. This circuitry converts an in-memory bitmap into a video signal that can be displayed on a computer monitor. In computing, a screen buffer is a part of computer memory used by a computer application for the representation of the content to be shown on the computer display. The screen buffer may also be called the video buffer, the regeneration buffer, or regen buffer for short. The phrase "screen buffer” refers to a logical function, while video memory refers to a hardware storage location. In particular, the screen buffer may be placed in the main RAM, the video memory, or some other hardware location. To reduce latency and avoid screen tearing, multiple frames can be buffered, and this technique is called multiple buffering. When this is so, at any time, only one frame would be visible, and the others would not be. The currently invisible frames are located in the off-screen buffer. The information in the buffer typically consists of color values for every pixel to be shown on the display. Color values are commonly stored in 1-bit binary (monochrome), 4-bit palettized, 8-bit palettized, 16-bit high color and 24-bit true color formats. An additional alpha channel is sometimes used to retain information about pixel transparency. The total amount of memory required for the framebuffer depends on the resolution of the output signal, and on the color depth or palette size. == History == Computer researchers had long discussed the theoretical advantages of a framebuffer but were unable to produce a machine with sufficient memory at an economically practicable cost. In 1947, the Manchester Baby computer used a Williams tube, later the Williams-Kilburn tube, to store 1024 bits on a cathode-ray tube (CRT) memory and displayed on a second CRT. Other research labs were exploring these techniques with MIT Lincoln Laboratory achieving a 4096 display in 1950. A color-scanned display was implemented in the late 1960s, called the Brookhaven RAster Display (BRAD), which used a drum memory and a television monitor. In 1969, A. Michael Noll of Bell Telephone Laboratories, Inc. implemented a scanned display with a frame buffer, using magnetic-core memory. A year or so later, the Bell Labs system was expanded to display an image with a color depth of three bits on a standard color TV monitor. The vector graphics used in the computer had to be converted for the scanned graphics of a TV display. In the early 1970s, the development of MOS memory (metal–oxide–semiconductor memory) integrated-circuit chips, particularly high-density DRAM (dynamic random-access memory) chips with at least 1 kb memory, made it practical to create, for the first time, a digital memory system with framebuffers capable of holding a standard video image. This led to the development of the SuperPaint system by Richard Shoup at Xerox PARC in 1972. Shoup was able to use the SuperPaint framebuffer to create an early digital video-capture system. By synchronizing the output signal to the input signal, Shoup was able to overwrite each pixel of data as it shifted in. Shoup also experimented with modifying the output signal using color tables. These color tables allowed the SuperPaint system to produce a wide variety of colors outside the range of the limited 8-bit data it contained. This scheme would later become commonplace in computer framebuffers. In 1974, Evans & Sutherland released the first commercial framebuffer, the Picture System, costing about $15,000. It was capable of producing resolutions of up to 512 by 512 pixels in 8-bit grayscale, and became a boon for graphics researchers who did not have the resources to build their own framebuffer. The New York Institute of Technology would later create the first 24-bit color system using three of the Evans & Sutherland framebuffers. Each framebuffer was connected to an RGB color output (one for red, one for green and one for blue), with a Digital Equipment Corporation PDP 11/04 minicomputer controlling the three devices as one. In 1975, the UK company Quantel produced the first commercial full-color broadcast framebuffer, the Quantel DFS 3000. It was first used in TV coverage of the 1976 Montreal Olympics to generate a picture-in-picture inset of the Olympic flaming torch while the rest of the picture featured the runner entering the stadium. The rapid improvement of integrated-circuit technology made it possible for many of the home computers of the late 1970s to contain low-color-depth framebuffers. Today, nearly all computers with graphical capabilities utilize a framebuffer for generating the video signal. Amiga computers, created in the 1980s, featured special design attention to graphics performance and included a unique Hold-And-Modify framebuffer capable of displaying 4096 colors. Framebuffers also became popular in high-end workstations and arcade system boards throughout the 1980s. SGI, Sun Microsystems, HP, DEC and IBM all released framebuffers for their workstation computers in this period. These framebuffers were usually of a much higher quality than could be found in most home computers, and were regularly used in television, printing, computer modeling and 3D graphics. Framebuffers were also used by Sega for its high-end arcade boards, which were also of a higher quality than on home computers. == Display modes == Framebuffers used in personal and home computing often had sets of defined modes under which the framebuffer can operate. These modes reconfigure the hardware to output different resolutions, color depths, memory layouts and refresh rate timings. In the world of Unix machines and operating systems, such conveniences were usually eschewed in favor of directly manipulating the hardware settings. This manipulation was far more flexible in that any resolution, color depth and refresh rate was attainable – limited only by the memory available to the framebuffer. An unfortunate side-effect of this method was that the display device could be driven beyond its capabilities. In some cases, this resulted in hardware damage to the display. More commonly, it simply produced garbled and unusable output. Modern CRT monitors fix this problem through the introduction of protection circuitry. When the display mode is changed, the monitor attempts to obtain a signal lock on the new refresh frequency. If the monitor is unable to obtain a signal lock or if the signal is outside the range of its design limitations, the monitor will ignore the framebuffer signal and possibly present the user with an error message. LCD monitors tend to contain similar protection circuitry, but for different reasons. Since the LCD must digitally sample the display signal (thereby emulating an electron beam), any signal that is out of range cannot be physically displayed on the monitor. == Color palette == Framebuffers have traditionally supported a wide variety of color modes. Due to the expense of memory, most early framebuffers used 1-bit (2 colors per pixel), 2-bit (4 colors), 4-bit (16 colors) or 8-bit (256 colors) color depths. The problem with such small color depths is that a full range of colors cannot be produced. The solution to this problem was indexed color, which adds a lookup table to the framebuffer. Each color stored in framebuffer memory acts as a color index. The lookup table serves as a palette with a limited number of different colors, while the rest is used as an index table. Here is a typical indexed 256-color image and its own palette (shown as a rectangle of swatches): In some designs, it was also possible to write data to the lookup table (or switch between existing palettes) on the fly, allowing dividing the picture into horizontal bars with their own palette and thus rendering an image that had a far wider palette. For example, viewing an outdoor shot photograph, the picture could be divided into four bars: the top one with emphasis on sky tones, the next with foliage tones, the next with skin and clothing tones, and the bottom one with ground colors. This required each palette to have overlapping colors, but, carefully done, allowed great flexibility. == Memory access == While framebuffers are commonly accessed via a memory mapping directly to the CPU memory space, this is not the only method by which they may be accessed. Framebuffers have varied widely in the methods used to access memory. Some of the most common are: Mapping the entire framebuffer to a given memory range. Port commands to set each pixel, range of pixels or palette entry. Mapping a memory range smaller than the framebuffer memory, then bank switching as necessary. The framebuffer organization may be packed pixel or planar. The framebuffer may be all
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Knuth–Plass line-breaking algorithm

The Knuth–Plass algorithm is a line-breaking algorithm designed for use in Donald Knuth's typesetting program TeX. It integrates the problems of text justification and hyphenation into a single algorithm by using a discrete dynamic programming method to minimize a loss function that attempts to quantify the aesthetic qualities desired in the finished output. The algorithm works by dividing the text into a stream of three kinds of objects: boxes, which are non-resizable chunks of content, glue, which are flexible, resizeable elements, and penalties, which represent places where breaking is undesirable (or, if negative, desirable). The loss function, known as "badness", is defined in terms of the deformation of the glue elements, and any extra penalties incurred through line breaking. Making hyphenation decisions follows naturally from the algorithm, but the choice of possible hyphenation points within words, and optionally their preference weighting, must be performed first, and that information inserted into the text stream in advance. Knuth and Plass' original algorithm does not include page breaking, but may be modified to interface with a pagination algorithm, such as the algorithm designed by Plass in his PhD thesis. Typically, the cost function for this technique should be modified so that it does not count the space left on the final line of a paragraph; this modification allows a paragraph to end in the middle of a line without penalty. The same technique can also be extended to take into account other factors such as the number of lines or costs for hyphenating long words. == Computational complexity == A naive brute-force exhaustive search for the minimum badness by trying every possible combination of breakpoints would take an impractical O ( 2 n ) {\displaystyle O(2^{n})} time. The classic Knuth-Plass dynamic programming approach to solving the minimization problem is a worst-case O ( n 2 ) {\displaystyle O(n^{2})} algorithm but usually runs much faster, in close to linear time. Solving for the Knuth-Plass optimum can be shown to be a special case of the convex least-weight subsequence problem, which can be solved in O ( n ) {\displaystyle O(n)} time. Methods to do this include the SMAWK algorithm. == Simple example of minimum raggedness metric == For the input text AAA BB CC DDDDD with line width 6, a greedy algorithm that puts as many words on a line as possible while preserving order before moving to the next line, would produce: ------ Line width: 6 AAA BB Remaining space: 0 CC Remaining space: 4 DDDDD Remaining space: 1 The sum of squared space left over by this method is 0 2 + 4 2 + 1 2 = 17 {\displaystyle 0^{2}+4^{2}+1^{2}=17} . However, the optimal solution achieves the smaller sum 3 2 + 1 2 + 1 2 = 11 {\displaystyle 3^{2}+1^{2}+1^{2}=11} : ------ Line width: 6 AAA Remaining space: 3 BB CC Remaining space: 1 DDDDD Remaining space: 1 The difference here is that the first line is broken before BB instead of after it, yielding a better right margin and a lower cost 11.
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Retention period

A retention period (associated with a retention schedule or retention program) is an aspect of records and information management (RIM) and the records life cycle that identifies the duration of time for which the information should be maintained or "retained", irrespective of format (paper, electronic, or other). Retention periods vary with different types of information, based on content and a variety of other factors, including internal organizational need, regulatory requirements for inspection or audit, legal statutes of limitation, involvement in litigation, and taxation and financial reporting needs, as well as other factors as defined by local, regional, state, national, and/or international governing entities. Once an applicable retention period has elapsed for a given type or series of information, and all holds/moratoriums have been released, the information is typically destroyed using an approved and effective destruction method, which renders the information completely and irreversibly unusable via any means. Alternatively, it may be converted from one form to another (e.g. from paper to electronic), depending on the defined retention period per format. Information with historical value beyond its "usable value" may be accessioned to the custody of an archive organization for permanent or extended long-term preservation. == Defensible disposition == Defensible disposition refers to the ability of an identified and applied retention period to effectively provide for the defense of the record, and its eventual destruction or accessioning when scrutinized within a court of law or by other review. It is commonly advised by records and information management (RIM) professionals that any and all retention periods applied to organizational information should be reviewed and approved for use by competent legal counsel, which represents the organization, and is familiar with the specific business needs and legal and regulatory requirements of the organization. Additionally, a practical approach to information assessment/classification, proper documentation of the disposition program, strategic review of disposition policy over time for efficacy are required for proper defensible disposition. == Guidance and education organizations == ARMA International Information and Records Management Society filerskeepers records retention FAQ
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Shapiro–Senapathy algorithm

The Shapiro—Senapathy algorithm (S&S) is a computational method for identifying splice sites in eukaryotic genes. The algorithm employs a Position Weight Matrix (PWM) scoring formula to predict donor and acceptor splice sites in any given gene. This methodology has been used to discover splice sites and disease-causing splice site mutations in the human genome, and has become a standard tool in clinical genomics. The S&S algorithm has been cited in thousands of clinical studies, according to Google Scholar. It has also formed the basis of widely used software, including Human Splicing Finder, SROOGLE, and Alamut, which identify splice sites and splice site mutations that cause disease. The algorithm has uncovered splicing mutations in diseases ranging from cancers to inherited disorders, and predicted the deleterious effects of these mutations including exon skipping, intron retention, and cryptic splice site activation. == The algorithm == A splice site defines the boundary between a coding exon and a non-coding intron in eukaryotic genes. The S&S algorithm employs a sliding window, corresponding to the length of the splice site motif, to scan a gene sequence and detect potential splice sites. For each sliding window, the algorithm calculates a score by comparing the nucleotide sequence to a Position Weight Matrix (PWM) derived from known splice sites. This formula generates a percentile score, indicating the likelihood that a given sequence functions as a donor or acceptor splice site. The majority of disease-causing mutations in the human genome are located in splice sites. Clinical genomics studies analyze the splice site scores generated by the S&S algorithm to predict the consequences of splice site mutations including exon skipping and intron retention. The algorithm's sensitivity to single-nucleotide changes allows it to determine mutations that may impact RNA splicing and contribute to disease. In addition to identifying real splice sites, the S&S algorithm has been used to discover cryptic splice sites — alternative splice sites activated by mutations — which may disrupt normal splicing. The algorithm detects mutations that lead to the activation of cryptic splice sites, which may be located proximal to real splice sites or deep within non-coding introns. It has thus been used to determine the causes of numerous diseases that are due to cryptic splicing. == Cancer gene discovery using S&S == The S&S algorithm has been used to identify splice-site mutations in genes associated with several cancers. For example, genes causing commonly occurring cancers including breast cancer, ovarian cancer, colorectal cancer, leukemia, head and neck cancers, prostate cancer, retinoblastoma, squamous cell carcinoma, gastrointestinal cancer, melanoma, liver cancer, Lynch syndrome, skin cancer, and neurofibromatosis have been found. In addition, splicing mutations in genes causing less commonly known cancers including gastric cancer, gangliogliomas, Li-Fraumeni syndrome, Loeys–Dietz syndrome, Osteochondromas (bone tumor), Nevoid basal cell carcinoma syndrome, and Pheochromocytomas have been identified. Specific mutations in different splice sites in various genes causing breast cancer (e.g., BRCA1, PALB2), ovarian cancer (e.g., SLC9A3R1, COL7A1, HSD17B7), colon cancer (e.g., APC, MLH1, DPYD), colorectal cancer (e.g., COL3A1, APC, HLA-A), skin cancer (e.g., COL17A1, XPA, POLH), and Fanconi anemia (e.g., FANC, FANA) have been uncovered. The mutations in the donor and acceptor splice sites in different genes causing a variety of cancers that have been identified by S&S are shown in Table 1. == Discovery of genes causing inherited disorders using S&S == Specific mutations in different splice sites in various genes that cause inherited disorders, including, for example, Type 1 diabetes (e.g., PTPN22, TCF1 (HCF-1A)), hypertension (e.g., LDL, LDLR, LPL), Marfan syndrome (e.g., FBN1, TGFBR2, FBN2), cardiac diseases (e.g., COL1A2, MYBPC3, ACTC1), eye disorders (e.g., EVC, VSX1) have been uncovered. A few example mutations in the donor and acceptor splice sites in different genes causing a variety of inherited disorders identified using S&S are shown in Table 2. == Genes causing immune system disorders == More than 100 immune system disorders affect humans, including inflammatory bowel diseases, multiple sclerosis, systemic lupus erythematosus, bloom syndrome, familial cold autoinflammatory syndrome, and dyskeratosis congenita. The Shapiro–Senapathy algorithm has been used to discover genes and mutations involved in many immune disorder diseases, including Ataxia telangiectasia, B-cell defects, epidermolysis bullosa, and X-linked agammaglobulinemia. Xeroderma pigmentosum, an autosomal recessive disorder is caused by faulty proteins formed due to new preferred splice donor site identified using S&S algorithm and resulted in defective nucleotide excision repair. Type I Bartter syndrome (BS) is caused by mutations in the gene SLC12A1. S&S algorithm helped in disclosing the presence of two novel heterozygous mutations c.724 + 4A > G in intron 5 and c.2095delG in intron 16 leading to complete exon 5 skipping. Mutations in the MYH gene, which is responsible for removing the oxidatively damaged DNA lesion are cancer-susceptible in the individuals. The IVS1+5C plays a causative role in the activation of a cryptic splice donor site and the alternative splicing in intron 1, S&S algorithm shows, guanine (G) at the position of IVS+5 is well conserved (at the frequency of 84%) among primates. This also supported the fact that the G/C SNP in the conserved splice junction of the MYH gene causes the alternative splicing of intron 1 of the β type transcript. Splice site scores were calculated according to S&S to find EBV infection in X-linked lymphoproliferative disease. Identification of Familial tumoral calcinosis (FTC) is an autosomal recessive disorder characterized by ectopic calcifications and elevated serum phosphate levels and it is because of aberrant splicing. == Application of S&S in hospitals for clinical practice and research == The Shapiro–Senapathy (S&S) algorithm has played a significant role in advancing the diagnosis and treatment of human diseases through its application in modern clinical genomics. With the widespread adoption of next-generation sequencing (NGS) technologies, the S&S algorithm is now routinely integrated into clinical practice by geneticists and diagnostic laboratories. It is implemented in various computational tools such as Human Splicing Finder (HSF), Splice Site Finder (SSF), and Alamut Visual, which assist in interpreting the functional impact of genetic variants on RNA splicing. The algorithm is particularly useful in identifying pathogenic splice site mutations in cases where the clinical presentation is unclear or where conventional diagnostic methods have failed to identify a causative gene. Its utility has been demonstrated across diverse patient cohorts, including individuals from different ethnic backgrounds with various cancers and inherited genetic disorders. The following are selected examples illustrating its application in clinical research. === Cancers === === Inherited disorders === == S&S - Algorithm for identifying splice sites, exons and split genes == The Shapiro–Senapathy algorithm (SSA) was developed to identify splice sites in uncharacterized genomic sequences, with early applications in the Human Genome Project. The method introduced a Position Weight Matrix (PWM)-based approach to analyze splicing sequences across eukaryotic organisms, marking the first computational framework to systematically define splice sites using probabilistic scoring. Key innovations of the algorithm included: Exon Detection – Exons were defined as sequences bounded by acceptor and donor splice sites with S&S scores above a threshold, requiring an open reading frame (ORF) for validation. Gene Prediction – The method enabled the identification of complete genes by assembling predicted exons, forming a basis for later gene-finding tools. Mutation Analysis – The algorithm distinguishes deleterious splice-site mutations (which disrupt protein function by lowering S&S scores) from neutral variations. This capability allowed researchers to study disease-linked cryptic splice sites in humans, animals, and plants. SSA's PWM-based framework influenced subsequent computational methods, including machine learning and neural network approaches, for splice-site prediction and alternative splicing research. It remains a foundational tool in genomics and disease studies. == Discovering the mechanisms of aberrant splicing in diseases == The Shapiro–Senapathy algorithm has been used to determine the various aberrant splicing mechanisms in genes due to deleterious mutations in the splice sites, which cause numerous diseases. Deleterious splice site mutations impair the normal splicing of the gene transcripts, and thereby make the encoded protei
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Augmented Analytics

Augmented Analytics is an approach of data analytics that employs the use of machine learning and natural language processing to automate analysis processes normally done by a specialist or data scientist. The term was introduced in 2017 by Rita Sallam, Cindi Howson, and Carlie Idoine in a Gartner research paper. Augmented analytics is based on business intelligence and analytics. In the graph extraction step, data from different sources are investigated. == Defining Augmented Analytics == Machine Learning – a systematic computing method that uses algorithms to sift through data to identify relationships, trends, and patterns. It is a process that allows algorithms to dynamically learn from data instead of having a set base of programmed rules. Natural language generation (NLG) – a software capability that takes unstructured data and translates it into plain-English, readable, language. Automating Insights – using machine learning algorithms to automate data analysis processes. Natural Language Query – enabling users to query data using business terms that are either typed onto a search box or spoken. == Data Democratization == Data Democratization is the democratizing data access in order to relieve data congestion and get rid of any sense of data "gatekeepers". This process must be implemented alongside a method for users to make sense of the data. This process is used in hopes of speeding up company decision making and uncovering opportunities hidden in data. There are three aspects to democratising data: Data Parameterisation and Characterisation. Data Decentralisation using an OS of blockchain and DLT technologies, as well as an independently governed secure data exchange to enable trust. Consent Market-driven Data Monetisation. When it comes to connecting assets, there are two features that will accelerate the adoption and usage of data democratisation: decentralized identity management and business data object monetization of data ownership. It enables multiple individuals and organizations to identify, authenticate, and authorize participants and organizations, enabling them to access services, data or systems across multiple networks, organizations, environments, and use cases. It empowers users and enables a personalized, self-service digital onboarding system so that users can self-authenticate without relying on a central administration function to process their information. Simultaneously, decentralized identity management ensures the user is authorized to perform actions subject to the system’s policies based on their attributes (role, department, organization, etc.) and/ or physical location. == Use cases == Agriculture – Farmers collect data on water use, soil temperature, moisture content and crop growth, augmented analytics can be used to make sense of this data and possibly identify insights that the user can then use to make business decisions. Smart Cities – Many cities across the United States, known as Smart Cities collect large amounts of data on a daily basis. Augmented analytics can be used to simplify this data in order to increase effectiveness in city management (transportation, natural disasters, etc.). Analytic Dashboards – Augmented analytics has the ability to take large data sets and create highly interactive and informative analytical dashboards that assist in many organizational decisions. Augmented Data Discovery – Using an augmented analytics process can assist organizations in automatically finding, visualizing and narrating potentially important data correlations and trends. Data Preparation – Augmented analytics platforms have the ability to take large amounts of data and organize and "clean" the data in order for it to be usable for future analyses. Business – Businesses collect large amounts of data, daily. Some examples of types of data collected in business operations include; sales data, consumer behavior data, distribution data. An augmented analytics platform provides access to analysis of this data, which could be used in making business decisions.
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Conceptions of Library and Information Science

Conceptions of Library and Information Science (CoLIS) is a series of conferences about historical, empirical and theoretical perspectives in Library and Information Science. == CoLIS conferences == CoLIS 1 1991 in Tampere, Finland CoLIS 2 1996 in Copenhagen, Denmark CoLIS 3 1999 in Dubrovnik, Croatia CoLIS 4 2002 in Seattle, US CoLIS 5 2005 in Glasgow, Scotland CoLIS 6 2007 in Borås, Sweden CoLIS 7 June 2010 in London, at City University London. CoLIS 8 August 19–22, 2013, in Copenhagen, Denmark, at The Royal School of Library and Information Science. CoLIS 9 June 27–29, 2016, in Uppsala, Sweden, at Uppsala University. CoLIS 10 June 16–19, 2019, in Ljubljana, Slovenia, Faculty of Arts CoLIS 11 May 29–June 1, 2022, in Oslo, Norway, Oslo Metropolitan University.
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Kinodynamic planning

In robotics and motion planning, kinodynamic planning is a class of problems for which velocity, acceleration, and force/torque bounds must be satisfied, together with kinematic constraints such as avoiding obstacles. The term was coined by Bruce Donald, Pat Xavier, John Canny, and John Reif. Donald et al. developed the first polynomial-time approximation schemes (PTAS) for the problem. By providing a provably polynomial-time ε-approximation algorithm, they resolved a long-standing open problem in optimal control. Their first paper considered time-optimal control ("fastest path") of a point mass under Newtonian dynamics, amidst polygonal (2D) or polyhedral (3D) obstacles, subject to state bounds on position, velocity, and acceleration. Later they extended the technique to many other cases, for example, to 3D open-chain kinematic robots under full Lagrangian dynamics. == Modern approaches == Since the foundational theoretical work of the 1990s, the field has evolved significantly with new algorithmic approaches that address the computational and practical limitations of early methods. === Sampling-based methods === Many practical heuristic algorithms based on stochastic optimization and iterative sampling have been developed by a wide range of authors to address the kinodynamic planning problem. Popular approaches include extensions of RRT algorithms such as RRT for kinodynamic systems, and sampling-based methods like Model Predictive Path Integral (MPPI) control. These stochastic techniques have been shown to work well in practice and can handle complex, high-dimensional state spaces more efficiently than deterministic methods. However, all motion planning methods are subject to the PSPACE-hardnesss of classical motion planning even without dynamics, which means (assuming the usual structural complexity conjectures) they all can be worst-case exponential-time in the state-space dimension (the number of degrees of freedom). On the other hand, the deterministic methods have provable guarantees of completeness, accuracy, and complexity (for fixed dimension, they are polynomial-time not only in the geometric complexity, but also in ( 1 / ε ) {\displaystyle (1/\varepsilon )} , the closeness of the desired approximation), whereas most of the recent heuristic/stochastic methods sacrifice at least one of these criteria. === Mixed-integer optimization approaches === Recent advances in mixed-integer programming have enabled new deterministic approaches to kinodynamic planning. These methods formulate the planning problem as an optimization task that simultaneously determines the spatial path and control sequence while respecting all kinodynamic constraints. By using techniques such as McCormick envelopes to handle bilinear constraints, these approaches can provide globally optimal solutions with mathematical guarantees while achieving significant computational speedups over traditional methods. === Genetic algorithm approaches === Genetic algorithms have also been adapted for kinodynamic planning, particularly for gradient-free optimization in challenging terrain. These methods use evolutionary computation to optimize trajectories over receding horizons, with specialized mutation operators that ensure vehicle controls remain within operational limits. This approach is particularly useful when dealing with non-differentiable cost functions or when gradient information is unavailable or unreliable. === Three-dimensional terrain planning === The foundational theoretical work of the 1990s was extended to higher degrees of freedom, and even to n {\displaystyle n} -link, 3D open-chain kinematic robots under full Lagrangian dynamics. However, many of the subsequent heuristic techniques (typically employing stochastic optimization) were confined to planar environments. More recent kinodynamic planning has extended beyond these planar environments to handle complex 3D terrains represented as simplicial complexes or triangular meshes. This advancement is particularly important for applications such as autonomous vehicle navigation in off-road environments, where elevation changes and terrain geometry significantly impact vehicle dynamics. These methods must account for pitch angles, surface curvature, and the coupling between terrain geometry and vehicle kinodynamic constraints. == Performance and guarantees == The landscape of performance guarantees in kinodynamic planning has evolved considerably. While early heuristic methods could not guarantee optimality, recent mixed-integer approaches have demonstrated the ability to find globally optimal solutions with proven constraint satisfaction. Experimental comparisons have shown that modern optimization-based planners can achieve execution times several orders of magnitude faster than sampling-based methods while maintaining strict adherence to kinodynamic constraints. However, the choice of method often depends on the specific application requirements. Sampling-based methods remain valuable for their ability to quickly find feasible solutions in high-dimensional spaces and their robustness to modeling uncertainties. Optimization-based methods excel when optimality guarantees and constraint compliance are critical, particularly in safety-critical applications. == Applications == Kinodynamic planning finds applications across numerous domains including: Autonomous vehicles: Path planning for cars, trucks, and other ground vehicles that must respect acceleration, steering, and velocity limits Aerial robotics: Trajectory planning for quadrotors and other unmanned aerial vehicles with dynamic constraints Manipulation: Planning for robotic arms where joint velocities, accelerations, and torques are limited Legged locomotion: Footstep and trajectory planning for walking and running robots Space robotics: Planning under thrust and fuel constraints for spacecraft and rovers
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Library history

Library history is a subdiscipline within library science and library and information science focusing on the history of libraries and their role in societies and cultures. Some see the field as a subset of information history. Library history is an academic discipline and should not be confused with its object of study (history of libraries): the discipline is much younger than the libraries it studies. Library history begins in ancient societies through contemporary issues facing libraries today. Topics include recording mediums, cataloguing systems, scholars, scribes, library supporters and librarians. == Earliest libraries == The earliest records of a library institution as it is presently understood can be dated back to around 5,000 years ago in the Southwest Asian regions of the world. One of the oldest libraries found is that of the ancient library at Ebla (circa 2500 BCE) in present-day Syria. In the 1970s, the excavation at Ebla's library unearthed over 20,000 clay tablets written in cuneiform script. === Library in Mesopotamia === The Assyrian King Assurbanipal created one of the greatest libraries in Nineveh in the seventh century BCE. The collection consisted of over 30,000 tablets written in a variety of languages. The collection was cataloged both by the shape of the tablet and by the subject of the content. The library had separate rooms for the different topics: government, history, law, astronomy, geography, and so on. The tablets also contained myths, hymns, and even jokes. Assurbanipal would send scribes to visit every corner of his kingdom to copy the content of other libraries. His library contained many of the most important literary works of the day, including the epic of Gilgamesh. Assurbanipal's Royal Library also had one of the first library catalogs. Unfortunately, Nineveh was eventually destroyed, and the library was lost in a fire. === Libraries in Ancient Greece === The Greek government was the first to sponsor public libraries. By 500 BCE both Athens and Samos had begun creating libraries for the public, though as most of the population was illiterate these spaces were serving a small, educated portion of the community. Athens developed a city archive at the Metroon in 405 BCE, where documents were stored in sealed jars. These would have saved the documents, but they would have been difficult to consult regularly. In Paros, around the same time, contracts were placed in the temple for safe keeping, and a book curse was placed for extra protection. === Library of Alexandria === The Library at Alexandria, Egypt, was renowned in the third century BCE while kings Ptolemy I Soter and Ptolemy II Philadelphus reigned. The library included a museum, garden, meeting areas and of course reading rooms. The Great Library, as it is known, was one of many in Alexandria. From its inception around the second century BCE, Alexandria was a well-known center for learning. It earned renown as the intellectual capital of the Western world up through the third century CE. The librarians at Alexandria collected, copied, and organized scrolls from across the known world. According to a primary source, every ship that came to Alexandria was required to hand over their books to be copied, and the copies would be returned to the owner, the library keeping the original. The Library of Alexandria was damaged by various disasters over time, including fire, invasion, and earthquake. Scholars believe the collection slowly diminished over time due to theft and efforts to remove it ahead of invading armies. While there are popular stories about how the library was ultimately destroyed, most of these are more myth than fact. === Libraries in Rome === Julius Caesar and his successor Augustus were the first to establish public libraries in ancient Rome, including the library of Apollo on the Palatine Hill. Several emperors followed suit over the next four centuries, including Hadrian, Tiberius, and Vespasian. Roman aristocrats also had personal libraries, which usually contained works in both Greek and Latin. A valuable example of this has been found at Herculaneum near Pompeii. Papyrus manuscripts in Herculaneum's Villa of the Papyri were encased in ash after the eruption of Vesuvius in 79 CE. Modern archaeology is now able to scan these artifacts and discern their contents, including many writings from Philodemus. The average Roman would not have been familiar with books beyond what they might hear read aloud in the forum. Public figures would pay for particular passages to be read aloud to the public from the steps of a public library. === Libraries in the Middle Ages === In the European Middle Ages, libraries began to become more prevalent, despite a widespread reduction in new writing beyond religious themes. Most libraries were initially connected to monasteries or religious institutions. Scriptoriums copied Christian religious texts to share with other religious centers or to be read aloud to their own parishioners. The Holy Roman Emperor Charlemagne (r. 786-814) had a large impact on the advancement of written culture in the Medieval Christian world, acquiring as many written works as he could, and employing many scribes to copy and recirculate vernacular versions of religious works. Most of the text held in small personal libraries was still religious in nature. == Early modern libraries == === Libraries of the Renaissance === During the Renaissance era the merchant middle class grew, and more people found benefits in education. They relied on libraries as a place to study and gain knowledge. Libraries provided a valuable resource, enriching the culture of those who were educated. Universities that had been started in the Middle Ages, founded their own libraries. Books in these libraries could not be borrowed from these libraries and were generally chained to the shelves to prevent theft. As more of the population became literate, new ideas like Humanism and Natural Law spawned an increase personal libraries, although they remained small. Gutenberg's invention of the printing press in 1456 opened the door to the modern era for libraries. == Oldest working libraries == According to the German librarian Michael Knoche, it is not possible to determine which library is the “oldest”: "Precise year dates are a construct, especially in the case of very old libraries. When a collection of books deserves to be called a library depends very much on the point of view of the observer." Various libraries are referred to as the “oldest”: The library founded in the 6th century of the Saint Catherine's Monastery in Sinai is "reputedly the oldest continuously run library in existence today", according to the Library of Congress. Its collection of religious and secular manuscripts is ranging from Bibles, liturgies and prayer books to legal documents such as deeds, court cases and fatwahs (legal opinions). The Al Qarawiyyin Library was founded in 859 by Fatima al-Fihri and is often regarded as the oldest working library in the world. It is in Fez, Morocco and is part of the oldest continually operating university in the world, the University of al-Qarawiyyin. The library houses approximately 4,000 ancient Islamic manuscripts. These manuscripts include 9th century Qurans and the oldest known accounts of the Islamic prophet Muhammed. The Malatestiana Library (Italian: Biblioteca Malatestiana) is a public library in the city of Cesena in northern Italy. Opened in 1454 it is significant for being the first civic library in Europe open to the general public. == Library history reports and writings of the early 19th and 20th century == In the early 19th and 20th century, representative titles were created reporting library history in the United States and the United Kingdom. American titles include Public Libraries in the United States of America, Their History, Condition, and Management (1876), Memorial History of Boston (1881) by Justin Winsor, Public Libraries in America (1894) by William I. Fletcher, and History of the New York Public Library (1923) by Henry M. Lydenberg. British titles include Old English Libraries (1911) by Earnest A. Savage and The Chained Library: A Survey of Four Centuries in the Evolution of the English Library by Burnett Hillman Streeter. In the beginning of the 20th century, library historians began applying scientific research methodologies to examine the library as a social agency. Two works that demonstrate this argument are Geschichte der Bibliotheken (1925) by Alfred Hessel and the Library Quarterly article from 1931, “The Sociological Beginnings of the Library Movement in America” by Arnold Borden. With the establishment of library schools, master's theses and doctoral dissertations represented the shift in serious research regarding libraries and library history. Two published doctoral dissertations that mark this trend are Foundations of the Public Library: The Origins of the American Public Library Movement in Ne
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Dimensions CM

Dimensions CM is a software change and configuration management product developed by OpenText Corporation. It includes revision control, change, build and release management capabilities. Since 2014 (v14.1) Dimensions CM includes PulseUno module providing Code review and Continuous integration capabilities. Starting with the version 14.5.2 (2020) it can also serve as a binary repository manager. == History == Previous product names: PCMS Dimensions (SQL Software) PVCS Dimensions (Merant, Intersolv)
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Algorithm IMED

In multi-armed bandit problems, IMED (for Indexed Minimum Empirical Divergence) is an algorithm developed in 2015 by Junya Honda and Akimichi Takemura. It is the first algorithm proved to be asymptotically optimal respect to the problem-dependant Lai–Robbins lower bound for distributions in ( − ∞ , 1 ] {\displaystyle (-\infty ,1]} . == Multi-armed bandit problem == The Multi-armed bandit problem is a sequential game where one player has to choose at each turn between K {\displaystyle K} actions (arms). Behind every arm a {\displaystyle a} there is an unknown distribution ν a {\displaystyle \nu _{a}} that lies in a set D {\displaystyle {\mathcal {D}}} known by the player (for example, D {\displaystyle {\mathcal {D}}} can be the set of Gaussian distributions or Bernoulli distributions). At each turn t {\displaystyle t} the player chooses (pulls) an arm a t {\displaystyle a_{t}} , he then gets an observation X t {\displaystyle X_{t}} of the distribution ν a t {\displaystyle \nu _{a_{t}}} . === Regret minimization === The goal is to minimize the regret at time T {\displaystyle T} that is defined as R T := ∑ a = 1 K Δ a E [ N a ( T ) ] {\displaystyle R_{T}:=\sum _{a=1}^{K}\Delta _{a}\mathbb {E} [N_{a}(T)]} where μ a := E [ ν a ] {\displaystyle \mu _{a}:=\mathbb {E} [\nu _{a}]} is the mean of arm a {\displaystyle a} μ ∗ := max a μ a {\displaystyle \mu ^{}:=\max _{a}\mu _{a}} is the highest mean Δ a := μ ∗ − μ a {\displaystyle \Delta _{a}:=\mu ^{}-\mu _{a}} N a ( t ) {\displaystyle N_{a}(t)} is the number of pulls of arm a {\displaystyle a} up to turn t {\displaystyle t} The player has to find an algorithm that chooses at each turn t {\displaystyle t} which arm to pull based on the previous actions and observations ( a s , X s ) s < t {\displaystyle (a_{s},X_{s})_{s μ } {\displaystyle {\mathcal {K}}_{inf}(\nu ,\mu ,{\mathcal {D}}):=\inf \left\{\mathrm {KL} (\nu ,{\tilde {\nu }})\ |\ {\tilde {\nu }}\in {\mathcal {P}}([-\infty ,1]),\ \mathbb {E} [{\tilde {\nu }}]>\mu \right\}} K L {\displaystyle \mathrm {KL} } is the Kullback–Leibler divergence P ( [ − ∞ , 1 ] ) {\displaystyle {\mathcal {P}}([-\infty ,1])} is the set of distribution in [ − ∞ , 1 ] {\displaystyle [-\infty ,1]} ν ^ a ( t ) {\displaystyle {\hat {\nu }}_{a}(t)} is the empirical distribution of arm a {\displaystyle a} at turn t {\displaystyle t} μ ^ ∗ ( t ) {\displaystyle {\hat {\mu }}^{}(t)} is the highest empirical mean of turn t {\displaystyle t} Remark : For arms a {\displaystyle a} that verify μ ^ a ( t ) = μ ^ ∗ ( t ) {\displaystyle {\hat {\mu }}_{a}(t)={\hat {\mu }}^{}(t)} we have K i n f ( ν ^ a ( t ) , μ ^ ∗ ( t ) ) = 0 {\displaystyle K_{inf}({\hat {\nu }}_{a}(t),{\hat {\mu }}^{}(t))=0} . Then there index is equal to ln ⁡ ( N a ( t ) ) {\displaystyle \ln(N_{a}(t))} === Pseudocode === for each arm i do: n[i] ← 1; nu[i] ← None; mu[i] ← None for t from 1 to K do: select arm t observe reward r n[t] ← n[t] + 1 nu[t] ← update empirical distribution mu[t] ← update empirical mean for t from K+1 to T do: mu ← highest mu for each arm i do: scoreK[i] ← n[i] K_inf(nu[i],mu) scoreN[i] ← ln(n[i]) index[i] ← scoreK[i] + scoreN[i] select arm a with smallest index[a] observe reward r n[a] ← n[a] + 1 nu[a] ← update empirical distribution mu[a] ← update empirical mean == Theoretical results == In the multi-armed bandit problem we have the asymptotic Lai–Robbins lower bound asymptotic lower bound on regret. The algorithm IMED is the first algorithm that matches this lower bound for distribution in ( − ∞ , 1 ] {\displaystyle (-\infty ,1]} in the first order. If the distribution are also bounded then it also match the second order. It is the first algorithm that match the second under of this lower bound. === Lai–Robbins lower bound === In 1985 Lai and Robbins proved an asymptotic, problem-dependent lower bound on regret. In 2018, Aurelien Garivier, Pierre Menard and Gilles Stoltz proved a refined lower bound that gives the second order It states that for every consistent algorithm on the set P ( [ − ∞ , 1 ] ) {\displaystyle {\mathcal {P}}([-\infty ,1])} — that is, an algorithm for which, for every ( ν 1 , … , ν K ) ∈ P ( [ − ∞ , 1 ] ) K {\displaystyle (\nu _{1},\dots ,\nu _{K})\in {\mathcal {P}}([-\infty ,1])^{K}} , the regret R T {\displaystyle R_{T}} is subpolynomial (i.e. R T = o T → + ∞ ( T α ) {\displaystyle R_{T}=o_{T\to +\infty }(T^{\alpha })} for all α > 0 {\displaystyle \alpha >0} ) — we have: R T ≥ ( ∑ a : μ a < μ ∗ Δ a K inf ( ν a , μ ∗ ) ) ln ⁡ T − Ω T → + ∞ ( ln ⁡ ln ⁡ T ) . {\displaystyle R_{T}\geq \left(\sum _{a:\mu _{a}<\mu ^{}}{\frac {\Delta _{a}}{{\mathcal {K}}_{\inf }(\nu _{a},\mu ^{})}}\right)\ln T-\Omega _{T\to +\infty }(\ln \ln T).} This bound is asymptotic (as T → + ∞ {\displaystyle T\to +\infty } ) and gives a first-order lower bound of order ln ⁡ T {\displaystyle \ln T} with the optimal constant in front of it and the second order in − Ω ( ln ⁡ ln ⁡ T ) {\displaystyle -\Omega (\ln \ln T)} . === Regret bound for IMED === If the distribution of every arm a {\displaystyle a} is ( − ∞ , 1 ] {\displaystyle (-\infty ,1]} ( i.e. ν a ∈ P ( [ − ∞ , 1 ] ) ) {\displaystyle \nu _{a}\in {\mathcal {P}}([-\infty ,1]))} then the regret of the algorithm IMED verify R T ≤ ( ∑ a : μ a < μ ∗ Δ a K inf ( ν a , μ ∗ ) ) ln ⁡ T + O ( 1 ) {\displaystyle R_{T}\leq \left(\sum _{a:\mu _{a}<\mu ^{}}{\frac {\Delta _{a}}{{\mathcal {K}}_{\inf }(\nu _{a},\mu ^{})}}\right)\ln T+O(1)} If all the distribution ν a {\displaystyle \nu _{a}} are bounded then it exists a constant C > 0 {\displaystyle C>0} such that for T {\displaystyle T} large enough the regret of IMED is upper bounded by R T ≤ ( ∑ a : μ a < μ ∗ Δ a K inf ( ν a , μ ∗ ) ) ln ⁡ T − C ln ⁡ ln ⁡ T {\displaystyle R_{T}\leq \left(\sum _{a:\mu _{a}<\mu ^{}}{\frac {\Delta _{a}}{{\mathcal {K}}_{\inf }(\nu _{a},\mu ^{})}}\right)\ln T-C\ln \ln T} == Computation time == The algorithm only requiere to compute the K i n f {\displaystyle K_{inf}} for suboptimal arms who are pulled O ( ln ⁡ T ) {\displaystyle O(\ln T)} times, which make it a lot faster than KL-UCB. A faster version of IMED was developed in 2023 to make it even faster, using a Taylor development of the K i n f {\displaystyle K_{inf}} in the first order .
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Knuth–Eve algorithm

In computer science, the Knuth–Eve algorithm is an algorithm for polynomial evaluation. It preprocesses the coefficients of the polynomial to reduce the number of multiplications required at runtime. Ideas used in the algorithm were originally proposed by Donald Knuth in 1962. His procedure opportunistically exploits structure in the polynomial being evaluated. In 1964, James Eve determined for which polynomials this structure exists, and gave a simple method of "preconditioning" polynomials (explained below) to endow them with that structure. == Algorithm == === Preliminaries === Consider an arbitrary polynomial p ∈ R [ x ] {\displaystyle p\in \mathbb {R} [x]} of degree n {\displaystyle n} . Assume that n ≥ 3 {\displaystyle n\geq 3} . Define m {\displaystyle m} such that: if n {\displaystyle n} is odd then n = 2 m + 1 {\displaystyle n=2m+1} , and if n {\displaystyle n} is even then n = 2 m + 2 {\displaystyle n=2m+2} . Unless otherwise stated, all variables in this article represent either real numbers or univariate polynomials with real coefficients. All operations in this article are done over R {\displaystyle \mathbb {R} } . Again, the goal is to create an algorithm that returns p ( x ) {\displaystyle p(x)} given any x {\displaystyle x} . The algorithm is allowed to depend on the polynomial p {\displaystyle p} itself, since its coefficients are known in advance. === Overview === ==== Key idea ==== Using polynomial long division, we can write p ( x ) = q ( x ) ⋅ ( x 2 − α ) + ( β x + γ ) , {\displaystyle p(x)=q(x)\cdot (x^{2}-\alpha )+(\beta x+\gamma ),} where x 2 − α {\displaystyle x^{2}-\alpha } is the divisor. Picking a value for α {\displaystyle \alpha } fixes both the quotient q {\displaystyle q} and the coefficients in the remainder β {\displaystyle \beta } and γ {\displaystyle \gamma } . The key idea is to cleverly choose α {\displaystyle \alpha } such that β = 0 {\displaystyle \beta =0} , so that p ( x ) = q ( x ) ⋅ ( x 2 − α ) + γ . {\displaystyle p(x)=q(x)\cdot (x^{2}-\alpha )+\gamma .} This way, no operations are needed to compute the remainder polynomial, since it's just a constant. We apply this procedure recursively to q {\displaystyle q} , expressing p ( x ) = ( ( q ( x ) ⋅ ( x 2 − α m ) + γ m ) ⋯ ) ⋅ ( x 2 − α 1 ) + γ 1 . {\displaystyle p(x)=\left(\left(q(x)\cdot (x^{2}-\alpha _{m})+\gamma _{m}\right)\cdots \right)\cdot (x^{2}-\alpha _{1})+\gamma _{1}.} After m {\displaystyle m} recursive calls, the quotient q {\displaystyle q} is either a linear or a quadratic polynomial. In this base case, the polynomial can be evaluated with (say) Horner's method. ==== "Preconditioning" ==== For arbitrary p {\displaystyle p} , it may not be possible to force β = 0 {\displaystyle \beta =0} at every step of the recursion. Consider the polynomials p e {\displaystyle p^{e}} and p o {\displaystyle p^{o}} with coefficients taken from the even and odd terms of p {\displaystyle p} respectively, so that p ( x ) = p e ( x 2 ) + x ⋅ p o ( x 2 ) . {\displaystyle p(x)=p^{e}(x^{2})+x\cdot p^{o}(x^{2}).} If every root of p o {\displaystyle p^{o}} is real, then it is possible to write p {\displaystyle p} in the form given above. Each α i {\displaystyle \alpha _{i}} is a different root of p o {\displaystyle p^{o}} , counting multiple roots as distinct. Furthermore, if at least n − 1 {\displaystyle n-1} roots of p {\displaystyle p} lie in one half of the complex plane, then every root of p o {\displaystyle p^{o}} is real. Ultimately, it may be necessary to "precondition" p {\displaystyle p} by shifting it — by setting p ( x ) ← p ( x + t ) {\displaystyle p(x)\gets p(x+t)} for some t {\displaystyle t} — to endow it with the structure that most of its roots lie in one half of the complex plane. At runtime, this shift has to be "undone" by first setting x ← x − t {\displaystyle x\gets x-t} . === Preprocessing step === The following algorithm is run once for a given polynomial p {\displaystyle p} . At this point, the values of x {\displaystyle x} that p {\displaystyle p} will be evaluated on are not known. ==== Better choice of t ==== While any t ≥ Re ( r 2 ) {\displaystyle t\geq {\text{Re}}(r_{2})} can work, it is possible to remove one addition during evaluation if t {\displaystyle t} is also chosen such that two roots of p ( x + t ) {\displaystyle p(x+t)} are symmetric about the origin. In that case, α 1 {\displaystyle \alpha _{1}} can be chosen such that the shifted polynomial has a factor of x 2 − α 1 {\displaystyle x^{2}-\alpha _{1}} , so γ 1 = 0 {\displaystyle \gamma _{1}=0} . It is always possible to find such a t {\displaystyle t} . One possible algorithm for choosing t {\displaystyle t} is: === Evaluation step === The following algorithm evaluates p {\displaystyle p} at some, now known, point x {\displaystyle x} . Assuming t {\displaystyle t} is chosen optimally, γ 1 = 0 {\displaystyle \gamma _{1}=0} . So, the final iteration of the loop can instead run y ← y ⋅ ( s − α i ) , {\displaystyle y\gets y\cdot (s-\alpha _{i}),} saving an addition. == Analysis == In total, evaluation using the Knuth–Eve algorithm for a polynomial of degree n {\displaystyle n} requires n {\displaystyle n} additions and ⌊ n / 2 ⌋ + 2 {\displaystyle \lfloor n/2\rfloor +2} multiplications, assuming t {\displaystyle t} is chosen optimally. No algorithm to evaluate a given polynomial of degree n {\displaystyle n} can use fewer than n {\displaystyle n} additions or fewer than ⌈ n / 2 ⌉ {\displaystyle \lceil n/2\rceil } multiplications during evaluation. This result assumes only addition and multiplication are allowed during both preprocessing and evaluation. The Knuth–Eve algorithm is not well-conditioned.
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