AI Generator Youtube Channel Name

AI Generator Youtube Channel Name — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

Image scaling

In computer graphics and digital imaging, image scaling is the resizing of a digital image. In video technology, the magnification of digital material is known as upscaling or resolution enhancement. When scaling a vector graphic image, the graphic primitives that make up the image can be rendered using geometric transformations at any resolution with no loss of image quality. When scaling a raster graphics image, a new image with a higher or lower number of pixels must be generated. In the case of decreasing the pixel number (scaling down), this usually results in a visible quality loss. From the standpoint of digital signal processing, the scaling of raster graphics is a two-dimensional example of sample-rate conversion, the conversion of a discrete signal from a sampling rate (in this case, the local sampling rate) to another. == Mathematical == Image scaling can be interpreted as a form of image resampling or image reconstruction from the view of the Nyquist sampling theorem. According to the theorem, downsampling to a smaller image from a higher-resolution original can only be carried out after applying a suitable 2D anti-aliasing filter to prevent aliasing artifacts. The image is reduced to the information that can be carried by the smaller image. In the case of up sampling, a reconstruction filter takes the place of the anti-aliasing filter. A more sophisticated approach to upscaling treats the problem as an inverse problem, solving the question of generating a plausible image that, when scaled down, would look like the input image. A variety of techniques have been applied for this, including optimization techniques with regularization terms and the use of machine learning from examples. == Algorithms == An image size can be changed in several ways. === Nearest-neighbor interpolation === One of the simpler ways of increasing image size is nearest-neighbor interpolation, replacing every pixel with the nearest pixel in the output; for upscaling, this means multiple pixels of the same color will be present. This can preserve sharp details but also introduce jaggedness in previously smooth images. 'Nearest' in nearest-neighbor does not have to be the mathematical nearest. One common implementation is to always round toward zero. Rounding this way produces fewer artifacts and is faster to calculate. This algorithm is often preferred for images which have little to no smooth edges. A common application of this can be found in pixel art. === Bilinear and bicubic interpolation === Bilinear interpolation works by interpolating pixel color values, introducing a continuous transition into the output even where the original material has discrete transitions. Although this is desirable for continuous-tone images, this algorithm reduces contrast (sharp edges) in a way that may be undesirable for line art. Bicubic interpolation yields substantially better results, with an increase in computational cost. === Sinc and Lanczos resampling === Sinc resampling, in theory, provides the best possible reconstruction for a perfectly bandlimited signal. In practice, the assumptions behind sinc resampling are not completely met by real-world digital images. Lanczos resampling, an approximation to the sinc method, yields better results. Bicubic interpolation can be regarded as a computationally efficient approximation to Lanczos resampling. === Box sampling === One weakness of bilinear, bicubic, and related algorithms is that they sample a specific number of pixels. When downscaling below a certain threshold, such as more than twice for all bi-sampling algorithms, the algorithms will sample non-adjacent pixels, which results in both losing data and rough results. The trivial solution to this issue is box sampling, which is to consider the target pixel a box on the original image and sample all pixels inside the box. This ensures that all input pixels contribute to the output. The major weakness of this algorithm is that it is hard to optimize. === Mipmap === Another solution to the downscale problem of bi-sampling scaling is mipmaps. A mipmap is a prescaled set of downscaled copies. When downscaling, the nearest larger mipmap is used as the origin to ensure no scaling below the useful threshold of bilinear scaling. This algorithm is fast and easy to optimize. It is standard in many frameworks, such as OpenGL. The cost is using more image memory, exactly one-third more in the standard implementation. === Fourier-transform methods === Simple interpolation based on the Fourier transform pads the frequency domain with zero components (a smooth window-based approach would reduce the ringing). Besides the good conservation (or recovery) of details, notable are the ringing and the circular bleeding of content from the left border to the right border (and the other way around). === Edge-directed interpolation === Edge-directed interpolation algorithms aim to preserve edges in the image after scaling, unlike other algorithms, which can introduce staircase artifacts. Examples of algorithms for this task include New Edge-Directed Interpolation (NEDI), Edge-Guided Image Interpolation (EGGI), Iterative Curvature-Based Interpolation (ICBI), and Directional Cubic Convolution Interpolation (DCCI). A 2013 analysis found that DCCI had the best scores in peak signal-to-noise ratio and structural similarity on a series of test images. === hqx === For magnifying computer graphics with low resolution and/or few colors (usually from 2 to 256 colors), better results can be achieved by hqx or other pixel-art scaling algorithms. These produce sharp edges and maintain a high level of detail. === Vectorization === Vector extraction, or vectorization, offers another approach. Vectorization first creates a resolution-independent vector representation of the graphic to be scaled. The resulting SVG vector file can then be exported and rendered at any required resolution without quality loss, serving directly as production-ready artwork for scalable display & printing. This technique is used by Adobe Illustrator, Live Trace, and Inkscape. Scalable Vector Graphics are well suited to simple geometric images, while photographs do not fare well with vectorization due to their complexity. === Deep convolutional neural networks === This method uses machine learning for more detailed images, such as photographs and complex artwork. Programs that use this method include waifu2x, Imglarger and Neural Enhance. Demonstration of conventional vs. waifu2x upscaling with noise reduction, using a detail of Phosphorus and Hesperus by Evelyn De Morgan. [Click image for full size] AI-driven upscaling software allows detail and sharpness to be added to historical photographs, where it is not present in the original. The availability of AI upscaling tools has led to confusion where a person believes that the upscaled version of a blurry image is genuinely showing them the subject of the original photograph. In 2025 a user of the social media site X posted an AI-upscaled version of a low resolution photo of Donald Trump that they had zoomed in on, and asked if anyone could "explain what the hell is happening to his forehead". Experts noted that the image had been distorted by the upscaling process, and that such tools "inevitably have to invent, or at least recreate, details that were or were not there". == Applications == === General === Image scaling is used in, among other applications, web browsers, image editors, image and file viewers, software magnifiers, digital zoom, the process of generating thumbnail images, and when outputting images through screens or printers. === Video === This application is the magnification of images for home theaters for HDTV-ready output devices from PAL-Resolution content, for example, from a DVD player. Upscaling is performed in real time, and the output signal is not saved. === Pixel-art scaling === As pixel-art graphics are usually low-resolution, they rely on careful placement of individual pixels, often with a limited palette of colors. This results in graphics that rely on stylized visual cues to define complex shapes with little resolution, down to individual pixels. This makes scaling pixel art a particularly difficult problem. Specialized algorithms were developed to handle pixel-art graphics, as the traditional scaling algorithms do not take perceptual cues into account. Since a typical application is to improve the appearance of fourth-generation and earlier video games on arcade and console emulators, many are designed to run in real time for small input images at 60 frames per second. On fast hardware, these algorithms are suitable for gaming and other real-time image processing. These algorithms provide sharp, crisp graphics, while minimizing blur. Scaling art algorithms have been implemented in a wide range of emulators such as HqMAME and DOSBox, as well as 2D game engines and game engine recreations such as ScummVM. They gained recognition with game
Read more →
Permutation automaton

In automata theory, a permutation automaton, or pure-group automaton, is a deterministic finite automaton such that each input symbol permutes the set of states. Formally, a deterministic finite automaton A may be defined by the tuple (Q, Σ, δ, q0, F), where Q is the set of states of the automaton, Σ is the set of input symbols, δ is the transition function that takes a state q and an input symbol x to a new state δ(q,x), q0 is the initial state of the automaton, and F is the set of accepting states (also: final states) of the automaton. A is a permutation automaton if and only if, for every two distinct states qi and qj in Q and every input symbol x in Σ, δ(qi,x) ≠ δ(qj,x). A formal language is p-regular (also: a pure-group language) if it is accepted by a permutation automaton. For example, the set of strings of even length forms a p-regular language: it may be accepted by a permutation automaton with two states in which every transition replaces one state by the other. == Applications == The pure-group languages were the first interesting family of regular languages for which the star height problem was proved to be computable. Another mathematical problem on regular languages is the separating words problem, which asks for the size of a smallest deterministic finite automaton that distinguishes between two given words of length at most n – by accepting one word and rejecting the other. The known upper bound in the general case is O ( n 2 / 5 ( log ⁡ n ) 3 / 5 ) {\displaystyle O(n^{2/5}(\log n)^{3/5})} . The problem was later studied for the restriction to permutation automata. In this case, the known upper bound changes to O ( n 1 / 2 ) {\displaystyle O(n^{1/2})} .
Read more →
Tamara Broderick

Tamara Ann Broderick is an American computer scientist at the Massachusetts Institute of Technology. She works on machine learning and Bayesian inference. == Education and early career == Broderick is from Parma Heights, Ohio. She attended Laurel School and graduated in 2003. Whilst at high school she took part in the inaugural Massachusetts Institute of Technology Women's Technology Program. She studied mathematics at Princeton University, earning a bachelor's degree in 2007. She was a Marshall scholar, allowing her to pursue graduate research at the University of Cambridge. She was a runner-up in the Association for Women in Mathematics Alice T. Shafer Prize for Excellence in Mathematics. She was co-president of the Princeton Math Club and organised a competition for high school maths teams. She won the Phi Beta Kappa Prize for the highest academic average at Princeton University. During her undergraduate degree, Broderick worked on dark matter haloes with Rachel Mandelbaum. Broderick moved to the United Kingdom for her graduate studies, earning a Master of Advanced Studies for completing Part III of the Mathematical Tripos at the University of Cambridge in 2009. Her Master's thesis looked at the Nomon selection method, improving the efficiency of communications. She returned to America in 2009, joining University of California, Berkeley for her Master's and PhD. Her graduate research was supported by the Berkeley Fellowship and a National Science Foundation Fellowship. Her PhD thesis Clusters and features from combinatorial stochastic processes looked at clustering and speeding up the analysis of large, streaming data sets. In 2013 she was selected for the Berkeley EECS Rising Stars conference. == Research and career == Broderick joined Massachusetts Institute of Technology as an assistant professor in 2015. She is interested in Bayesian statistics and graphical models. She was the recipient of a Google Faculty Research Grant and International Society for Bayesian Analysis Lifetime Members Junior Researcher Award. She was awarded an Army Research Office young investigator program award to investigate machine-learning to quantify uncertainty in data analysis. Broderick is also Alfred P. Sloan Foundation scholar. === Academic service === In 2018, Broderick spoke at the Harvard University Institute for Applied Computational Science Women in Data Science conference. She spoke about Bayesian inference at the 2018 International Conference on Machine Learning. She led a three-day Masterclass on machine learning at University College London in June 2018. Broderick is a scientific advisor for AI.Reverie and WiML (Women in Machine Learning). She has developed a high-school level introduction to machine learning with the Women's Technology Program (WTP). Software she has developed is available on her website. === Awards and honors === Broderick was awarded the Evelyn Fix Memorial Medal and Citation and the International Society for Bayesian Analysis Savage Award for her doctoral thesis. She was awarded a National Science Foundation CAREER Award to scale her machine learning techniques. She was a 2021 Leadership Academy winner of the Committee of Presidents of Statistical Societies.
Read more →
OCR Systems

OCR Systems, Inc., was an American computer hardware manufacturer and software publisher dedicated to optical character recognition technologies. The company's first product, the System 1000 in 1970, was used by numerous large corporations for bill processing and mail sorting. Following a series of pitfalls in the 1970s and early 1980s, founder Theodor Herzl Levine put the company in the hands of Gregory Boleslavsky and Vadim Brikman, the company's vice presidents and recent immigrants from the Soviet Ukraine, who were able to turn OCR System's fortunes around and expand its employee base. The company released the software-based OCR application ReadRight for DOS, later ported to Windows, in the late 1980s. Adobe Inc. bought the company in 1992. == History == OCR Systems was co-founded by Theodor Herzl Levine (c. 1923 – May 30, 2005). Levine served in the U.S. Army Signal Corps during World War II in the Solomon Islands, where he helped develop a sonar to find ejected pilots in the ocean. After the war, Levine spent 22 years at the University of Pennsylvania, earning his bachelor's degree in 1951, his master's degree in electrical engineering in 1957, and his doctorate in 1968. Alongside his studies, Levine taught statistics and calculus at Temple University, Rutgers University, La Salle University and Penn State Abington. Sometime in the 1960s, Levine was hired at Philco. He and two of his co-workers decided to form their own company dedicated to optical character recognition, founding OCR Systems in 1969 in Bensalem, Pennsylvania. OCR Systems's first product, the System 1000, was announced in 1970. OCR Systems entered a partnership with 3M to resell the System 1000 throughout the United States in March 1973. This was 3M's entry into the data entry field, managed by the company's Microfilm Products Division and accompanying 3M's suite of data retrieval systems. It soon found use among Texas Instruments, AT&T, Ricoh, Panasonic and Canon for bill processing and mail sorting. Later in the mid-1970s an unspecified Fortune 500 company reneged on a contract to distribute the System 1000; later still a Canadian company distributing the System 1000 in Canada went defunct. Both incidents led OCR Systems to go nearly bankrupt, although it eventually recovered. By the early 1980s, however, the company was almost insolvent. In 1983 Levine had only $8,000 in his savings and became bedridden with an illness. He left the company in the hands of Gregory Boleslavsky and Vadim Brikman, two Soviet Ukraine expats whom Levine had hired earlier in the 1980s. Boleslavsky was hired as a wire wrapper for the System 1000 and as a programmer and beta tester for ReadRight—a software package developed by Levine implementing patents from Nonlinear Technology, another OCR-centric company from Greenbelt, Maryland. Boleslavsky in turn recommended Brikman to Levine. The two soon became vice presidents of the company while Levine was bedridden; in Boleslavsky's case, he worked 14-hour work days for over half a year in pursuit of the title. The two presented OCR Systems' products to the National Computer Conference in Chicago, where they were massively popular. The company soon gained such clients as Allegheny Energy in Pennsylvania and the postal service of Belgium and received an influx of employees—mostly expats from Russia but also Poland and South Korea, as well as American-born workers. To accommodate the company's employee base, which had grown to over 30 in 1988, Levine moved OCR System's headquarters from Bensalem to the Masons Mill Business Park in Bryn Athyn. Chinon Industries of Japan signed an agreement with OCR Systems in 1987 to distribute OCR's ReadRight 1.0 software with Chinon's scanners, starting with their N-205 overhead scanner. In 1988, OCR opened their agreement to distribute ReadRight to other scanner manufacturers, including Canon, Hewlett-Packard, Skyworld, Taxan, Diamond Flower and Abaton. That year, the company posted a revenue of $3 million. OCR Systems extended their agreement with Chinon in 1989 and introduced version 2.0 of ReadRight. OCR Systems faced stiff competition in the software OCR market in the turn of the 1990s. The Toronto-based software firm Delrina signed a letter of intent to purchase the company in November 1991, expecting the deal to close in December and have OCR software available by Christmas. OCR was to receive $3 million worth of Delrina shares in a stock swap, but the deal collapsed in January 1992. Delrine later marketed its own Extended Character Recognition, or XCR, software package to compete with ReadRight. In July 1992, OCR Systems was purchased by Adobe Inc. for an undisclosed sum. == Products == === System 1000 === The System 1000 was based on the 16-bit Varian Data 620/i minicomputer with 4 KB of core memory. The system used the 620/i for controlling the paper feed, interpreting the format of the documents, the optical character recognition process itself, error detection, sequencing and output. The System was initially programmed to recognize 1428 OCR (used by Selectrics); IBM 407 print; and the full character sets of OCR-A, OCR-B and Farrington 7B; as well as optical marks and handwritten numbers. OCR Systems promised added compatibility with more fonts available down the line—per request—in 1970. The number of fonts supported was limited by the amount of core memory, which was expandable in 4 KB increments up to 32 KB. The System 1000 later supported generalized typewriter and photocopier fonts. The rest of the System 1000 comprised the document transport, one or more scanner elements, a CRT display and a Teletype Model 33 or 35. Pages are fed via friction with a rubber belt. Up to three lines could be scanned per document, while the rest of the scanned document could be laid out in any manner granted there was enough space around the fields to be read. The reader initially supported pages as small as 3.25 in by 3.5 in dimension (later supporting 2.6 in by 3.5 in utility cash stubs) all the way to the standard ANSI letter size (8.5 in by 11 in; later 8.5 in by 12 in as used in stock certificates). The initial System 1000 had a maximum throughput of 420 documents per minute per transport (later 500 documents per minute), contingent on document size and content. A feature unique to the System 1000 over other optical character recognition systems of the time was its ability to alert the operator when a field was unreadable or otherwise invalid. This feature, called Document Referral, placed the document in front of the operator and displayed a blank field on the screen of the included CRT monitor for manual re-entry via keyboard. Once input, data could be output to 7- or 9-track tape, paper tape, punched cards and other mass storage media or to System/360 mainframes for further processing. The complete System 1000 could be purchased for US$69,000. Options for renting were $1,800 per month on a three-year lease or $1,600 per month for five years. Computerworld wrote that it was less than half the cost of its competitors while more capable and user-friendly. Competing systems included the Recognition Equipment Retina, the Scan-Optics IC/20 and the Scan-Data 250/350. === ReadRight === ReadRight processes individual letters topographically: it breaks down the scanned letter into parts—strokes, curves, angles, ascenders and descenders—and follows a tree structure of letters broken down into these parts to determine the corresponding character code. ReadRight was entirely software-based, requiring no expansion card to work. Version 2.01, the last version released for DOS, runs in real mode in under 640 KB of RAM. OCR Systems released the Windows-only version 3.0 in 1991 while offering version 2.01 alongside it. The company unveiled a sister product, ReadRight Personal, dedicated to handheld scanners and for Windows only in October 1991. This version adds real-time scanning—each word is updated to the screen while lines are being scanned. ReadRight proper was later made a Windows-only product with version 3.1 in 1992. The inclusion of ReadRight 2.0 with Canon's IX-12F flatbed scanner led PC Magazine to award it an Editor's Choice rating in 1989. Despite this, reviewer Robert Kendall found qualification with ReadRight's ability to parse proportional typefaces such as Helvetica and Times New Roman. Mitt Jones of the same publication found version 2.01 to have improved its ability to read such typefaces and praised its ease of use and low resource intensiveness. Jones disliked the inability to handle uneven page paragraph column widths and graphics, noting that the manual recommended the user block out graphics with a Post-it Note. Version 3.1 for Windows received mixed reviews. Mike Heck of InfoWorld wrote that its "low cost and rich collection of features are hard to ignore" but rated its speed and accuracy average. Barry Simon of PC Magazine called it economical but inaccurate, unable to correct errors it did
Read more →
Light scanning photomacrography

Light Scanning Photomacrography (LSP), also known as Scanning Light Photomacrography (SLP) or Deep-Field Photomacrography, is a photographic film technique that allows for high magnification light imaging with exceptional depth of field (DOF). This method overcomes the limitations of conventional macro photography, which typically only keeps a portion of the subject in acceptable focus at high magnifications. == Historical background == The principles of LSP were first documented in the early 1960s by Dan McLachlan Jr., who highlighted its capability for extreme focal depth in microscopy and in 1968 patented the process. The technique was revived and further developed in the 1980s by photographers such as Darwin Dale and Nile Root, a faculty member at the Rochester Institute of Technology. In the early 1990s, William Sharp and Charles Kazilek, both researchers at Arizona State University, also published articles describing their technique and system setup for capturing SLP images. == Predecessor to stack image photography == Light Scanning Photomacrography offered a powerful analog tool for high-detail imaging in the age of film photography. It provided a comprehensive depth of field, making it invaluable in scientific and biomedical photography. As technology and techniques continue to evolve, LSP has been replaced by digital image focus stacking. This technique uses a collection of images captured in series at different focal depths, which are then processed using computer software to create a single image with a greater focus depth than any single image. == LSP technique and results == LSP involves the use of a thin plane of light that scans across the subject, which is mounted on a stage moving perpendicular to the film plane. The technique utilizes traditional optics and is governed by the physical laws of depth of field. By moving the subject through a narrow band of illumination, the entire subject can be recorded in sharp focus from the nearest details to the farthest ones. This analog process produces sharp and detailed images by slowly recording the image on film as the specimen passes through the sheet of light that is thinner than the effective DOF. Because the image is captured at the same relative distance from the camera lens, the resulting images are axonometric rather than perspective projection, which is what the human eye sees and is typically captured by a film camera. Because all parts of an LSP image are captured at the same distance from the lens, relative measurements can be taken from an LSP photograph and can be used for comparison. == Equipment and setup == A typical LSP setup includes: A stage that can move the subject perpendicular to the film plane. Light sources, in some cases modified projectors, are used to project a thin plane of light. A camera mounted on a stable stand such as a tabletop copy stand. In 1991, Sharp and Kazilek described their SLP system that used three Kodak Ektagraphic slide projectors with zoom lenses to create a thin plane of light. The projectors each had a slide mount with two razor blades placed edge-to-edge to create a thin slit for the light to pass through. The image was captured using a Nikon FE-2 SLR camera mounted above the specimen. Kodachrome 25 slide film was used to record the image and to minimize film grain size and maximize image sharpness == Commercial systems == A commercial SLP instrument was produced by the Irvine Optical Corp. Their DYNAPHOT system was based on a photomacroscope and could capture images on 4x5 film. The instrument came with two or three illumination sources and a motorized specimen stage. The system advertised a 2X – 40X magnification range and the ability to capture images in black and white and color. Other systems have been developed by Nile Root and Theodore Clarke and reported higher magnification (up to 100X). == LSP process == Alignment and Focusing: The light sources are aligned and focused to project a thin, consistent plane of light across the subject. Stage Movement: The subject stage moves at a controlled speed, scanning through the plane of light. Image Capture: The camera shutter is set to a long exposure or can be opened and closed manually. As the subject moves through the illuminated plane, it is recorded on the film. This process is very much like painting an image onto the film using photons instead of paint. == Applications == LSP was particularly useful in biomedical photography, where it was used to document magnified subjects with increased depth of field over traditional macro and micro photography. It has been employed to capture detailed images of biological specimens, such as imaging small insects and their parts. SLP has been used to document shell collections for scientific documentation and research. Other applications include forensic science, mineralogy, and the imaging of fractured surfaces and parts == Advantages and challenges of LSP imaging == === Advantages === Exceptional depth of field: Subjects are rendered in sharp focus throughout. High magnification: Detailed images at significant magnification without sacrificing DOF. Analog precision: Provides a non-digital solution with accurate image representation. Versatility: Can be used for a range of subject sizes, from macro to non-macro scales. === Challenges === Technical complexity: Requires precise setup and alignment. Exposure time: Typically requires long exposure times due to the scanning process. Contrast control: The highly directional lighting can create harsh shadows and high contrast, which may need to be managed. Digital competition: Focus stacking has largely replaced LSP in the digital era due to convenience and flexibility. == DIY contributions == Enthusiasts and researchers have contributed to the development and accessibility of LSP by creating and sharing DIY guides. These contributions have enabled others to build their own LSP systems using readily available materials and components. Nile Root's publications provide detailed instructions and recommendations for constructing an LSP setup. These DIY systems have allowed a wider audience to explore and utilize the benefits of LSP imaging in various fields.
Read more →
Dynamic topic model

Within statistics, Dynamic topic models' are generative models that can be used to analyze the evolution of (unobserved) topics of a collection of documents over time. This family of models was proposed by David Blei and John Lafferty and is an extension to Latent Dirichlet Allocation (LDA) that can handle sequential documents. In LDA, both the order the words appear in a document and the order the documents appear in the corpus are oblivious to the model. Whereas words are still assumed to be exchangeable, in a dynamic topic model the order of the documents plays a fundamental role. More precisely, the documents are grouped by time slice (e.g.: years) and it is assumed that the documents of each group come from a set of topics that evolved from the set of the previous slice. == Topics == Similarly to LDA and pLSA, in a dynamic topic model, each document is viewed as a mixture of unobserved topics. Furthermore, each topic defines a multinomial distribution over a set of terms. Thus, for each word of each document, a topic is drawn from the mixture and a term is subsequently drawn from the multinomial distribution corresponding to that topic. The topics, however, evolve over time. For instance, the two most likely terms of a topic at time t could be "network" and "Zipf" (in descending order) while the most likely ones at time t+1 could be "Zipf" and "percolation" (in descending order). == Model == Define α t {\displaystyle \alpha _{t}} as the per-document topic distribution at time t. β t , k {\displaystyle \beta _{t,k}} as the word distribution of topic k at time t. η t , d {\displaystyle \eta _{t,d}} as the topic distribution for document d in time t, z t , d , n {\displaystyle z_{t,d,n}} as the topic for the nth word in document d in time t, and w t , d , n {\displaystyle w_{t,d,n}} as the specific word. In this model, the multinomial distributions α t + 1 {\displaystyle \alpha _{t+1}} and β t + 1 , k {\displaystyle \beta _{t+1,k}} are generated from α t {\displaystyle \alpha _{t}} and β t , k {\displaystyle \beta _{t,k}} , respectively. Even though multinomial distributions are usually written in terms of the mean parameters, representing them in terms of the natural parameters is better in the context of dynamic topic models. The former representation has some disadvantages due to the fact that the parameters are constrained to be non-negative and sum to one. When defining the evolution of these distributions, one would need to assure that such constraints were satisfied. Since both distributions are in the exponential family, one solution to this problem is to represent them in terms of the natural parameters, that can assume any real value and can be individually changed. Using the natural parameterization, the dynamics of the topic model are given by β t , k | β t − 1 , k ∼ N ( β t − 1 , k , σ 2 I ) {\displaystyle \beta _{t,k}|\beta _{t-1,k}\sim N(\beta _{t-1,k},\sigma ^{2}I)} and α t | α t − 1 ∼ N ( α t − 1 , δ 2 I ) {\displaystyle \alpha _{t}|\alpha _{t-1}\sim N(\alpha _{t-1},\delta ^{2}I)} . The generative process at time slice 't' is therefore: Draw topics β t , k | β t − 1 , k ∼ N ( β t − 1 , k , σ 2 I ) ∀ k {\displaystyle \beta _{t,k}|\beta _{t-1,k}\sim N(\beta _{t-1,k},\sigma ^{2}I)\forall k} Draw mixture model α t | α t − 1 ∼ N ( α t − 1 , δ 2 I ) {\displaystyle \alpha _{t}|\alpha _{t-1}\sim N(\alpha _{t-1},\delta ^{2}I)} For each document: Draw η t , d ∼ N ( α t , a 2 I ) {\displaystyle \eta _{t,d}\sim N(\alpha _{t},a^{2}I)} For each word: Draw topic Z t , d , n ∼ Mult ( π ( η t , d ) ) {\displaystyle Z_{t,d,n}\sim {\textrm {Mult}}(\pi (\eta _{t,d}))} Draw word W t , d , n ∼ Mult ( π ( β t , Z t , d , n ) ) {\displaystyle W_{t,d,n}\sim {\textrm {Mult}}(\pi (\beta _{t,Z_{t,d,n}}))} where π ( x ) {\displaystyle \pi (x)} is a mapping from the natural parameterization x to the mean parameterization, namely π ( x i ) = exp ⁡ ( x i ) ∑ i exp ⁡ ( x i ) {\displaystyle \pi (x_{i})={\frac {\exp(x_{i})}{\sum _{i}\exp(x_{i})}}} . == Inference == In the dynamic topic model, only W t , d , n {\displaystyle W_{t,d,n}} is observable. Learning the other parameters constitutes an inference problem. Blei and Lafferty argue that applying Gibbs sampling to do inference in this model is more difficult than in static models, due to the nonconjugacy of the Gaussian and multinomial distributions. They propose the use of variational methods, in particular, the Variational Kalman Filtering and the Variational Wavelet Regression. == Applications == In the original paper, a dynamic topic model is applied to the corpus of Science articles published between 1881 and 1999 aiming to show that this method can be used to analyze the trends of word usage inside topics. The authors also show that the model trained with past documents is able to fit documents of an incoming year better than LDA. A continuous dynamic topic model was developed by Wang et al. and applied to predict the timestamp of documents. Going beyond text documents, dynamic topic models were used to study musical influence, by learning musical topics and how they evolve in recent history.
Read more →
Tomáš Mikolov

Tomáš Mikolov is a Czech computer scientist working in the field of machine learning. In March 2020, Mikolov became a senior research scientist at the Czech Institute of Informatics, Robotics and Cybernetics. == Career == Mikolov obtained his PhD in Computer Science from Brno University of Technology for his work on recurrent neural network-based language models. He is the lead author of the 2013 paper that introduced the Word2vec technique in natural language processing and is an author on the FastText architecture. Mikolov came up with the idea to generate text from neural language models in 2007 and his RNNLM toolkit was the first to demonstrate the capability to train language models on large corpora, resulting in large improvements over the state of the art. Prior to joining Facebook in 2014, Mikolov worked as a visiting researcher at Johns Hopkins University, Université de Montréal, Microsoft and Google. He left Facebook at some time in 2019/2020 to join the Czech Institute of Informatics, Robotics and Cybernetics. Mikolov has argued that humanity might be at a greater existential risk if an artificial general intelligence is not developed.
Read more →
Büchi automaton

In computer science and automata theory, a deterministic Büchi automaton is a theoretical machine which either accepts or rejects infinite inputs. Such a machine has a set of states and a transition function, which determines which state the machine should move to from its current state when it reads the next input character. Some states are accepting states and one state is the start state. The machine accepts an input if and only if it will pass through an accepting state infinitely many times as it reads the input. A non-deterministic Büchi automaton, later referred to just as a Büchi automaton, has a transition function which may have multiple outputs, leading to many possible paths for the same input; it accepts an infinite input if and only if some possible path is accepting. Deterministic and non-deterministic Büchi automata generalize deterministic finite automata and nondeterministic finite automata to infinite inputs. Each are types of ω-automata. Büchi automata recognize the ω-regular languages, the infinite word version of regular languages. They are named after the Swiss mathematician Julius Richard Büchi, who invented them in 1962. Büchi automata are often used in model checking as an automata-theoretic version of a formula in linear temporal logic. == Formal definition == Formally, a deterministic Büchi automaton is a tuple A = ( Q , Σ , δ , q 0 , F ) {\textstyle A=(Q,\Sigma ,\delta ,q_{0},\mathbf {F} )} that consists of the following components: Q {\textstyle Q} is a finite set. The elements of Q {\textstyle Q} are called the states of A {\textstyle A} . Σ {\textstyle \Sigma } is a finite set called the alphabet of A {\textstyle A} . δ : Q × Σ → Q {\textstyle \delta \colon Q\times \Sigma \to Q} is a function, called the transition function of A {\textstyle A} . q 0 {\textstyle q_{0}} is an element of Q {\textstyle Q} , called the initial state of A {\textstyle A} . F ⊆ Q {\textstyle \mathbf {F} \subseteq Q} is the acceptance condition. A run i _ = i 0 i 1 i 2 ⋯ ∈ Σ ω {\displaystyle {\underline {i}}=i_{0}i_{1}i_{2}\cdots \in \Sigma ^{\omega }} is an infinite string of inputs of A {\displaystyle A} . By calling δ {\displaystyle \delta } recursively, we can extend it to a function δ ω : Σ ω → Q ω {\displaystyle \delta ^{\omega }:\Sigma ^{\omega }\to Q^{\omega }} . A state q ∈ Q {\displaystyle q\in Q} is said to occur infinitely often for a run i _ {\displaystyle {\underline {i}}} when the set { n ∈ N ∣ δ ω ( i _ ) n = q } {\displaystyle \{n\in \mathbb {N} \mid \delta ^{\omega }({\underline {i}})_{n}=q\}} is infinite. Let I n f ( i _ ) {\displaystyle \mathrm {Inf} ({\underline {i}})} be the set of states occurring infinitely often for i _ {\displaystyle {\underline {i}}} . The language of A {\displaystyle A} is then the set of runs of A {\displaystyle A} in which at least one of the infinitely-often occurring states is in F {\textstyle \mathbf {F} } ; in symbols: L ( A ) = { i _ ∈ Σ ω ∣ I n f ( i _ ) ∩ F ≠ ∅ } . {\displaystyle L(A)=\{{\underline {i}}\in \Sigma ^{\omega }\mid \mathrm {Inf} ({\underline {i}})\cap \mathbf {F} \neq \varnothing \}.} In a (non-deterministic) Büchi automaton, the transition function δ {\textstyle \delta } is replaced with a transition relation Δ {\textstyle \Delta } that returns a set of states, and the single initial state q 0 {\textstyle q_{0}} is replaced by a set I {\textstyle I} of initial states. Generally, the term Büchi automaton without qualifier refers to non-deterministic Büchi automata. For more comprehensive formalism see also ω-automaton. == Closure properties == The set of Büchi automata is closed under the following operations. Let A = ( Q A , Σ , Δ A , I A , F A ) {\displaystyle A=(Q_{A},\Sigma ,\Delta _{A},I_{A},{F}_{A})} and B = ( Q B , Σ , Δ B , I B , F B ) {\displaystyle B=(Q_{B},\Sigma ,\Delta _{B},I_{B},{F}_{B})} be Büchi automata and C = ( Q C , Σ , Δ C , I C , F C ) {\displaystyle C=(Q_{C},\Sigma ,\Delta _{C},I_{C},{F}_{C})} be a finite automaton. Union: There is a Büchi automaton that recognizes the language L ( A ) ∪ L ( B ) . {\displaystyle L(A)\cup L(B).} Proof: If we assume, w.l.o.g., Q A ∩ Q B {\displaystyle Q_{A}\cap Q_{B}} is empty then L ( A ) ∪ L ( B ) {\displaystyle L(A)\cup L(B)} is recognized by the Büchi automaton ( Q A ∪ Q B , Σ ∪ Σ , Δ A ∪ Δ B , I A ∪ I B , F A ∪ F B ) . {\displaystyle (Q_{A}\cup Q_{B},\Sigma \cup \Sigma ,\Delta _{A}\cup \Delta _{B},I_{A}\cup I_{B},{F}_{A}\cup {F}_{B}).} Intersection: There is a Büchi automaton that recognizes the language L ( A ) ∩ L ( B ) . {\displaystyle L(A)\cap L(B).} Proof: The Büchi automaton A ′ = ( Q ′ , Σ , Δ ′ , I ′ , F ′ ) {\displaystyle A'=(Q',\Sigma ,\Delta ',I',F')} recognizes L ( A ) ∩ L ( B ) , {\displaystyle L(A)\cap L(B),} where Q ′ = Q A × Q B × { 1 , 2 } {\displaystyle Q'=Q_{A}\times Q_{B}\times \{1,2\}} Δ ′ = Δ 1 ∪ Δ 2 {\displaystyle \Delta '=\Delta _{1}\cup \Delta _{2}} Δ 1 = { ( ( q A , q B , 1 ) , a , ( q A ′ , q B ′ , i ) ) | ( q A , a , q A ′ ) ∈ Δ A and ( q B , a , q B ′ ) ∈ Δ B and if q A ∈ F A then i = 2 else i = 1 } {\displaystyle \Delta _{1}=\{((q_{A},q_{B},1),a,(q'_{A},q'_{B},i))|(q_{A},a,q'_{A})\in \Delta _{A}{\text{ and }}(q_{B},a,q'_{B})\in \Delta _{B}{\text{ and if }}q_{A}\in F_{A}{\text{ then }}i=2{\text{ else }}i=1\}} Δ 2 = { ( ( q A , q B , 2 ) , a , ( q A ′ , q B ′ , i ) ) | ( q A , a , q A ′ ) ∈ Δ A and ( q B , a , q B ′ ) ∈ Δ B and if q B ∈ F B then i = 1 else i = 2 } {\displaystyle \Delta _{2}=\{((q_{A},q_{B},2),a,(q'_{A},q'_{B},i))|(q_{A},a,q'_{A})\in \Delta _{A}{\text{ and }}(q_{B},a,q'_{B})\in \Delta _{B}{\text{ and if }}q_{B}\in F_{B}{\text{ then }}i=1{\text{ else }}i=2\}} I ′ = I A × I B × { 1 } {\displaystyle I'=I_{A}\times I_{B}\times \{1\}} F ′ = { ( q A , q B , 2 ) | q B ∈ F B } {\displaystyle F'=\{(q_{A},q_{B},2)|q_{B}\in F_{B}\}} By construction, r ′ = ( q A 0 , q B 0 , i 0 ) , ( q A 1 , q B 1 , i 1 ) , … {\displaystyle r'=(q_{A}^{0},q_{B}^{0},i^{0}),(q_{A}^{1},q_{B}^{1},i^{1}),\dots } is a run of automaton A' on input word w {\textstyle w} if r A = q A 0 , q A 1 , … {\displaystyle r_{A}=q_{A}^{0},q_{A}^{1},\dots } is run of A {\textstyle A} on w {\textstyle w} and r B = q B 0 , q B 1 , … {\displaystyle r_{B}=q_{B}^{0},q_{B}^{1},\dots } is run of B {\textstyle B} on w {\textstyle w} . r A {\textstyle r_{A}} is accepting and r B {\textstyle r_{B}} is accepting if r ′ {\textstyle r'} is concatenation of an infinite series of finite segments of 1-states (states with third component 1) and 2-states (states with third component 2) alternatively. There is such a series of segments of r ′ {\textstyle r'} if r ′ {\textstyle r'} is accepted by A ′ {\textstyle A'} . Concatenation: There is a Büchi automaton that recognizes the language L ( C ) ⋅ L ( A ) . {\displaystyle L(C)\cdot L(A).} Proof: If we assume, w.l.o.g., Q C ∩ Q A {\displaystyle Q_{C}\cap Q_{A}} is empty then the Büchi automaton A ′ = ( Q C ∪ Q A , Σ , Δ ′ , I ′ , F A ) {\displaystyle A'=(Q_{C}\cup Q_{A},\Sigma ,\Delta ',I',F_{A})} recognizes L ( C ) ⋅ L ( A ) {\displaystyle L(C)\cdot L(A)} , where Δ ′ = Δ A ∪ Δ C ∪ { ( q , a , q ′ ) | q ′ ∈ I A and ∃ f ∈ F C . ( q , a , f ) ∈ Δ C } {\displaystyle \Delta '=\Delta _{A}\cup \Delta _{C}\cup \{(q,a,q')|q'\in I_{A}{\text{ and }}\exists f\in F_{C}.(q,a,f)\in \Delta _{C}\}} if I C ∩ F C is empty then I ′ = I C otherwise I ′ = I C ∪ I A {\displaystyle {\text{ if }}I_{C}\cap F_{C}{\text{ is empty then }}I'=I_{C}{\text{ otherwise }}I'=I_{C}\cup I_{A}} ω-closure: If L ( C ) {\displaystyle L(C)} does not contain the empty word then there is a Büchi automaton that recognizes the language L ( C ) ω . {\displaystyle L(C)^{\omega }.} Proof: The Büchi automaton that recognizes L ( C ) ω {\displaystyle L(C)^{\omega }} is constructed in two stages. First, we construct a finite automaton A ′ {\textstyle A'} such that A ′ {\textstyle A'} also recognizes L ( C ) {\displaystyle L(C)} but there are no incoming transitions to initial states of A ′ {\textstyle A'} . So, A ′ = ( Q C ∪ { q new } , Σ , Δ ′ , { q new } , F C ) , {\displaystyle A'=(Q_{C}\cup \{q_{\text{new}}\},\Sigma ,\Delta ',\{q_{\text{new}}\},F_{C}),} where Δ ′ = Δ C ∪ { ( q new , a , q ′ ) | ∃ q ∈ I C . ( q , a , q ′ ) ∈ Δ C } . {\displaystyle \Delta '=\Delta _{C}\cup \{(q_{\text{new}},a,q')|\exists q\in I_{C}.(q,a,q')\in \Delta _{C}\}.} Note that L ( C ) = L ( A ′ ) {\displaystyle L(C)=L(A')} because L ( C ) {\displaystyle L(C)} does not contain the empty string. Second, we will construct the Büchi automaton A ″ {\textstyle A''} that recognize L ( C ) ω {\displaystyle L(C)^{\omega }} by adding a loop back to the initial state of A ′ {\textstyle A'} . So, A ″ = ( Q C ∪ { q new } , Σ , Δ ″ , { q new } , { q new } ) {\displaystyle A''=(Q_{C}\cup \{q_{\text{new}}\},\Sigma ,\Delta '',\{q_{\text{new}}\},\{q_{\text{new}}\})} , where Δ ″ = Δ ′ ∪ { ( q , a , q new ) | ∃ q ′ ∈ F C . ( q , a , q ′ ) ∈ Δ ′ } . {\displaystyle \Delta ''=\Delta '\cup \{(q,a,q_{\text{new}})|\exists q'\in F_{C}.(q,a,q')\in \Delta '\}.} Complementation:
Read more →
ActivTrak

ActivTrak is an American company that produces workforce analytics and productivity software. The company was founded in 2009 by Birch Grove Software and is headquartered in Austin, Texas. The company has raised US$77.5 million in funding and is backed by Sapphire Ventures and Elsewhere Partners. == History == ActivTrak was founded in 2009 by Herb Axilrod and Anton Seidler in Dallas, Texas. ActivTrak's first on-demand software product launched in 2012, and the workforce analytics platform launched in 2015. It uses data sourced from more than 9,500 customers and 900,000 users. In 2019, ActivTrak raised $20 million in a Series A round of funding with Elsewhere Partners, a growth-stage venture capital firm that principally invests in B2B startups. Rita Selvaggi assumed the role of CEO. In 2020, ActivTrak raised $50M in a Series B round of funding with Sapphire Ventures and Elsewhere Partners. The company also introduced the ActivTrak Productivity Lab, an online resource about workforce productivity research, industry benchmark data, and best practices. == Product == ActivTrak is a workforce analytics and productivity platform that uses reports, dashboards, and data analysis. The platform uses machine learning (AI) to collect and analyze user activity data and produce reports about workforce productivity. The software runs on Microsoft Windows, Mac, Chrome, Terminal Services, and VDI. It includes the ActivTrak Agent, which runs in the background and collects data. It responds to user activity, sensing mouse and keyboard movement in the active window(s) of the user's device. This data is collected and stored in a database that aggregates the data based on the user's request. ActivTrak does not utilize keystroke logging, content scraping, camera access, video recording or mobile device monitoring. The database leverages data analytics to generate account and team benchmarks, and identify productivity patterns and outliers. == Awards == Built In, 100 Best Midsize Places to Work in Austin, 2025 G2, Winter: Best Estimated ROI, High Performer, Best Relationship, Best Support, Users Most Likely to Recommend, Easiest Setup, Easiest Admin, Best Meets Requirements, Users Love Us, 2025 TrustRadius, Buyer’s Choice, 2025 Deloitte Technology Fast 500, No. 468 Fastest-Growing Company, 2024 Product Marketing Alliance, AI Marketing Innovation, 2024 Fortune Best Workplaces in Technology™, 2024 Inc. 5000, No. 2335 of America’s Fastest-Growing Private Companies, 2024 Fortune Best Workplaces in Texas™, 2024 Reworked IMPACT Gold Award: Most Innovative Workplace Productivity Solution, 2024 TrustRadius, Most Loved, 2024 Great Place To Work-Certified™, 2024 Inc. 5000 Regionals: Southwest, 2024 Brandon Hall Group, Best Advance in HR Predictive Analytics Technology, 2024
Read more →
The Best Free AI Avatar Generator for Beginners

Curious about the best AI avatar generator? An AI avatar generator is software that uses machine learning to help you get more done — it combines speed, accuracy, and an interface that just works. Hands-on testing shows real-world results vary, so a short free trial is the smartest way to decide. Whether you are a beginner or a pro, the right AI avatar generator slots into your workflow and pays for itself fast. This guide breaks down the top picks, their pros and cons, and who each one is best for.
Read more →
Model inversion attack

Model inversion attack is a type of adversarial machine learning attack where an attacker tries to reconstruct or infer sensitive information about a model's training data by analyzing the outputs of a trained machine learning model. Instead of directly querying the underlying dataset, attackers query the model (usually via APIs or prediction interfaces), and leverage patterns in the model responses to infer properties of the original inputs. These attacks leverage the fact that machine learning models encode statistical information about their training data in their parameters and outputs, which can unintentionally leak private or proprietary information. Depending on the access level to the target model, model inversion attacks can be performed in both black-box and white-box settings. In a generic attack, an adversary makes several queries to a model and leverages the responses (e.g. confidence scores, predictions) to train a surrogate or inversion model that learns to approximate the inverse mapping from outputs to inputs. This process may enable the reconstruction of sensitive attributes, e.g., facial features, medical data, or user behavior patterns, from models trained on such data. The technique has been demonstrated against various models like deep neural networks, classification systems etc. The technique has significant privacy risks in areas like healthcare, finance, biometric identification etc. Mitigation strategies include restricting model access, reducing output granularity, using differential privacy and monitoring anomalous query patterns.
Read more →
Pedro Domingos

Pedro Domingos (born 1965) is a Professor Emeritus of computer science and engineering at the University of Washington. He is a researcher in machine learning known for Markov logic network enabling uncertain inference. == Education == Domingos received an undergraduate degree and Master of Science degree from Instituto Superior Técnico (IST). He moved to the University of California, Irvine, where he received a Master of Science degree followed by his PhD. == Research and career == After spending two years as an assistant professor at IST, he joined the University of Washington as an assistant professor of Computer Science and Engineering in 1999 and became a full professor in 2012. He started a machine learning research group at the hedge fund D. E. Shaw & Co. in 2018, but left in 2019. He co-founded the International Machine Learning Society. As of 2018, he was on the editorial board of Machine Learning journal. === Publications === Pedro Domingos, The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World, New York, Basic Books, 2015, ISBN 978-0-465-06570-7. Pedro Domingos, "Our Digital Doubles: AI will serve our species, not control it", Scientific American, vol. 319, no. 3 (September 2018), pp. 88–93. "AIs are like autistic savants and will remain so for the foreseeable future.... AIs lack common sense and can easily make errors that a human never would... They are also liable to take our instructions too literally, giving us precisely what we asked for instead of what we actually wanted." (p. 93.) Pedro Domingos, 2040: A Silicon Valley Satire, BookBaby, 2024, ISBN 979-8-350-96334-2. === Awards and honors === 2014: ACM SIGKDD Innovation Award. for his foundational research in data stream analysis, cost-sensitive classification, adversarial learning, and Markov logic networks, as well as applications in viral marketing and information integration. 2010: Elected an Association for the Advancement of Artificial Intelligence (AAAI) Fellow. For significant contributions to the field of machine learning and to the unification of first-order logic and probability. 2003: Sloan Fellowship 1992–1997: Fulbright Scholarship
Read more →
Superintelligence ban

Superintelligence ban refers to proposed legal, ethical, or policy measures intended to restrict or prohibit the development of artificial superintelligence, AI systems that would surpass human cognitive abilities in nearly all domains. The idea arises from concerns that such systems could become uncontrollable, potentially posing existential threats to humanity or causing severe social and economic disruption. == Background == The concept of limiting or banning superintelligence research has roots in early 21st-century debates on artificial general intelligence (AGI) safety. Thinkers such as Nick Bostrom and Eliezer Yudkowsky warned that self-improving AI could rapidly exceed human oversight. As advanced models like large-scale language models and autonomous agents began demonstrating complex reasoning abilities, policymakers and ethicists increasingly discussed the need for legal constraints on the creation of systems capable of recursive self-improvement. In October 2025, the Future of Life Institute published a statement calling for "a prohibition on the development of superintelligence, not lifted before there is broad scientific consensus that it will be done safely and controllably, and strong public buy-in." This statement was signed by various public personalities, such as Richard Branson and Steve Wozniak, and AI experts, such as Yoshua Bengio and Geoffrey Hinton. == Rationale == Supporters of a superintelligence ban argue that once AI systems surpass human intelligence, traditional containment, alignment, and control methods may fail. They contend that even limited experimentation with such systems could lead to irreversible outcomes, including loss of human decision-making power or unintended global harm. Some propose international treaties modeled after the nuclear non-proliferation framework to prevent a competitive AI arms race. Opponents argue that a ban would be difficult to define and enforce, given the lack of a precise threshold distinguishing advanced AGI from superintelligence. They also warn that excessive restriction could slow scientific progress, hinder beneficial automation, and encourage unregulated underground research. == Global discussion == Although no government has enacted an explicit superintelligence ban, the idea has been debated within the European Union, United Nations, and several independent AI safety organizations. The Future of Life Institute, Center for AI Safety, and other organizations have called for international cooperation to manage risks associated with the pursuit of superintelligent systems. In 2024 and 2025, proposals for a temporary moratorium on frontier AI research were circulated among major technology firms and research institutes, reflecting growing public concern over the trajectory of AI capabilities.
Read more →
Is an AI Avatar Generator Worth It in 2026?

Looking for the best AI avatar generator? An AI avatar generator is software that uses machine learning to help you get more done — it can save you hours every week by automating repetitive work. Most options offer a generous free tier, with paid plans unlocking higher limits, faster processing, and team features. Whether you are a beginner or a pro, the right AI avatar generator slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.
Read more →
AI Marketing Tools Reviews: What Actually Works in 2026

In search of the best AI marketing tool? An AI marketing tool is software that uses machine learning to help you get more done — it turns a rough idea into a polished result in seconds. When choosing one, weigh output quality, pricing, export formats, and how well it fits the tools you already use. Whether you are a beginner or a pro, the right AI marketing tool slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.
Read more →