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  Subpixel rendering

  Subpixel rendering is a method used to increase the effective resolution of a color display device. It utilizes the composition of each pixel, which consists of three subpixels of which are red, green, and blue that can each be individually addressable on the display matrix. Subpixel rendering is primarily used for text rendering on standard DPI displays. Despite the inherent color anomalies, it can also be used to render general graphics. == History == The origin of subpixel rendering as used today remains controversial. Apple Inc., IBM, and Microsoft patented various implementations that differed in technical details owing to the different purposes for which their technologies were intended. Microsoft held several patents in the United States for subpixel rendering technology used in text rendering on RGB Stripe layouts. The patents 6,219,025; 6,239,783; 6,307,566; 6,225,973; 6,243,070; 6,393,145; 6,421,054; 6,282,327; and 6,624,828 were filed between October 7, 1998, and October 7, 1999, and expired on July 30, 2019. Analysis of the patent by FreeType indicates that the patent does not cover the idea of subpixel rendering, but rather the actual filter used as a last step to balance the color. Microsoft's patent describes the smallest possible filter that distributes each subpixel value equally among the R, G, and B pixels. Any other filter will either be blurrier or will introduce color artifacts. Apple was able to use it in Mac OS X due to a patent cross-licensing agreement. == Characteristics == A single pixel on a color display is made of several subpixels, typically three arranged left-to-right as red, green, and blue (RGB). The components are readily visible with a small magnifying glass, such as a loupe. These pixel components appear as a single color to the human eye because of blurring by optics and spatial integration by nerve cells in the eye. However, the eye is much more sensitive to the location. Therefore, turning on the G and B of one pixel and the R of the next pixel to the right will produce a white dot, but it will appear to be 1/3 of a pixel to the right of the white dot that would be seen from the RGB of only the first pixel. Subpixel rendering leverages this to provide three times the horizontal resolution of the rendered image. However, it has to blur this image to produce the correct color by ensuring the same amount of red, green, and blue are turned on as when no subpixel rendering is being done. Subpixel rendering does not necessitate the use of antialiasing. It gives a smoother result regardless of whether antialiasing is used or not since it artificially increases the resolution. However, it introduces color aliasing since subpixels are colored. Subsequent filtering applied to remove the color artifacts is a form of antialiasing, although its purpose is not smoothing jagged shapes as in conventional antialiasing. Subpixel rendering requires the software to know the layout of the subpixels. The most common reason it is wrong is monitors that can be rotated 90 (or 180) degrees, though monitors are manufactured with other arrangements of the subpixels, such as BGR or in triangles, or with 4 colors like RGBW squares. On any such display the result of incorrect subpixel rendering will be worse than if no subpixel rendering was done at all (it will not produce color artifacts, but it will produce noisy edges). == Implementations == === Apple II === Steve Gibson has claimed that the Apple II, introduced in 1977, supports an early form of subpixel rendering in its high-resolution (280×192) graphics mode. The Wozniak patent only used 2 "sub-pixels". The bytes that comprise the Apple II high-resolution screen buffer contain seven visible bits (each corresponding directly to a pixel) and a flag bit used to select between purple/green or blue/orange color sets. Each pixel, since it is represented by a single bit, is either on or off; there are no bits within the pixel itself for specifying color or brightness. Color is instead created as an artifact of the NTSC color encoding scheme, determined by horizontal position: pixels with even horizontal coordinates are always purple (or blue, if the flag bit is set), and odd pixels are always green (or orange). Two lit pixels next to each other are always white, regardless of whether the pair is even/odd or odd/even, and irrespective of the value of the flag bit. This is an approximation, but it is what most programmers of the time would have in mind while working with the Apple's high-resolution mode. Gibson's example claims that because two adjacent bits form a white block, there are, in fact, two bits per pixel: one that activates the pixel's purple left half and the other that activates its green right half. If the programmer instead activates the green right half of a pixel and the purple left half of the next pixel, the result is a white block 1/2 pixel to the right, which is indeed an instance of subpixel rendering. However, it is not clear whether any programmers of the Apple II have considered the pairs of bits as pixels—instead calling each bit a pixel. The flag bit in each byte affects color by shifting pixels half a pixel-width to the right. This half-pixel shift was exploited by some graphics software, such as HRCG (High-Resolution Character Generator), an Apple utility that displayed text using the high-resolution graphics mode, to smooth diagonals. === ClearType === Microsoft announced its subpixel rendering technology, called ClearType, at COMDEX in 1998. Microsoft published a paper in May 2000, Displaced Filtering for Patterned Displays, describing the filtering behind ClearType. It was then made available in Windows XP. Still, it was not activated by default until Windows Vista, while Windows XP OEMs could and did change the default setting. === FreeType === FreeType, the library used by most current software on the X Window System, contains two open source implementations. The original implementation uses the ClearType antialiasing filters and carries the following notice: "The colour filtering algorithm of Microsoft's ClearType technology for subpixel rendering is covered by patents; for this reason, the corresponding code in FreeType is disabled by default. Note that subpixel rendering per se is prior art; using a different colour filter thus easily circumvents Microsoft's patent claims." FreeType offers a variety of color filters. Since version 2.6.2, the default filter is light, a filter that is both normalized (value sums up to 1) and color-balanced (eliminate color fringes at the cost of resolution). Since version 2.8.1, a second implementation exists, called Harmony, that "offers high quality LCD-optimized output without resorting to ClearType techniques of resolution tripling and filtering". This is the method enabled by default. When using this method, "each color channel is generated separately after shifting the glyph outline, capitalizing on the fact that the color grids on LCD panels are shifted by a third of a pixel. This output is indistinguishable from ClearType with a light 3-tap filter." Since the Harmony method does not require additional filtering, it is not covered by the ClearType patents. === CoolType === Adobe created their own subpixel renderer called CoolType, allowing them to display documents the same way across various operating systems: Windows, MacOS, Linux etc. When it was launched around the year 2001, CoolType supported a wider range of fonts than Microsoft's ClearType, which at the time was limited to TrueType fonts. In contrast, Adobe's CoolType also supported PostScript fonts (and their OpenType equivalents). === macOS === Mac OS X (later OS X, now macOS) also used subpixel rendering, as part of Quartz 2D. However, it was removed after the introduction of Retina displays. Unlike Microsoft's implementation, which favors a tight fit to the grid (font hinting) to maximize legibility, Apple's implementation prioritizes the shape of the glyphs as set out by their designer.

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  Transportation Economic Development Impact System

  Transportation Economic Development Impact System (TREDIS) is an economic analysis system sold by consulting firm Economic Development Research Group that is used in planning major transportation investments in the US and Canada. The role of economic impact analysis and TREDIS in the transportation planning process is explained in guidebooks of the US Department of Transportation and the American Association of State Highway and Transportation Officials. TREDIS has been most commonly used for assessing the expected economic impacts of statewide highway programs, regional multi-modal plans and public transport investment. Its history and theoretical foundation are explained in peer reviewed journal articles. == How It Works == TREDIS has a series of modules that calculate different forms of impacts and benefits. One module is an accounting framework that calculates user benefits, including impacts on cargo transportation and commuting costs, based on transportation forecasting results. A second module calculates wider economic development benefits, including impacts on business productivity, economic development and multiplier effects from the input-output analysis. It applies an economic model to estimate impacts on jobs, income, gross regional product and business output, by sector of the economy. A third module applies cost-benefit analysis from alternative perspectives.

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  Supper (Spotify)

  Supper is a web-based application on the Spotify digital music streaming platform. The Supper app was born from a group of friends who had backgrounds in the music and gastronomy industries. Digital music solutions company Artisan Council later executed it. The app now sits in the top 40 applications on Spotify. == About == The Supper Spotify application matches recipes for all occasions and skill levels with a playlist for both preparation and presentation, as envisioned by the chefs themselves. Supper is credited with being one of the first apps to pair music with food. Playing on the social nature of music and food culture, users can seamlessly experience both for the first time with real time music streaming. == Supper.mx == In May 2014 Supper was launched outside of the Spotify streaming platform. Though still in partnership with Spotify, supper.mx allows users to view Supper's music + food collaborations on mobile, tablet and desktop, without the need to download Spotify directly. == Curators == All of the recipes and playlists featured on the Supper app come straight from a growing network of tastemakers, including chefs, musicians and institutions around the world. Each month the recipes and playlists are updated in conjunction with current holidays, events and seasons. === Launch === Launching in October 2013 the first edition of Supper featured content from a range of eating institutions and culture makers from the US and Australia. Brooklyn Bowl (Brooklyn) Roberta's Pizza (Brooklyn) Fancy Hanks (Melbourne) The Foresters/Queenies Upstairs (Sydney) Hipstamatic Panama House (Bondi) Sweetwater Inn (Melbourne) Soul Clap (Syd record label) Yellow Birds (Melbourne) === November 2013 === Yardbird (Hong Kong) Sonoma Bakery (Sydney) Do or Dine (Brooklyn) Cameo Gallery (Brooklyn) Hypertrak (Blog) Blue Smoke (NYC) The Crepes of Wrath (Blog) Willin Low // Wild Rocket - Wild Oats - Relish === December 2013 === The Copper Mill (Sydney) Thug Kitchen Mamak (Sydney) Tutu's (Brooklyn) Chin Chin (Melbourne) Flat Iron Steak (London) Greasy Spoon (Copenhagen) === January 2014 === Mexicali Taco & Co. (LA) Church & State (LA) Salts Cure (LA) Nopa (SF) L & E Oyster (LA) 4100 bar (LA) Golden Gopher (LA) The Pie Hole (LA) State Bird Provisions (SF) === Momofuku === In February 2014 Supper teamed up with restaurant heavy weights Momofuku. The recipes featured came from their iconic New York, Toronto and Sydney restaurants. Head office also got involved with an instructional from Brand Director Sue Chan on how to paint Momofuku vibes on to any party. === SXSW === March sees the Supper team migrate to Austin, Texas for SXSW, bringing together the best eateries the city has to offer as well as the music that has influenced them. Restaurants and eateries on board in 2014 included: The Backspace Kelis Swifts Attic Uchi Jackalope Paul Qui/East Side King Thai Kun Wonderland Hole in the Wall Justine's Brasserie The Liberty === Kelis === In April 2014 Kelis presented 5 of her recipes paired with a personal playlist for Supper. Kelis shared her recipes for apple farro, jerk ribs, New York vanilla bean cheesecake and Jerk Ribs. The Kelis/Supper collaboration coincided with the release of Kelis' 2014 album titled 'Food'. === Roberta's Pizza === In May 2014 Bushwick's Roberta's Pizza was guest curator on the Supper app and website. Included in their selections were restaurants and bars from across New York including Bun-ker Vietnamese, Old Stanley's Bar, St. Anselm, Chuko, Frank's Cocktail Lounge, Junior's Cheesecake, Xi'an Famous Foods, Xe Lua, 124 Old Rabbit and Yuji Ramen.

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  Azure Data Lake

  Azure Data Lake is a scalable data storage and analytics service. The service is hosted in Azure, Microsoft's public cloud. == History == Azure Data Lake service was released on November 16, 2016. It is based on COSMOS, which is used to store and process data for applications such as Azure, AdCenter, Bing, MSN, Skype and Windows Live. COSMOS features a SQL-like query engine called SCOPE upon which U-SQL was built. == Storage == Data Lake Storage is a cloud service to store structured, semi-structured or unstructured data produced from applications including social networks, relational data, sensors, videos, web apps, mobile or desktop devices. A single account can store trillions of files where a single file can be greater than a petabyte in size. == Analytics == Data Lake Analytics is a parallel on-demand job service. The parallel processing system is based on Microsoft Dryad. Dryad can represent arbitrary Directed Acyclic Graphs (DAGs) of computation. Data Lake Analytics provides a distributed infrastructure that can dynamically allocate resources so that customers pay for only the services they use. The system uses Apache YARN, the part of Apache Hadoop which governs resource management across clusters. Data Lake Store supports any application that uses the Hadoop Distributed File System (HDFS) interface. == U-SQL == U-SQL is a query language for Data Lake Analytics parallel data transformation and processing programs. It combines SQL and C#: it is and an evolution of the declarative SQL language with native extensibility through user code written in C#. U-SQL uses C# data types and the C# expression language. == Retirement == In 2021, Microsoft announced the 2024 retirement of the original Azure Data Lake Storage, now called "Gen1". The related Azure Data Lake Analytics / U-SQL technologies are also being retired. Azure Data Lake Storage Gen2, an extension of Azure Storage, will continue. The suggested replacement technologies are Azure Synapse Analytics and Apache Spark.

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  Elastix (image registration)

  Elastix is an image registration toolbox built upon the Insight Segmentation and Registration Toolkit (ITK). It is entirely open-source and provides a wide range of algorithms employed in image registration problems. Its components are designed to be modular to ease a fast and reliable creation of various registration pipelines tailored for case-specific applications. It was first developed by Stefan Klein and Marius Staring under the supervision of Josien P.W. Pluim at Image Sciences Institute (ISI). Its first version was command-line based, allowing the final user to employ scripts to automatically process big data-sets and deploy multiple registration pipelines with few lines of code. Nowadays, to further widen its audience, a version called SimpleElastix is also available, developed by Kasper Marstal, which allows the integration of elastix with high level languages, such as Python, Java, and R. == Image registration fundamentals == Image registration is a well-known technique in digital image processing that searches for the geometric transformation that, applied to a moving image, obtains a one-to-one map with a target image. Generally, the images acquired from different sensors (multimodal), time instants (multitemporal), and points of view (multiview) should be correctly aligned to proceed with further processing and feature extraction. Even though there are a plethora of different approaches to image registration, the majority is composed of the same macro building blocks, namely the transformation, the interpolator, the metric, and the optimizer. Registering two or more images can be framed as an optimization problem that requires multiple iterations to converge to the best solution. Starting from an initial transformation computed from the image moments the optimization process searches for the best transformation parameters based on the value of the selected similarity metric. The figure on the right shows the high-level representation of the registration of two images, where the reference remains constant during the entire process, while the moving one will be transformed according to the transformation parameters. In other words, the registration ends when the similarity metric, which is a mathematical function with a certain number of parameters to be optimized, reaches the optimal value which is highly dependent on the specific application. == Main building blocks == Following the structure of the image registration workflow, the elastix toolbox proposes a modular solution that implements for each of the building blocks different algorithms, highly employed in medical image registration, and helps the final users to build their specific pipeline by selecting the most suitable algorithm for each of the main building blocks. Each block is easily configurable both by selecting pre-defined initialization values or by trying multiple sets of parameters and then choosing the most performing one. The registration is performed on images, and the elastix toolbox supports all the data formats supported by ITK, ranging from JPEG and PNG to medical standard formats such as DICOM and NIFTI. It also stores physical pixel spacing, the origin and the relative position to an external world reference system, when provided in the metadata, to facilitate the registration process, especially in medical field applications. === Transformation === The transformation is an essential building block, since it defines the allowable transformations. In image registration, the main distinction can be done between parallel-to-parallel and parallel-to-non parallel (deformable) line mapping transformations. In the elastix toolbox, the final users can select one transformation or compose more transformations either through addition or via composition. Below are reported the different transformation models in order of increasing flexibility, along with the corresponding elastix class names between brackets. Translation (TranslationTransform) allows only translations Rigid (EulerTransform) expands the translation adding rotations and the object is seen as a rigid body Similarity (SimilarityTransform) expands the rigid transformation by introducing isotropic scaling Affine (AffineTransform) expands the rigid transformation allowing both scaling and shear B-splines (BSplineTransform) is a deformable transformation usually preceded by a rigid or affine one Thin-plate splines (SplineKernelTransform) is a deformable transformation belonging to the class of kernel-based transformations that is a composition of and affine and a non-rigid part === Metric === The similarity metric is the mathematical function whose parameters should be optimized to reach the desired registration, and, during the process, it is computed multiple times. Below are reported the available metrics computed employing the reference and the transformed images and the corresponding elastix class names between brackets. Mean squared difference (AdvancedMeanSquares) to be used for mono-modal applications Normalized correlation coefficient (AdvancedNormalizedCorrelation) to be used for images that have an intensity linear relationship Mutual information (AdvancedMattesMutualInformation) to be used for both mono- and multi-modal applications and optimized to reach better performance compared to the normalized version Normalized mutual information (NormalizedMutualInformation) for both mono- and multi-modal applications Kappa statistic (AdvancedKappaStatistic) to be used only for binary images === Sampler === For the computation of the similarity metrics, it is not always necessary to consider all the voxels and, sometimes, it can be useful to use only a fraction of the voxels of the images, i.e. to reduce the execution time for big input images. Below are reported the available criteria for selecting a fraction of the voxels for the similarity metric computation and the corresponding elastix class names between brackets. Full (Full) to employ all the voxels Grid (Grid) to employ a regular grid defined by the user to downsample the image Random (Random) to randomly select a percentage of voxels defined by the users (all voxels have equal probability to be selected) Random coordinate (RandomCoordinate) like the random criterion, but in this case also off-grid positions can be selected to simplify the optimization process === Interpolator === After the application of the transformation, it may occur that the voxels used for the similarity metric computation are at non-voxel positions, so intensity interpolation should be performed to ensure the correctness of the computed values. Below are reported the implemented interpolators and the corresponding elastix class names between brackets. Nearest neighbor (NearestNeighborInterpolator) exploits little resources, but gives low quality results Linear (LinearInterpolator) is sufficient in general applications N-th order B-spline (BSplineInterpolator) can be used to increase the order N, increasing quality and computation time. N=0 and N=1 indicate the nearest neighbor and linear cases respectively. === Optimizer === The optimizer defines the strategy employed for searching the best transformation parameter to reach the correct registration, and it is commonly an iterative strategy. Below are reported some of the implemented optimization strategies. Gradient descent Robbins-Monro, similar to the gradient descent, but employing an approximation of the cost function derivatives A wider range of optimizers is also available, such as Quasi-Newton or evolutionary strategies. === Other features === The elastix software also offers other features that can be employed to speed up the registration procedure and to provide more advanced algorithms to the end-users. Some examples are the introduction of blur and Gaussian pyramid to reduce data complexity, and multi-image and multi-metric framework to deal with more complex applications. == Applications == Elastix has applications mainly in the medical field, where image registration is fundamental to get comprehensive information regarding the analysed anatomical region. It is widely employed in image-guided surgery, tumour monitoring, and treatment assessment. For example, in radiotherapy planning, image registration allows to correctly deliver the treatment and evaluate the obtained results. Thanks to the wide range of implemented algorithms, the use of the elastix software allows physicians and researchers to test different registration pipelines from the simplest to more complex ones, and to save the best one as a configuration file. This file and the fact that the software is completely open-source makes it easy to reproduce the work, that can help supporting the open science paradigm, and allows fast reuse on different patients data. In image-guided surgery, registration time and accuracy are critical points, considering that, during the registration, the patient is on the operating table, and the imag

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  Local Economic Assessment Package

  The Local Economic Assessment Package (also known as “EDR-LEAP” or “LEAP Model”) is a web-based, interactive database and software tool used by local and regional agencies in the US to improve strategies for economic development. It provides local economic performance measures, and benchmarks for comparison of economic development factors against competing regions. It works by incorporating elements of economic base analysis as well as gap analysis and business cluster analysis to identify needs for improvement and paths for economic growth. The LEAP Model was originally developed for the Appalachian Regional Commission. Its theory and applications are discussed in peer-reviewed journal articles.

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  Curvelet

  Curvelets are a non-adaptive technique for multi-scale object representation. Being an extension of the wavelet concept, they are becoming popular in similar fields, namely in image processing and scientific computing. Wavelets generalize the Fourier transform by using a basis that represents both location and spatial frequency. For 2D or 3D signals, directional wavelet transforms go further, by using basis functions that are also localized in orientation. A curvelet transform differs from other directional wavelet transforms in that the degree of localisation in orientation varies with scale. In particular, fine-scale basis functions are long ridges; the shape of the basis functions at scale j is 2 − j {\displaystyle 2^{-j}} by 2 − j / 2 {\displaystyle 2^{-j/2}} so the fine-scale bases are skinny ridges with a precisely determined orientation. Curvelets are an appropriate basis for representing images (or other functions) which are smooth apart from singularities along smooth curves, where the curves have bounded curvature, i.e. where objects in the image have a minimum length scale. This property holds for cartoons, geometrical diagrams, and text. As one zooms in on such images, the edges they contain appear increasingly straight. Curvelets take advantage of this property, by defining the higher resolution curvelets to be more elongated than the lower resolution curvelets. However, natural images (photographs) do not have this property; they have detail at every scale. Therefore, for natural images, it is preferable to use some sort of directional wavelet transform whose wavelets have the same aspect ratio at every scale. When the image is of the right type, curvelets provide a representation that is considerably sparser than other wavelet transforms. This can be quantified by considering the best approximation of a geometrical test image that can be represented using only n {\displaystyle n} wavelets, and analysing the approximation error as a function of n {\displaystyle n} . For a Fourier transform, the squared error decreases only as O ( 1 / n ) {\displaystyle O(1/{\sqrt {n}})} . For a wide variety of wavelet transforms, including both directional and non-directional variants, the squared error decreases as O ( 1 / n ) {\displaystyle O(1/n)} . The extra assumption underlying the curvelet transform allows it to achieve O ( ( log ⁡ n ) 3 / n 2 ) {\displaystyle O({(\log n)}^{3}/{n^{2}})} . Efficient numerical algorithms exist for computing the curvelet transform of discrete data. The computational cost of the discrete curvelet transforms proposed by Candès et al. (Discrete curvelet transform based on unequally-spaced fast Fourier transforms and based on the wrapping of specially selected Fourier samples) is approximately 6–10 times that of an FFT, and has the same dependence of O ( n 2 log ⁡ n ) {\displaystyle O(n^{2}\log n)} for an image of size n × n {\displaystyle n\times n} . == Curvelet construction == To construct a basic curvelet ϕ {\displaystyle \phi } and provide a tiling of the 2-D frequency space, two main ideas should be followed: Consider polar coordinates in frequency domain Construct curvelet elements being locally supported near wedges The number of wedges is N j = 4 ⋅ 2 ⌈ j 2 ⌉ {\displaystyle N_{j}=4\cdot 2^{\left\lceil {\frac {j}{2}}\right\rceil }} at the scale 2 − j {\displaystyle 2^{-j}} , i.e., it doubles in each second circular ring. Let ξ = ( ξ 1 , ξ 2 ) T {\displaystyle {\boldsymbol {\xi }}=\left(\xi _{1},\xi _{2}\right)^{T}} be the variable in frequency domain, and r = ξ 1 2 + ξ 2 2 , ω = arctan ⁡ ξ 1 ξ 2 {\displaystyle r={\sqrt {\xi _{1}^{2}+\xi _{2}^{2}}},\omega =\arctan {\frac {\xi _{1}}{\xi _{2}}}} be the polar coordinates in the frequency domain. We use the ansatz for the dilated basic curvelets in polar coordinates: ϕ ^ j , 0 , 0 := 2 − 3 j 4 W ( 2 − j r ) V ~ N j ( ω ) , r ≥ 0 , ω ∈ [ 0 , 2 π ) , j ∈ N 0 {\displaystyle {\hat {\phi }}_{j,0,0}:=2^{\frac {-3j}{4}}W(2^{-j}r){\tilde {V}}_{N_{j}}(\omega ),r\geq 0,\omega \in [0,2\pi ),j\in N_{0}} To construct a basic curvelet with compact support near a ″basic wedge″, the two windows W {\displaystyle W} and V ~ N j {\displaystyle {\tilde {V}}_{N_{j}}} need to have compact support. Here, we can simply take W ( r ) {\displaystyle W(r)} to cover ( 0 , ∞ ) {\displaystyle (0,\infty )} with dilated curvelets and V ~ N j {\displaystyle {\tilde {V}}_{N_{j}}} such that each circular ring is covered by the translations of V ~ N j {\displaystyle {\tilde {V}}_{N_{j}}} . Then the admissibility yields ∑ j = − ∞ ∞ | W ( 2 − j r ) | 2 = 1 , r ∈ ( 0 , ∞ ) . {\displaystyle \sum _{j=-\infty }^{\infty }\left|W(2^{-j}r)\right|^{2}=1,r\in (0,\infty ).} see Window Functions for more information For tiling a circular ring into N {\displaystyle N} wedges, where N {\displaystyle N} is an arbitrary positive integer, we need a 2 π {\displaystyle 2\pi } -periodic nonnegative window V ~ N {\displaystyle {\tilde {V}}_{N}} with support inside [ − 2 π N , 2 π N ] {\displaystyle \left[{\frac {-2\pi }{N}},{\frac {2\pi }{N}}\right]} such that ∑ l = 0 N − 1 V ~ N 2 ( ω − 2 π l N ) = 1 {\displaystyle \sum _{l=0}^{N-1}{\tilde {V}}_{N}^{2}\left(\omega -{\frac {2\pi l}{N}}\right)=1} , for all ω ∈ [ 0 , 2 π ) {\displaystyle \omega \in \left[0,2\pi \right)} , V ~ N {\displaystyle {\tilde {V}}_{N}} can be simply constructed as 2 π {\displaystyle 2\pi } -periodizations of a scaled window V ( N ω 2 π ) {\displaystyle V\left({\frac {N\omega }{2\pi }}\right)} . Then, it follows that ∑ l = 0 N j − 1 | 2 3 j 4 ϕ ^ j , 0 , 0 ( r , ω − 2 π l N j ) | 2 = | W ( 2 − j r ) | 2 ∑ l = 0 N j − 1 V ~ N j 2 ( ω − 2 π l N ) = | W ( 2 − j r ) | 2 {\displaystyle \sum _{l=0}^{N_{j}-1}\left|2^{\frac {3j}{4}}{\hat {\phi }}_{j,0,0}\left(r,\omega -{\frac {2\pi l}{N_{j}}}\right)\right|^{2}=\left|W(2^{-j}r)\right|^{2}\sum _{l=0}^{N_{j}-1}{\tilde {V}}_{N_{j}}^{2}\left(\omega -{\frac {2\pi l}{N}}\right)=\left|W(2^{-j}r)\right|^{2}} For a complete covering of the frequency plane including the region around zero, we need to define a low pass element ϕ ^ − 1 := W 0 ( | ξ | ) {\displaystyle {\hat {\phi }}_{-1}:=W_{0}(\left|\xi \right|)} with W 0 2 ( r ) 2 := 1 − ∑ j = 0 ∞ W ( 2 − j r ) 2 {\displaystyle W_{0}^{2}(r)^{2}:=1-\sum _{j=0}^{\infty }W(2^{-j}r)^{2}} that is supported on the unit circle, and where we do not consider any rotation. == Applications == Image processing Seismic exploration Fluid mechanics PDEs solving Compressed sensing

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  Apache Drill

  Apache Drill is an open-source software framework that supports data-intensive distributed applications for interactive analysis of large-scale datasets. Built chiefly by contributions from developers from MapR, Drill is inspired by Google's Dremel system. Drill is an Apache top-level project. Drill supports a variety of NoSQL databases and file systems, including Alluxio, HBase, MongoDB, MapR-DB, HDFS, MapR-FS, Amazon S3, Azure Blob Storage, Google Cloud Storage, Swift, NAS and local files. A single query can join data from multiple datastores. Drill's datastore-aware optimizer automatically restructures a query plan to leverage the datastore's internal processing capabilities. In addition, Drill supports data locality, if Drill and the datastore are on the same nodes. Tom Shiran is the founder of the Apache Drill Project. It was designated an Apache Software Foundation top-level project in December 2016. == Features == One explicitly stated design goal is that Drill is able to scale to 10,000 servers or more and to be able to process petabytes of data and trillions of records in seconds. Schema-free JSON document model similar to MongoDB and Elasticsearch, without requiring a formal schema to be declared Industry-standard APIs: ANSI SQL, ODBC/JDBC, RESTful APIs Extremely user and developer friendly Pluggable architecture enables connectivity to multiple datastores Version 1.9 added dynamic user-defined functions Version 1.11 added cryptographic-related functions and PCAP file format support == Back-end support == Drill is primarily focused on non-relational datastores, including Apache Hadoop text files, NoSQL, and cloud storage. A notable feature also includes in situ querying of local JSON and Apache Parquet files. Some additional datastores that it supports include: All Hadoop distributions (HDFS API 2.3+), including Apache Hadoop, MapR, CDH and Amazon EMR NoSQL: MongoDB, Apache HBase, Apache Cassandra Online Analytical Processing: Apache Kudu, Apache Druid, OpenTSDB Cloud storage: Amazon S3, Google Cloud Storage, Azure Blob Storage, Swift, IBM Cloud Object Storage Diverse data formats, including Apache Avro, Apache Parquet and JSON RDBMs storage plugins (Using JDBC to connect to MySQL, PostgreSQL, and others) A new datastore can be added by developing a storage plugin. Drill's "schema-free" JSON data model enables it to query non-relational datastores in-situ . == Front-end support == Drill itself can be queried via JDBC, ODBC, or REST through a variety of methods and languages including Python and Java. The default install includes a web interface allowing end-users to execute ANSI SQL directly and export data tables as CSV files without any programming. The dashboard library, Apache Superset, is particularly well suited for visualization of data queried with Drill.

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  Google Research

  Google Research (also known as Research at Google) is the research division of Google, a subsidiary of Alphabet Inc.. According to its official website, Google Research publishes findings, releases open-source software, and applies research results within Google products and services as well as within the wider scientific community. == Notable contributions == The 2017 landmark paper Attention Is All You Need, which introduced the Transformer architecture, which has subsequently been used to build modern large language models. Advances in neural machine translation powering Google Translate. Time series forecasting. Development of scalable learning systems and infrastructure for large-model training. Flood forecasting. Research into computational discovery via Google Accelerated Science including demonstrating the first below-threshold quantum calculations.

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  FreshBooks

  FreshBooks is accounting software operated by 2ndSite Inc. primarily for small and medium-sized businesses. It is a web-based software as a service (SaaS) model, that can be accessed through a desktop or mobile device. The company was founded in 2003 and is based in Toronto, Canada. == History == FreshBooks was founded in 2004 by Mike McDerment, Levi Cooperman, and Joe Sawada in Toronto, Ontario. McDerment incorporated a second company, BillSpring in January 2015 to work on new product development. It was rolled back into FreshBooks as an updated interface in 2016. Initially FreshBooks functioned like an electronic invoicing program targeting IT professionals. After the release of the new interface, the initial release of FreshBooks was referred to as "FreshBooks Classic." FreshBooks Classic was discontinued in 2022 after migrating users to the new platform. FreshBooks Classic's front-end application was built in PHP, and the backend services were built in Python while the new FreshBooks uses the same backend services with a JavaScript single-page application. == Product == FreshBooks is a subscription-based accounting software platform that provides features such as invoicing, accounts payable, expense and time tracking, retainers, fixed asset depreciation, purchase orders, payroll integrations, mileage tracking, double-entry accounting, and standard business reporting. Financial data is stored in the cloud on a unified ledger, enabling access from desktop and mobile devices. The platform includes a free API for integration with external applications and supports multiple tax rates and currencies. It also offers project management and payroll functionalities. Pricing is based on a recurring monthly fee. FreshBooks supports country-specific tax calculations, including GST and HST in Canada, sales taxes in the United States, and MTD compliance in the UK. == Operations == FreshBooks has its headquarters in Toronto, Canada with operations in North America, Europe and Australia. Founder Mike McDerment was the chief executive officer of the company from 2003 until 2021, when he stepped down and was replaced by Don Epperson, but stayed as the executive chair. Don Epperson had previously joined FreshBooks as executive director in 2019. == Funding == FreshBooks was initially self-funded. In 2014, the company raised a Series A venture investment of $30 million led by the venture capital firm Oak Investment Partners, with participation by Georgian Partners and Atlas Venture. In 2017, FreshBooks announced that it raised another $43 million in funding from Accomplice, Georgian Partners and Oak Investment Partners. On August 10, 2021, FreshBooks announced that it had secured $80.75 million in Series E funding and $50 million in debt financing. FreshBooks also reached a valuation of more than $1 billion.

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  OpenFog Consortium

  The OpenFog Consortium (sometimes stylized as Open Fog Consortium) was a consortium of high tech industry companies and academic institutions across the world aimed at the standardization and promotion of fog computing in various capacities and fields. The consortium was founded by Cisco Systems, Intel, Microsoft, Princeton University, Dell, and ARM Holdings in 2015 and now has 57 members across the North America, Asia, and Europe, including Forbes 500 companies and noteworthy academic institutions. The OpenFog consortium merged with the Industrial Internet Consortium, now the Industry IoT Consortium, on January 31, 2019. == History == OpenFog was created on November 19, 2015, by ARM Holdings, Cisco Systems, Dell, Intel, Microsoft, and Princeton University. The idea for a consortium centered on the advancement and dissemination of fog computing was thought up by Helder Antunes, a Cisco executive with a history in IoT, Mung Chiang, then a Princeton University professor and now President of Purdue University, and Dr. Tao Zhang, a Cisco Distinguished Engineer and CIO for the IEEE Communications Society then and now a manager at the National Institute of Standards and Technologies (NIST). The project was executed from concept to launch by Armando Pereira at PVentures Consulting, a Silicon Valley–based high-tech consulting firm. OpenFog released its reference architecture for fog computing on February 13, 2017. The Fog World Congress 2017, with Dr. Tao Zhang as its General Chair, was hosted in October 2017 by OpenFog, in conjunction with the IEEE Communications Society, as the first congress devoted to fog computing. == Administration == The OpenFog Consortium was governed by its board of directors, which is chaired by Cisco Senior Director Helder Antunes. The board of directors is made up of 11 seats, each representing one of the following companies and institutions: ARM, AT&T, Cisco, Dell, Intel, Microsoft, Princeton University, IEEE, GE, ZTE and Shanghai Tech University. The consortium's general membership comprised 13 academic members: Aalto University, Arizona State University, California Institute of Technology, Georgia State University, National Chiao Tung University, National Taiwan University, Shanghai Research Centre for Wireless Communication, Chinese University of Hong Kong, University of Colorado Boulder, University of Southern California, University of Pisa, Vanderbilt University, Wayne State University, and 20 additional members: Hitachi, Internet Initiative Japan, Itochu, Kii, Nebbiolo, PrismTech, NEC, NGD Systems, NTT Communications, OSIsoft, Real-time Innovations, relayr, Sakura Internet, Stichting imec Nederland, Toshiba, TTT Tech, Fujitsu, FogHorn Systems, TTTech and MARSEC. == Published work == The OpenFog Consortium published the white paper, "OpenFog Reference Architecture". This document outlines the eight pillars of an OpenFog architecture:Security; Scalability; Open; Autonomy; Programmability; RAS (reliability, availability and serviceability); Agility; and Hierarchy. It also incorporates a glossary for fog computing terms. In July 2018, the IEEE Standards Association announced it had adopted the OpenFog Reference Architecture as the first standard for fog computing.

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  Color image pipeline

  An image pipeline or video pipeline is the set of components commonly used between an image source (such as a camera, a scanner, or the rendering engine in a computer game), and an image renderer (such as a television set, a computer screen, a computer printer or cinema screen), or for performing any intermediate digital image processing consisting of two or more separate processing blocks. An image/video pipeline may be implemented as computer software, in a digital signal processor, on an FPGA, or as fixed-function ASIC. In addition, analog circuits can be used to do many of the same functions. Typical components include image sensor corrections (including debayering or applying a Bayer filter), noise reduction, image scaling, gamma correction, image enhancement, colorspace conversion (between formats such as RGB, YUV or YCbCr), chroma subsampling, framerate conversion, image compression/video compression (such as JPEG), and computer data storage/data transmission. Typical goals of an imaging pipeline may be perceptually pleasing end-results, colorimetric precision, a high degree of flexibility, low cost/low CPU utilization/long battery life, or reduction in bandwidth/file size. Some functions may be algorithmically linear. Mathematically, those elements can be connected in any order without changing the end-result. As digital computers use a finite approximation to numerical computing, this is in practice not true. Other elements may be non-linear or time-variant. For both cases, there is often one or a few sequences of components that makes sense for optimum precision and minimum hardware-cost/CPU-load.

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  Site Security Handbook

  The Site Security Handbook, RFC 2196, is a guide on setting computer security policies and procedures for sites that have systems on the Internet (however, the information provided should also be useful to sites not yet connected to the Internet). The guide lists issues and factors that a site must consider when setting their own policies. It makes a number of recommendations and provides discussions of relevant areas. This guide is only a framework for setting security policies and procedures. In order to have an effective set of policies and procedures, a site will have to make many decisions, gain agreement, and then communicate and implement these policies. The guide is a product of the IETF SSH working group, and was published in 1997, obsoleting the earlier RFC 1244 from 1991.

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  Cloud-based quantum computing

  Cloud-based quantum computing refers to the remote access of quantum computing resources—such as quantum emulators, simulators, or processors—via the internet. Cloud access enables users to develop, test, and execute quantum algorithms without the need for direct interaction with specialized hardware, facilitating broader participation in quantum software development and experimentation. In 2016, IBM launched the IBM Quantum Experience, one of the first publicly accessible quantum processors connected to the cloud. In early 2017, researchers at Rigetti Computing demonstrated programmable quantum cloud access through their software platform Forest, which included the pyQuil Python library. Since the early-2020s, cloud-based quantum computing has grown significantly, with multiple providers offering access to a variety of quantum hardware modalities, including superconducting qubits, trapped ions, neutral atoms, and photonic systems. Major platforms such as Amazon Braket, Azure Quantum, and qBraid aggregate quantum devices from hardware developers like IonQ, Rigetti Computing, QuEra, Pasqal, Oxford Quantum Circuits, and IBM Quantum. These platforms provide unified interfaces for users to write and execute quantum algorithms across diverse backends, often supporting open-source SDKs such as Qiskit, Cirq, and PennyLane. The proliferation of cloud-based access has played a key role in accelerating quantum education, algorithm research, and early-stage application development by lowering the barrier to experimentation with real quantum hardware. Cloud-based quantum computing has expanded access to quantum hardware and tools beyond traditional research laboratories. These platforms support educational initiatives, algorithm development, and early-stage commercial applications. == Applications == Cloud-based quantum computing is used across education, research, and software development, offering remote access to quantum systems without the need for on-site infrastructure. === Education === Quantum cloud platforms have become valuable tools in education, allowing students and instructors to engage with real quantum processors through user-friendly interfaces. Educators use these platforms to teach foundational concepts in quantum mechanics and quantum computing, as well as to demonstrate and implement quantum algorithms in a classroom or laboratory setting. === Scientific Research === Cloud-based access to quantum hardware has enabled researchers to conduct experiments in quantum information, test quantum algorithms, and compare quantum hardware platforms. Experiments such as testing Bell's theorem or evaluating quantum teleportation protocols have been performed on publicly available quantum processors. === Software Development and Prototyping === Developers use cloud-based platforms to prototype quantum software applications across fields such as optimization, machine learning, and chemistry. These platforms offer SDKs and APIs that integrate classical and quantum workflows, enabling experimentation with quantum algorithms in real-world or simulated environments. === Public Engagement and Games === Quantum cloud tools have also been used to create educational games and interactive applications aimed at increasing public understanding of quantum concepts. These efforts help bridge the gap between theoretical content and intuitive learning. == Existing platforms == qBraid Lab by qBraid is a cloud-based platform for quantum computing. It provides software tools for researchers and developers in quantum, as well as access to quantum hardware. qBraid provides cloud based access to Microsoft Azure Quantum and Amazon Braket devices including IQM, QuEra, Pasqal, Rigetti, IonQ, QIR simulators, Amazon Braket simulators, and the NEC Vector Annealer, as of August 2025. qBraid's base version is free, where unlimited hardware and simulator access is available with the purchase of credits. Quandela Cloud by Quandela is the platform to access first cloud-accessible European photonic quantum computer. The computer is interfaced using the Perceval scripting language, with tutorials and documentation available online for free. Xanadu Quantum Cloud by Xanadu is a platform with cloud-based access to three fully programmable photonic quantum computers. Forest by Rigetti Computing is a tool suite for cloud-based quantum computing. It includes a programming language, development tools and example algorithms. LIQUi> by Microsoft is a software architecture and tool suite for quantum computing. It includes a programming language, example optimization and scheduling algorithms, and quantum simulators. Q#, a quantum programming language by Microsoft on the .NET Framework seen as a successor to LIQUi|>. IBM Quantum Platform by IBM, providing access to quantum hardware as well as HPC simulators. These can be accessed programmatically using the Python-based Qiskit framework, or via graphical interface with the IBM Q Experience GUI. Both are based on the OpenQASM standard for representing quantum operations. There is also a tutorial and online community. Quantum in the Cloud by The University of Bristol, which consists of a quantum simulator and a four qubit optical quantum system. Quantum Playground by Google is an educational resource which features a simulator with a simple interface, and a scripting language and 3D quantum state visualization. Quantum in the Cloud is an experimental quantum cloud platform for access to a four-qubit nuclear magnetic resonance-NMRCloudQ computer, managed by Tsinghua University. Quantum Inspire by Qutech is the first platform in Europe providing cloud-based quantum computing to two hardware chips. Next to a 5-qubit transmon processor, Quantum Inspire is the first platform in the world to provide online access to a fully programmable 2-qubit electron spin quantum processor. Amazon Braket is a cloud-based quantum computing platform hosted by AWS which, as of June 2025, provides access to quantum computers built by IonQ, Rigetti, IQM, and QuEra. Braket also provides a quantum algorithm development environment and simulator. Forge by QC Ware is a cloud-based quantum computing platform that provides access to D-Wave hardware, as well as Google and IBM simulators. The platform offers a 30-day free trial, including one minute of quantum computing time. Quantum-as-a-Service by Scaleway is a cloud-based platform created in 2022 to access to real quantum hardware from IQM Quantum Computers, Alpine Quantum Technologies, Quandela and Pasqal. It also include access to GPU-powered emulators such as Aer, Qsim and Quandela proprietary emulation.

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  Flektor

  Flektor was a web application that allowed users the ability to create and "mashup" their own content (photos, videos, music, etc.) and share it via email, on social networking websites MySpace, Facebook, Blogger, Digg, eBay or on personal blogs. The company's website (Flektor.com) launched on April 2, 2007, and over 40,000 people began utilizing its features just one month later. Flektor closed down in January 2009. Flektor offered tools and widgets that included audio, video, photos, text, and approximately 100 effects, transitions and filters to be used with media. Users could create personalized slideshows, polls, postcards, and streaming video projects which the website calls "fleks". Flektor also offered Chat (used as a MySpace addon) and Movie Editor, which provided the ability to edit content and assets together. Users of Flektor could import media from websites like Photobucket and Google's YouTube, and then edit their content with the site's editing tools. Flektor's erstwhile competitors include Slide.com (founded by PayPal co-founder Max Levchin), RockYou!, Yahoo's JumpCut and Brightcove. == History == Flektor was created by Jason Rubin, Andy Gavin and former HBO executive Jason R. Kay. Both Rubin and Gavin spent most of their careers in the video game industry developing games for publishers like Electronic Arts, Universal Interactive Studios and Sony Computer Entertainment America. They founded a successful game development studio called Naughty Dog and were responsible for games such as Crash Bandicoot and Jak and Daxter. After selling Naughty Dog to Sony, Rubin focused on a comic book series called Iron and the Maiden before teaming up again with Gavin to venture into the web industry with Flektor. Jason Kay spent four years at Home Box Office, working as a consultant to the EVP of Business Development. They recruited former employee and then Naughty Dog Lead Programmer Scott Shumaker to lead the technology team along with Gavin. Ryan Evans joined shortly thereafter, spearheading product development. Flektor is based in Culver City, California. In May 2007, the company was sold to Fox Interactive Media, which is a division of News Corp., for more than $20 million. The deal coincided with Fox's acquisition of Photobucket, an image-hosting and sharing website. Fox Interactive Media already holds possession of MySpace, IGN Entertainment, FOXSports.com, AmericanIdol.com and Rotten Tomatoes. After the acquisition, Rubin, Gavin and Kay departed, leaving the studio in the hands of Shumaker and Evans. In the fall of 2007, Flektor partnered with its sister company, MySpace, and MTV to provide instant audience feedback via polls for the interactive MySpace/ MTV Presidential Dialogues series with presidential candidates Senator Barack Obama, Senator John McCain and John Edwards. Use of Flektor's polling system, enabled hosts John McLaughlin and Geoffrey Garin to cater their questions towards subjects of voter-interest. In the fall of 2008, Flektor built the official site for the 2008 Presidential debates, hosted at MyDebates. In January 2009, due to a company directive to focus on the core MySpace property, Fox Interactive announced that Flektor would be shut down, with some of its technology being incorporated into MySpace.

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