Ordered dithering is any image dithering algorithm which uses a pre-set threshold map tiled across an image. It is commonly used to display a continuous image on a display of smaller color depth. For example, Microsoft Windows uses it in 16-color graphics modes. With the most common "Bayer" threshold map, the algorithm is characterized by noticeable crosshatch patterns in the result. == Threshold map == The algorithm reduces the number of colors by applying a threshold map M to the pixels displayed, causing some pixels to change color, depending on the distance of the original color from the available color entries in the reduced palette. The first threshold maps were designed by hand to minimise the perceptual difference between a grayscale image and its two-bit quantisation for up to a 4x4 matrix. An optimal threshold matrix is one that for any possible quantisation of color has the minimum possible texture so that the greatest impression of the underlying feature comes from the image being quantised. It can be proven that for matrices whose side length is a power of two there is an optimal threshold matrix. The map may be rotated or mirrored without affecting the effectiveness of the algorithm. This threshold map (for sides with length as power of two) is also known as a Bayer matrix or, when unscaled, an index matrix. For threshold maps whose dimensions are a power of two, the map can be generated recursively via: M 2 n = 1 ( 2 n ) 2 [ 4 M n 4 M n + 2 J n 4 M n + 3 J n 4 M n + J n ] = J 2 ⊗ M n + 1 n 2 M 2 ⊗ J n , {\displaystyle \mathbf {M} _{2n}={\frac {1}{(2n)^{2}}}{\begin{bmatrix}4\mathbf {M} _{n}&4\mathbf {M} _{n}+2\mathbf {J} _{n}\\4\mathbf {M} _{n}+3\mathbf {J} _{n}&4\mathbf {M} _{n}+\mathbf {J} _{n}\end{bmatrix}}=\mathbf {J} _{2}\otimes \mathbf {M} _{n}+{\frac {1}{n^{2}}}\mathbf {M} _{2}\otimes \mathbf {J} _{n},} where J n {\displaystyle \mathbf {J} _{n}} are n × n {\displaystyle n\times n} matrices of ones and ⊗ {\displaystyle \otimes } is the Kronecker product. While the metric for texture that Bayer proposed could be used to find optimal matrices for sizes that are not a power of two, such matrices are uncommon as no simple formula for finding them exists, and relatively small matrix sizes frequently give excellent practical results (especially when combined with other modifications to the dithering algorithm). This function can also be expressed using only bit arithmetic: M(i, j) = bit_reverse(bit_interleave(bitwise_xor(i, j), i)) / n ^ 2 == Pre-calculated threshold maps == Rather than storing the threshold map as a matrix of n {\displaystyle n} × n {\displaystyle n} integers from 0 to n 2 {\displaystyle n^{2}} , depending on the exact hardware used to perform the dithering, it may be beneficial to pre-calculate the thresholds of the map into a floating point format, rather than the traditional integer matrix format shown above. For this, the following formula can be used: Mpre(i,j) = Mint(i,j) / n^2 This generates a standard threshold matrix. for the 2×2 map: this creates the pre-calculated map: Additionally, normalizing the values to average out their sum to 0 (as done in the dithering algorithm shown below) can be done during pre-processing as well by subtracting 1⁄2 of the largest value from every value: Mpre(i,j) = Mint(i,j) / n^2 – 0.5 maxValue creating the pre-calculated map: == Algorithm == The ordered dithering algorithm renders the image normally, but for each pixel, it offsets its color value with a corresponding value from the threshold map according to its location, causing the pixel's value to be quantized to a different color if it exceeds the threshold. For most dithering purposes, it is sufficient to simply add the threshold value to every pixel (without performing normalization by subtracting 1⁄2), or equivalently, to compare the pixel's value to the threshold: if the brightness value of a pixel is less than the number in the corresponding cell of the matrix, plot that pixel black, otherwise, plot it white. This lack of normalization slightly increases the average brightness of the image, and causes almost-white pixels to not be dithered. This is not a problem when using a gray scale palette (or any palette where the relative color distances are (nearly) constant), and it is often even desired, since the human eye perceives differences in darker colors more accurately than lighter ones, however, it produces incorrect results especially when using a small or arbitrary palette, so proper normalization should be preferred. In other words, the algorithm performs the following transformation on each color c of every pixel: c ′ = n e a r e s t _ p a l e t t e _ c o l o r ( c + r × ( M ( x mod n , y mod n ) − 1 / 2 ) ) {\displaystyle c'=\mathrm {nearest\_palette\_color} {\mathopen {}}\left(c+r\times \left(M(x{\bmod {n}},y{\bmod {n}})-1/2\right){\mathclose {}}\right)} where M(i, j) is the threshold map on the i-th row and j-th column, c′ is the transformed color, and r is the amount of spread in color space. Assuming an RGB palette with 23N evenly distanced colors where each color (a triple of red, green and blue values) is represented by an octet from 0 to 255, one would typically choose r ≈ 255 N {\textstyle r\approx {\frac {255}{N}}} . (1⁄2 is again the normalizing term.) Because the algorithm operates on single pixels and has no conditional statements, it is very fast and suitable for real-time transformations. Additionally, because the location of the dithering patterns always stays the same relative to the display frame, it is less prone to jitter than error-diffusion methods, making it suitable for animations. Because the patterns are more repetitive than error-diffusion method, an image with ordered dithering compresses better. Ordered dithering is more suitable for line-art graphics as it will result in straighter lines and fewer anomalies. The values read from the threshold map should preferably scale into the same range as the minimal difference between distinct colors in the target palette. Equivalently, the size of the map selected should be equal to or larger than the ratio of source colors to target colors. For example, when quantizing a 24 bpp image to 15 bpp (256 colors per channel to 32 colors per channel), the smallest map one would choose would be 4×2, for the ratio of 8 (256:32). This allows expressing each distinct tone of the input with different dithering patterns. === A variable palette: pattern dithering === == Non-Bayer approaches == The above thresholding matrix approach describes the Bayer family of ordered dithering algorithms. A number of other algorithms are also known; they generally involve changes in the threshold matrix, which changes the distribution of the "noise" introduced by all kinds of dithering (the difference between the original image and the dithered image). === Halftone === Halftone dithering performs a form of clustered dithering, creating a look similar to halftone patterns, using a specially crafted matrix. === Void and cluster === The Void and cluster algorithm uses a pre-generated blue noise as the matrix for the dithering process. The blue noise matrix keeps the Bayer's good high frequency content, but with a more uniform coverage of all the frequencies involved shows a much lower amount of patterning. The "voids-and-cluster" method gets its name from the matrix generation procedure, where a black image with randomly initialized white pixels is gaussian-blurred to find the brightest and darkest parts, corresponding to voids and clusters. After a few swaps have evenly distributed the bright and dark parts, the pixels are numbered by importance. It takes significant computational resources to generate the blue noise matrix: on a modern computer a 64×64 matrix requires a couple seconds using the original algorithm. This algorithm can be extended to make animated dither masks which also consider the axis of time. This is done by running the algorithm in three dimensions and using a kernel which is a product of a two-dimensional gaussian kernel on the XY plane, and a one-dimensional Gaussian kernel on the Z axis. === Simulated Annealing === Simulated annealing can generate dither masks by starting with a flat histogram and swapping values to optimize a loss function. The loss function controls the spectral properties of the mask, allowing it to make blue noise or noise patterns meant to be filtered by specific filters. The algorithm can also be extended over time for animated dither masks with chosen temporal properties.
Time-compressed speech
Time-compressed speech refers to an audio recording of verbal text in which the text is presented in a much shorter time interval than it would through normally-paced real time speech. The basic purpose is to make recorded speech contain more words in a given time, yet still be understandable. For example: a paragraph that might normally be expected to take 20 seconds to read, might instead be presented in 15 seconds, which would represent a time-compression of 25% (5 seconds out of 20). The term "time-compressed speech" should not be confused with "speech compression", which controls the volume range of a sound, but does not alter its time envelope. == Methods == While some voice talents are capable of speaking at rates significantly in excess of general norms, the term "time-compressed speech" most usually refers to examples in which the time-reduction has been accomplished through some form of electronic processing of the recorded speech. In general, recorded speech can be electronically time-compressed by: increasing its speed (linear compression); removing silences (selective editing); a combination of the two (non-linear compression). The speed of a recording can be increased, which will cause the material to be presented at a faster rate (and hence in a shorter amount of time), but this has the undesirable side-effect of increasing the frequency of the whole passage, raising the pitch of the voices, which can reduce intelligibility. There are normally silences between words and sentences, and even small silences within certain words, both of which can be reduced or removed ("edited-out") which will also reduce the amount of time occupied by the full speech recording. However, this can also have the effect of removing verbal "punctuation" from the speech, causing words and sentences to run together unnaturally, again reducing intelligibility. Vowels are typically held a minimum of 20 milliseconds, over many cycles of the fundamental pitch. DSP systems can detect the beginning and end of each cycle and then skip over some fraction of those cycles, causing the material to be presented at a faster rate, without changing the pitch, maintaining a "normal" tone of voice. The current preferred method of time-compression is called "non-linear compression", which employs a combination of selectively removing silences; speeding up the speech to make the reduced silences sound normally-proportioned to the text; and finally applying various data algorithms to bring the speech back down to the proper pitch. This produces a more acceptable result than either of the two earlier techniques; however, if unrestrained, removing the silences and increasing the speed can make a selection of speech sound more insistent, possibly to the point of unpleasantness. == Applications == === Advertising === Time-compressed speech is frequently used in television and radio advertising. The advantage of time-compressed speech is that the same number of words can be compressed into a smaller amount of time, reducing advertising costs, and/or allowing more information to be included in a given radio or TV advertisement. It is usually most noticeable in the information-dense caveats and disclaimers presented (usually by legal requirement) at the end of commercials—the aural equivalent of the "fine print" in a printed contract. This practice, however, is not new: before electronic methods were developed, spokespeople who could talk extremely quickly and still be understood were widely used as voice talents for radio and TV advertisements, and especially for recording such disclaimers. === Education === Time-compressed speech has educational applications such as increasing the information density of trainings, and as a study aid. A number of studies have demonstrated that the average person is capable of relatively easily comprehending speech delivered at higher-than-normal rates, with the peak occurring at around 25% compression (that is, 25% faster than normal); this facility has been demonstrated in several languages. Conversational speech (in English) takes place at a rate of around 150 wpm (words per minute), but the average person is able to comprehend speech presented at rates of up to 200-250 wpm without undue difficulty. Blind and severely visually impaired subjects scored similar comprehension levels at even higher rates, up to 300-350 wpm. Blind people have been found to use time-compressed speech extensively, for example, when reviewing recorded lectures from high school and college classes, or professional trainings. Comprehension rates in older blind subjects have been found to be as good, or in some cases better than those found in younger sighted subjects. Other studies have determined that the ability to comprehend highly time-compressed speech tends to fall off with increased age, and is also reduced when the language of the time-compressed speech is not the listener's native language. Non-native speakers can, however, improve their comprehension level of time-compressed speech with multiday training. === Voice Mail === Voice mail systems have employed time-compressed speech since as far back as the 1970s. In this application, the technology enables the rapid review of messages in high-traffic systems, by a relatively small number of people. === Streaming Multimedia === Time-compressed speech has been explored as one of a variety of interrelated factors which may be manipulated to increase the efficiency of streaming multimedia presentations, by significantly reducing the latency times involved in the transfer of large digitally encoded media files.
Mozilla VPN
Mozilla VPN is an open-source virtual private network developed by Mozilla. It launched in beta as Firefox Private Network on September 10, 2019, and officially launched on July 15, 2020, as Mozilla VPN. Mozilla VPN should not be confused with the built-in VPN in Firefox since version 149 released in March 2026, which is free with a monthly data limit of 50 GB but only masks traffic that originates in Firefox unlike Mozilla VPN that protects the entire device. == History == The Firefox Private Network web browser extension beta version was released on September 10, 2019, as part of the relaunch of Mozilla's Test Pilot Program, a program that allowed Firefox users to test experimental new features which had been shuttered in January 2019. The beta of the subscription-based standalone virtual private network for Android, Microsoft Windows, and Chromebook launched on February 19, 2020, with the iOS version following soon after. Firefox Private Network was rebranded as "Mozilla VPN" on June 18, 2020, and officially launched as Mozilla VPN on July 15, 2020. At launch, Mozilla VPN was available in six countries (the United States, Canada, the United Kingdom, Singapore, Malaysia, and New Zealand) for Windows 10, Android, and iOS (beta). Over time, the service also launched in Germany, France, Italy, Spain, Switzerland, Austria, Belgium, Netherlands, Ireland, Finland, Sweden, Poland, Czechia, Hungary, Romania, Bulgaria, Slovakia, Portugal, Denmark, Croatia, Lithuania, Slovenia, Latvia, Luxembourg, Estonia, Cyprus, and Malta. == Audits history == Cybersecurity firm Cure53 conducted a security audit for Mozilla VPN in August 2020 and identified multiple vulnerabilities, including one critical-severity vulnerability. In March 2021, Cure53 conducted a second security audit, which noted significant improvements since the 2020 audit. The second audit identified multiple issues, including two medium-severity and one high-severity vulnerability, but concluded that by the time of publication, only one vulnerability remained unresolved, and that it would require "a strong state-funded attacker-model" to be exploitable. Mozilla disclosed most of the vulnerabilities in July 2021 and released the full report by Cure53 in August 2021. In April 2023, Cure53 conducted a third security audit, the results of which Mozilla disclosed in December that year, along with the full report by Cure53. == Features == Mozilla VPN masks the user's IP address, hiding the user's location data from the websites accessed by the user, and encrypts all network activity. The service allows for up to 5 simultaneous connections, to any of more than 500 servers in 30+ countries, and is available on the mobile operating systems iOS and Android and the desktop operating systems Microsoft Windows, macOS and Linux. Mozilla VPN's infrastructure is provided by the Swedish Mullvad VPN service, which uses the WireGuard VPN protocol. The VPN software comes with additional features, like recommended server locations, the ability to block ads, block ad trackers and malware, the ability to exclude certain applications from protection, the ability to set multi-hop connections, and to set custom DNS servers. When used with Firefox and the official extension, Mozilla VPN allows the use of different settings per container as well as bypassing the VPN for specific websites.
TigerGraph
TigerGraph is a private company headquartered in Redwood City, California. It provides graph database and graph analytics software. == History == TigerGraph was founded in 2012 by programmer Yu, Ruoming, Li, Like and Mingxi, under the name GraphSQL. In September 2017, the company came out of stealth mode under the name TigerGraph with $33 million in funding. It raised an additional $32 million in funding in September 2019 and another $105 million in a series C round in February 2021. Cumulative funding as of March 2021 is $170 million. == Products == TigerGraph's hybrid transactional/analytical processing database and analytics software can scale to hundreds of terabytes of data with trillions of edges, and is used for data intensive applications such as fraud detection, customer data analysis (customer 360), IoT, artificial intelligence and machine learning. It is available using the cloud computing delivery model. The analytics uses C++ based software and a parallel processing engine to process algorithms and queries. It has its own graph query language that is similar to SQL. TigerGraph also provides a software development kit for creating graphs and visual representations. As of Mar 2024, TigerGraph version is up to version 4.2.0 TigerGraph offers free Community Edition for developers, researchers, and educators. It can be obtained from https://dl.tigergraph.com/ == Query Language == GSQL , designed by Mingxi Wu and Alin Deutsch in 2015, is a SQL-like Turing complete query language. GSQL includes additions to make it compliant with the Graph Query Language standard.
Wide-column store
A wide-column store (or extensible record store) is a type of NoSQL database. It uses tables, rows, and columns, but unlike a relational database, the names and format of the columns can vary from row to row in the same table. A wide-column store can be interpreted as a two-dimensional key–value store. Google's Bigtable is one of the prototypical examples of a wide-column store. == Wide-column stores versus columnar databases == Wide-column stores such as Bigtable and Apache Cassandra are not column stores in the original sense of the term, since their two-level structures do not use a columnar data layout. In genuine column stores, a columnar data layout is adopted such that each column is stored separately on disk. Wide-column stores do often support the notion of column families that are stored separately. However, each such column family typically contains multiple columns that are used together, similar to traditional relational database tables. Within a given column family, all data is stored in a row-by-row fashion, such that the columns for a given row are stored together, rather than each column being stored separately. Wide-column stores that support column families are also known as column family databases. == Notable examples == Notable wide-column stores include: Apache Accumulo Apache Cassandra Apache HBase Bigtable DataStax Enterprise (uses Apache Cassandra) DataStax Astra DB (uses Apache Cassandra) Hypertable Azure Tables ScyllaDB
Meta AI
Meta AI is a research division of Meta (formerly Facebook) that develops artificial intelligence and augmented reality technologies. == History == Meta AI was founded in 2013 as Facebook Artificial Intelligence Research (FAIR). It has workspaces in Menlo Park, London, New York City, Paris, Seattle, Pittsburgh, Tel Aviv, and Montreal as of 2025. In 2016, FAIR partnered with Google, Amazon, IBM, and Microsoft in creating the Partnership on Artificial Intelligence to Benefit People and Society. Meta AI was directed by Yann LeCun until 2018, when Jérôme Pesenti succeeded the role. Pesenti is formerly the CTO of IBM's big data group. FAIR's research includes self-supervised learning, generative adversarial networks, document classification and translation, and computer vision. FAIR released Torch deep-learning modules as well as PyTorch in 2017, an open-source machine learning framework, which was subsequently used in several deep learning technologies, such as Tesla's autopilot and Uber's Pyro. That same year, a pair of chatbots were falsely rumored to be discontinued for developing a language that was unintelligible to humans. FAIR clarified that the research had been shut down because they had accomplished their initial goal to understand how languages are generated by their models, rather than out of fear. FAIR was renamed Meta AI following the rebranding that changed Facebook, Inc. to Meta Platforms Inc. On October 1, 2025, Facebook announced "We will soon use your interactions with AI at Meta to personalize the content and ads you see". == Virtual assistant == Meta AI is also the name of the virtual assistant developed by the team, now integrated as a chatbot into Meta's social networking products. It is also available as a subscription-based stand-alone app. The virtual assistant was pre-installed on the second generation of Ray-Ban Meta smartglasses, and can incorporate inputs from the glasses' cameras after an update. It is also available on Quest 2 and newer HMDs. Since May 2024, the chatbot has summarized news from various outlets without linking directly to original articles, including in Canada, where news links are banned on its platforms. This use of news content without compensation and attribution has raised ethical and legal concerns, especially as Meta continues to reduce news visibility on its platforms. == Current research == === Natural language processing and chatbot === Natural language processing is the ability for machines to understand and generate natural language. The team is also researching unsupervised machine translation and multilingual chatbots. ==== Galactica ==== Galactica is a large language model (LLM) designed for generating scientific text. It was available for three days from 15 November 2022, before being withdrawn for generating racist and inaccurate content. ==== Llama ==== Llama is an LLM released in February 2023. As of January 2026, the most recent release is the Llama 4. === Hardware === Meta used CPUs and in-house custom chips before 2022; they switched to Nvidia GPUs since then. MTIA v1, one of their early chips, is designed for the company's content recommendation algorithms. It was fabricated on TSMC's 7 nm process technology and consumed 25W, capable of 51.2 TFlops FP16. == Controversy == The French media outlet Mediapart reports that in 2022, Facebook's parent company illegally used works accumulated by the pirate site LibGen to train its artificial intelligence.
Device-independent pixel
A device-independent pixel (also: density-independent pixel, dip, dp) is a unit of length. A typical use is to allow mobile device software to scale the display of information and user interaction to different screen sizes. The abstraction allows an application to work in pixels as a measurement, while the underlying graphics system converts the abstract pixel measurements of the application into real pixel measurements appropriate to the particular device. For example, on the Android operating system a device-independent pixel is equivalent to one physical pixel on a 160 dpi screen, while the Windows Presentation Foundation specifies one device-independent pixel as equivalent to 1/96th of an inch. As dp is a physical unit it has an absolute value which can be measured in traditional units, e.g. for Android devices 1 dp equals 1/160 of inch or 0.15875 mm. While traditional pixels only refer to the display of information, device-independent pixels may also be used to measure user input such as input on a touch screen device.