On November 17, 2023, OpenAI's board of directors ousted co-founder and chief executive Sam Altman. In an official post on the company's website, it was stated that "the board no longer has confidence in his ability to continue leading OpenAI". The removal was predicated by employee concerns about his handling of artificial intelligence safety, and allegations of abusive behavior. Altman was reinstated on November 22 after pressure from employees and investors. The removal and subsequent reinstatement caused widespread reactions, including impacts felt in the financial markets and technology sector. Microsoft, a partner of OpenAI, received little notice of the removal and experienced a drop in the share price of its stock. The removal also promoted interest in investigations from regulatory agencies. == Background == === OpenAI === OpenAI is an artificial intelligence firm founded in December 2015 as a non-profit entity. The for-profit division of the organization released ChatGPT in November 2022, contributing to a resurgence in generative artificial intelligence funding. The board of directors of the controlling non-profit formerly comprised chief scientist Ilya Sutskever, as well as Adam D'Angelo, chief executive of Quora, entrepreneur Tasha McCauley, and Helen Toner, strategy director for the Center for Security and Emerging Technology. As of October 2023, the company is valued at US$80 billion and was set to bring in US$1 billion in revenue. Altman has described OpenAI's relationship with Microsoft as the "best bromance in tech". OpenAI is uniquely structured, an intentional decision to avoid investor control. A board of directors controls the non-profit OpenAI, Inc. The non-profit owns and controls a for-profit company itself controlling a capped-profit company, OpenAI Global, LLC and a holding company owned by employees and other investors. The holding company is the majority owner of OpenAI Global, LLC.; Microsoft owns a minority stake in the capped-profit company. OpenAI's bylaws, enacted in January 2016, allow a majority of its board of directors to remove any director without prior warning or a formal meeting with written consent. === Sam Altman === Sam Altman is a co-founder of OpenAI and its former chief executive; Altman took over the company following co-chair Elon Musk's resignation in 2018. Under Altman, OpenAI has shifted to becoming a for-profit entity. Altman is credited with convincing Microsoft chief executive Satya Nadella with investing US$10 billion in cash and computing credits into OpenAI and leading several tender offer transactions that tripled the company's valuation. Altman testified before the United States Congress speaking critically of artificial intelligence and appeared at the 2023 AI Safety Summit. In the days leading up to his removal, Altman made several public appearances, announcing the GPT-4 Turbo platform at OpenAI's DevDay conference, attending APEC United States 2023, and speaking at an event related to Burning Man. == Events leading up to the removal == The resignation of LinkedIn co-founder Reid Hoffman, venture capitalist Shivon Zilis, and former Republican representative Will Hurd from the board allowed the remaining members to remove Altman. According to Kara Swisher and The Wall Street Journal, Sutskever was instrumental in Altman's removal. Disagreements over the safety of artificial intelligence divided employees prior to Altman's removal. The release of ChatGPT created divisions with OpenAI as a for-profit company without considerations for the safety of artificial intelligence and a non-profit cautious of artificial intelligence's capabilities; in a staff email sent in 2019 and obtained by The Atlantic, Altman referred to these divisions as "tribes". Prior to his removal, Altman was seeking billions from Middle Eastern sovereign wealth funds to develop an artificial intelligence chip to compete with Nvidia and courted SoftBank chairman Masayoshi Son to develop artificial intelligence hardware with former Apple designer Jony Ive. Sutskever and his allies opposed these efforts, viewing them as unjustly using the OpenAI name. Altman reduced Sutskever's role in October 2023, furthering divisions; Sutskever successfully appealed to several members of the board. Swisher and The Verge reporter Alex Heath stated that opposition to Altman's profit-driven strategy culminated in the DevDay conference in which Altman announced custom ChatGPT instances. According to Axios, the removal was driven by growing discontent and distrust with Altman. On November 22, 2023, reports emerged suggesting that Sam Altman's dismissal from OpenAI might be linked to his alleged mishandling of a significant breakthrough in the organization's secretive project codenamed Q. According to sources within OpenAI, Q is aimed at developing AI capabilities in logical and mathematical reasoning, and reportedly involves performing math on the level of grade-school students. Concerns about Altman's response to this development, specifically regarding the potential safety implications of the discovery, were reportedly raised to the company's board shortly before his firing. A report from The Washington Post in December stated that OpenAI's board of directors were concerned over Altman's allegedly abusive behavior; the complaints were purportedly a major factor in his removal. The Post previously reported that Altman's alleged pattern of deception and subversiveness that ostensibly resulted in his removal from Y Combinator ultimately resulted in the board's decision to remove him. In April 2026, an investigative report from The New Yorker found that Sutskever and others, in response to the board's request, had compiled an approximately 70-page-long annotated dossier consisting of internal communications, documents, and photos. The dossier claimed that Altman "exhibits a consistent pattern of [...] Lying", and that Altman misrepresented information to the company's senior management and board, particularly regarding safety issues. == Removal == On November 17, 2023, at approximately noon PST, OpenAI's board of directors ousted Altman effective immediately following a "deliberative review process". The board concluded that Altman was not "consistently candid in his communications". Altman was informed of his removal five to ten minutes before it occurred on a Google Meet while watching the Las Vegas Grand Prix. Within thirty minutes, Sutskever invited OpenAI chairman and president Greg Brockman to a Google Meet to inform him of Altman's removal. According to an internal memo obtained by Axios, the removal was not due to "malfeasance", and OpenAI chief executive Emmett Shear denied accusations that the removal was due to disagreements. The board publicly announced Altman's removal thirty minutes later. Chief Technology Officer Mira Murati was immediately appointed to interim chief executive officer. Hours after Altman's removal, Brockman resigned as chairman, joined by director of research Jakub Pachocki and researchers Aleksander Mądry and Szymon Sidor. During an all-hands meeting, Sutskever defended the ouster and denied accusations of a hostile takeover. An OpenAI representative requested former board member Will Hurd's presence. == Reinstatement == According to The New Yorker, Altman retreated to his San Francisco home and enlisted the help of communications consultant Chris Lehane and Airbnb chief executive Brian Chesky, as well as former staff and a legal team, to plan his reinstatement. Lehane encouraged Altman to engage on social media, while Chesky sent a journalist negative information about the board. Altman told interim CEO Murati that his team was conducting opposition research on her and the individuals responsible for his removal; Altman later stated he did not remember saying this. Altman insisted multiple times that all board members who supported his removal should resign. Tiger Global Management and Sequoia Capital had attempted to reinstate Altman, according to The Information; Bloomberg News reported that Microsoft and Thrive Capital were seeking Altman's reinstatement. On November 18, The Verge reported that OpenAI's board of directors discussed reinstating Altman. The board agreed in principle to resign and to allow Altman to return, but missed the deadline. According to The Verge, Altman was ambivalent about returning and would seek significant changes to the company, including replacing the board. A list of directors had been prepared by investors in the event that the board steps down, and purportedly included former Salesforce executive Bret Taylor. According to chief strategy officer Jason Kwon, OpenAI was optimistic it could return Altman, Brockman, and other employees. On November 19, Altman and Brockman appeared at OpenAI's headquarters to negotiate, mediated by Nadella. According to Bloomberg News, Murati, Kwon, and chief operating officer Brad Lightcap were pushing for a new board of direc
Digital art
Digital art, or the digital arts, is artistic work that uses digital technology as part of the creative or presentational process. It can also refer to computational art that uses and engages with digital media. Since the 1960s, various names have been used to describe digital art, including computer art, electronic art, multimedia art, and new media art. Digital art includes pieces stored on physical media, such as with digital painting, as well as digital galleries on websites. Digital art also extends to the field of visual computing. == History == In the early 1960s, John Whitney developed the first computer-generated art using mathematical operations. In 1963, Ivan Sutherland invented the first user interactive computer-graphics interface known as Sketchpad. Between 1974 and 1977, Salvador Dalí created two big canvases of Gala Contemplating the Mediterranean Sea which at a distance of 20 meters is transformed into the portrait of Abraham Lincoln (Homage to Rothko) and prints of Lincoln in Dalivision based on a portrait of Abraham Lincoln processed on a computer by Leon Harmon published in "The Recognition of Faces". The technique is similar to what later became known as photographic mosaics. Andy Warhol created digital art using an Amiga where the computer was publicly introduced at the Lincoln Center in July 1985. An image of Debbie Harry was captured in monochrome from a video camera and digitized into a graphics program called ProPaint. Warhol manipulated the image by adding color using flood fills. == Art made for digital media == Artwork that is highly computational, presented through digital media, and explicitly engages with digital technologies are categorized as "art made for digital media". This differs from art using digital tools, which incorporate digital technology in the creation process but may exist outside the digital world. Digital art historian Christiane Paul writes that it "is highly problematic to classify all art that makes use of digital technologies somewhere in its production and dissemination process as digital art since it makes it almost impossible to arrive at any unifying statement about the art form". == Art that uses digital tools == Digital art can be purely computer-generated (such as fractals and algorithmic art) or taken from other sources, such as a scanned photograph or an image drawn using vector graphics software using a mouse or graphics tablet. Artworks are considered digital paintings when created similarly to non-digital paintings but using software on a computer platform and digitally outputting the resulting image as painted on canvas. Despite differing viewpoints on digital technology's impact on the arts, a consensus exists within the digital art community about its significant contribution to expanding the creative domain, i.e., that it has greatly broadened the creative opportunities available to professional and non-professional artists alike. == Art theorists and art historians == Notable art theorists and historians in this field include: Oliver Grau, Jon Ippolito, Christiane Paul, Frank Popper, Jasia Reichardt, Mario Costa, Christine Buci-Glucksmann, Dominique Moulon, Roy Ascott, Catherine Perret, Margot Lovejoy, Edmond Couchot, Tina Rivers Ryan, Fred Forest and Edward A. Shanken. === Digital painting === Digital painting is either a physical painting made with the use of digital electronics and spray paint robotics within the digital art fine art context or pictorial art imagery made with pixels on a computer screen that mimics artworks from the traditional histories of painting and illustration. === Artificial intelligence art === Artists have used artificial intelligence to create artwork since at least the 1960s. Since their design in 2014, some artists have created artwork using a generative adversarial network (GAN), which is a machine learning framework that allows two "algorithms" to compete with each other and iterate. It can be used to generate pictures that have visual effects similar to traditional fine art. The essential idea of image generators is that people can use text descriptions to let AI convert their text into visual picture content. Anyone can turn their language into a painting through a picture generator. == Digital art education == Digital art education has become more common with the advancement of digital hardware and software. From hardware such as graphics tablets, styluses, tablets, 3D scanners, virtual reality headsets, and digital cameras; to software such as digital art software, 3D modeling software, 3D rendering, digital sculpting, 2D graphics software, digital painting, 3D terrain generation, 2D animation software, 3D animation software, raster graphics editors, vector graphics editors, mathematical art software, and video editing software. == Scholarship and archives == In addition to the creation of original art, research methods that utilize AI have been generated to quantitatively analyze digital art collections. This has been made possible due to the large-scale digitization of artwork in the past few decades. Although the main goal of digitization was to allow for accessibility and exploration of these collections, the use of AI in analyzing them has brought about new research perspectives. Two computational methods, close reading and distant viewing, are the typical approaches used to analyze digitized art. Close reading focuses on specific visual aspects of one piece. Some tasks performed by machines in close reading methods include computational artist authentication and analysis of brushstrokes or texture properties. In contrast, through distant viewing methods, the similarity across an entire collection for a specific feature can be statistically visualized. Common tasks relating to this method include automatic classification, object detection, multimodal tasks, knowledge discovery in art history, and computational aesthetics. Whereas distant viewing includes the analysis of large collections, close reading involves one piece of artwork. Whilst 2D and 3D digital art is beneficial as it allows the preservation of history that would otherwise have been destroyed by events like natural disasters and war, there is the issue of who should own these 3D scans – i.e., who should own the digital copyrights. === Computer demos === Computer demos are based on computer programs, usually non-interactive. It produces audiovisual presentations. They are a novel form of art, which emerged as a consequence of the home computer revolution in the early 1980s. In the classification of digital art, they can be best described as real-time procedurally generated animated audio-visuals. This form of art does not concentrate only on the aesthetics of the final presentation, but also on the complexities and skills involved in creating the presentation. As such, it can be fully enjoyed only by persons with a relatively high knowledge level of relevant computer technologies. An example is that, as said by Hua Jin and Jie Yang, Using computer-aided design software to present the class content in art design teaching," is not to advocate computer-aided design instead of hand-drawn performance, but to make it serve the profession earlier through a more reasonable course arrangement." On the other hand, many of the created pieces of art are primarily aesthetic or amusing, and those can be enjoyed by the general public. === Digital installation art === Digital installation art constitutes a broad field of artistic practices and a variety of forms. Some resemble video installations, especially large-scale works involving projections and live video capture. By using projection techniques that enhance an audience's impression of sensory envelopment, many digital installations attempt to create immersive environments. While others go even further and attempt to facilitate a complete immersion in virtual realms. This type of installation is generally site-specific, scalable, and without fixed dimensionality, meaning it can be reconfigured to accommodate different presentation spaces. Scott Snibbe's "Boundary Functions" is an example of augmented reality digital installation art, which responds to people who enter the installation by drawing lines between people, indicating their personal space.Noah Wardrip-Fruin's "Screen"(2003) utilizes a Cave Automatic Virtual Environment (CAVE) to create an interactive, text-based digital experience that engages the viewer in a multi-sensory interaction. === Internet art and net.art === Internet art is digital art that uses the specific characteristics of the Internet and is exhibited on the Internet. The term "internet art" is included by "net art" for which artists assume that network will be refreshed through history. So the term "post-internet art" is used to exclude artworks outside of the internet media. A representative example is Protocols for Achievements, which is a digital photo frame that confronts the aestheti
Multispectral pattern recognition
Multispectral remote sensing is the collection and analysis of reflected, emitted, or back-scattered energy from an object or an area of interest in multiple bands of regions of the electromagnetic spectrum (Jensen, 2005). Subcategories of multispectral remote sensing include hyperspectral, in which hundreds of bands are collected and analyzed, and ultraspectral remote sensing where many hundreds of bands are used (Logicon, 1997). The main purpose of multispectral imaging is the potential to classify the image using multispectral classification. This is a much faster method of image analysis than is possible by human interpretation. == Multispectral remote sensing systems == Remote sensing systems gather data via instruments typically carried on satellites in orbit around the Earth. The remote sensing scanner detects the energy that radiates from the object or area of interest. This energy is recorded as an analog electrical signal and converted into a digital value though an A-to-D conversion. There are several multispectral remote sensing systems that can be categorized in the following way: === Multispectral imaging using discrete detectors and scanning mirrors === Landsat Multispectral Scanner (MSS) Landsat Thematic Mapper (TM) NOAA Geostationary Operational Environmental Satellite (GOES) NOAA Advanced Very High Resolution Radiometer (AVHRR) NASA and ORBIMAGE, Inc., Sea-viewing Wide field-of-view Sensor (SeaWiFS) Daedalus, Inc., Aircraft Multispectral Scanner (AMS) NASA Airborne Terrestrial Applications Sensor (ATLAS) === Multispectral imaging using linear arrays === SPOT 1, 2, and 3 High Resolution Visible (HRV) sensors and Spot 4 and 5 High Resolution Visible Infrared (HRVIR) and vegetation sensor Indian Remote Sensing System (IRS) Linear Imaging Self-scanning Sensor (LISS) Space Imaging, Inc. (IKONOS) Digital Globe, Inc. (QuickBird) ORBIMAGE, Inc. (OrbView-3) ImageSat International, Inc. (EROS A1) NASA Terra Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) NASA Terra Multiangle Imaging Spectroradiometer (MISR) === Imaging spectrometry using linear and area arrays === NASA Jet Propulsion Laboratory Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) Compact Airborne Spectrographic Imager 3 (CASI 3) NASA Terra Moderate Resolution Imaging Spectrometer (MODIS) NASA Earth Observer (EO-1) Advanced Land Imager (ALI), Hyperion, and LEISA Atmospheric Corrector (LAC) === Satellite analog and digital photographic systems === Russian SPIN-2 TK-350, and KVR-1000 NASA Space Shuttle and International Space Station Imagery == Multispectral classification methods == A variety of methods can be used for the multispectral classification of images: Algorithms based on parametric and nonparametric statistics that use ratio-and interval-scaled data and nonmetric methods that can also incorporate nominal scale data (Duda et al., 2001), Supervised or unsupervised classification logic, Hard or soft (fuzzy) set classification logic to create hard or fuzzy thematic output products, Per-pixel or object-oriented classification logic, and Hybrid approaches == Supervised classification == In this classification method, the identity and location of some of the land-cover types are obtained beforehand from a combination of fieldwork, interpretation of aerial photography, map analysis, and personal experience. The analyst would locate sites that have similar characteristics to the known land-cover types. These areas are known as training sites because the known characteristics of these sites are used to train the classification algorithm for eventual land-cover mapping of the remainder of the image. Multivariate statistical parameters (means, standard deviations, covariance matrices, correlation matrices, etc.) are calculated for each training site. All pixels inside and outside of the training sites are evaluated and allocated to the class with the more similar characteristics. === Classification scheme === The first step in the supervised classification method is to identify the land-cover and land-use classes to be used. Land-cover refers to the type of material present on the site (e.g. water, crops, forest, wet land, asphalt, and concrete). Land-use refers to the modifications made by people to the land cover (e.g. agriculture, commerce, settlement). All classes should be selected and defined carefully to properly classify remotely sensed data into the correct land-use and/or land-cover information. To achieve this purpose, it is necessary to use a classification system that contains taxonomically correct definitions of classes. If a hard classification is desired, the following classes should be used: Mutually exclusive: there is not any taxonomic overlap of any classes (i.e., rain forest and evergreen forest are distinct classes). Exhaustive: all land-covers in the area have been included. Hierarchical: sub-level classes (e.g., single-family residential, multiple-family residential) are created, allowing that these classes can be included in a higher category (e.g., residential). Some examples of hard classification schemes are: American Planning Association Land-Based Classification System United States Geological Survey Land-use/Land-cover Classification System for Use with Remote Sensor Data U.S. Department of the Interior Fish and Wildlife Service U.S. National Vegetation and Classification System International Geosphere-Biosphere Program IGBP Land Cover Classification System === Training sites === Once the classification scheme is adopted, the image analyst may select training sites in the image that are representative of the land-cover or land-use of interest. If the environment where the data was collected is relatively homogeneous, the training data can be used. If different conditions are found in the site, it would not be possible to extend the remote sensing training data to the site. To solve this problem, a geographical stratification should be done during the preliminary stages of the project. All differences should be recorded (e.g. soil type, water turbidity, crop species, etc.). These differences should be recorded on the imagery and the selection training sites made based on the geographical stratification of this data. The final classification map would be a composite of the individual stratum classifications. After the data are organized in different training sites, a measurement vector is created. This vector would contain the brightness values for each pixel in each band in each training class. The mean, standard deviation, variance-covariance matrix, and correlation matrix are calculated from the measurement vectors. Once the statistics from each training site are determined, the most effective bands for each class should be selected. The objective of this discrimination is to eliminate the bands that can provide redundant information. Graphical and statistical methods can be used to achieve this objective. Some of the graphic methods are: Bar graph spectral plots Cospectral mean vector plots Feature space plots Cospectral parallelepiped or ellipse plots === Classification algorithm === The last step in supervised classification is selecting an appropriate algorithm. The choice of a specific algorithm depends on the input data and the desired output. Parametric algorithms are based on the fact that the data is normally distributed. If the data is not normally distributed, nonparametric algorithms should be used. The more common nonparametric algorithms are: One-dimensional density slicing Parallelipiped Minimum distance Nearest-neighbor Expert system analysis Convolutional neural network == Unsupervised classification == Unsupervised classification (also known as clustering) is a method of partitioning remote sensor image data in multispectral feature space and extracting land-cover information. Unsupervised classification require less input information from the analyst compared to supervised classification because clustering does not require training data. This process consists in a series of numerical operations to search for the spectral properties of pixels. From this process, a map with m spectral classes is obtained. Using the map, the analyst tries to assign or transform the spectral classes into thematic information of interest (i.e. forest, agriculture, urban). This process may not be easy because some spectral clusters represent mixed classes of surface materials and may not be useful. The analyst has to understand the spectral characteristics of the terrain to be able to label clusters as a specific information class. There are hundreds of clustering algorithms. Two of the most conceptually simple algorithms are the chain method and the ISODATA method. === Chain method === The algorithm used in this method operates in a two-pass mode (it passes through the multispectral dataset two times. In the first pass, the program reads through the dataset and sequentially builds clusters (groups of p
Wolfram Mathematica
Wolfram Mathematica (also known as Mathematica) is a software system with built-in libraries for several areas of technical computing that allows machine learning, statistics, symbolic computation, data manipulation, network analysis, time series analysis, NLP, optimization, plotting functions and various types of data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other programming languages. It was conceived by Stephen Wolfram, and is developed by Wolfram Research of Champaign, Illinois. The Wolfram Language is the programming language used in Mathematica. Mathematica 1.0 was released on June 23, 1988 in Champaign, Illinois and Santa Clara, California. Mathematica's Wolfram Language is fundamentally based on Lisp; for example, the Mathematica command Most is identically equal to the Lisp command butlast. == Notebook interface == Mathematica is split into two parts: the kernel and the front end. The kernel interprets expressions (Wolfram Language code) and returns result expressions, which can then be displayed by the front end. The original front end, designed by Theodore Gray in 1988, consists of a notebook interface and allows the creation and editing of notebook documents that can contain code, plaintext, images, and graphics. Code development is also supported through support in a range of standard integrated development environment (IDE) including Eclipse, IntelliJ IDEA, Atom, Vim, Visual Studio Code and Git. The Mathematica Kernel also includes a command line front end. Other interfaces include JMath, based on GNU Readline and WolframScript which runs self-contained Mathematica programs (with arguments) from the UNIX command line. == High-performance computing == Capabilities for high-performance computing were extended with the introduction of packed arrays in version 4 (1999) and sparse matrices (version 5, 2003), and by adopting the GNU Multiple Precision Arithmetic Library to evaluate high-precision arithmetic. Version 5.2 (2005) added automatic multi-threading when computations are performed on multi-core computers. This release included CPU-specific optimized libraries. In addition Mathematica is supported by third party specialist acceleration hardware such as ClearSpeed. In 2002, gridMathematica was introduced to allow user level parallel programming on heterogeneous clusters and multiprocessor systems and in 2008 parallel computing technology was included in all Mathematica licenses including support for grid technology such as Windows HPC Server 2008, Microsoft Compute Cluster Server and Sun Grid. Support for CUDA and OpenCL GPU hardware was added in 2010. == Extensions == As of Version 14, there are 6,602 built-in functions and symbols in the Wolfram Language. Stephen Wolfram announced the launch of the Wolfram Function Repository in June 2019 as a way for the public Wolfram community to contribute functionality to the Wolfram Language. There are currently more than 3000 functions contributed as Resource Functions. In addition to the Wolfram Function Repository, there is a Wolfram Data Repository with computable data and the Wolfram Neural Net Repository for machine learning. Wolfram Mathematica is the basis of the Combinatorica package, which adds discrete mathematics functionality in combinatorics and graph theory to the program. == Connections to other applications, programming languages, and services == Communication with other applications can be done using a protocol called Wolfram Symbolic Transfer Protocol (WSTP). It allows communication between the Wolfram Mathematica kernel and the front end and provides a general interface between the kernel and other applications. Wolfram Research freely distributes a developer kit for linking applications written in the programming language C to the Mathematica kernel through WSTP using J/Link., a Java program that can ask Mathematica to perform computations. Similar functionality is achieved with .NET /Link, but with .NET programs instead of Java programs. Other languages that connect to Mathematica include Haskell, AppleScript, Racket, Visual Basic, Python, and Clojure. Mathematica supports the generation and execution of Modelica models for systems modeling and connects with Wolfram System Modeler. Links are also available to many third-party software packages and APIs. Mathematica can also capture real-time data from a variety of sources and can read and write to public blockchains (Bitcoin, Ethereum, and ARK). It supports import and export of over 220 data, image, video, sound, computer-aided design (CAD), geographic information systems (GIS), document, and biomedical formats. In 2019, support was added for compiling Wolfram Language code to LLVM. Version 12.3 of the Wolfram Language added support for Arduino. == Computable data == Mathematica is also integrated with Wolfram Alpha, an online answer engine that provides additional data, some of which is kept updated in real time, for users who use Mathematica with an internet connection. Some of the data sets include astronomical, chemical, geopolitical, language, biomedical, airplane, and weather data, in addition to mathematical data (such as knots and polyhedra). == Reception == BYTE in 1989 listed Mathematica as among the "Distinction" winners of the BYTE Awards, stating that it "is another breakthrough Macintosh application ... it could enable you to absorb the algebra and calculus that seemed impossible to comprehend from a textbook". Mathematica has been criticized for being closed source. Wolfram Research claims keeping Mathematica closed source is central to its business model and the continuity of the software.
Quantum neural network
Quantum neural networks are computational neural network models which are based on the principles of quantum mechanics. The first ideas on quantum neural computation were published independently in 1995 by Subhash Kak and Ron Chrisley, engaging with the theory of quantum mind, which posits that quantum effects play a role in cognitive function. However, typical research in quantum neural networks involves combining classical artificial neural network models (which are widely used in machine learning for the important task of pattern recognition) with the advantages of quantum information in order to develop more efficient algorithms. One important motivation for these investigations is the difficulty to train classical neural networks, especially in big data applications. The hope is that features of quantum computing such as quantum parallelism or the effects of interference and entanglement can be used as resources. Since the technological implementation of a quantum computer is still in a premature stage, such quantum neural network models are mostly theoretical proposals that await their full implementation in physical experiments. Most Quantum neural networks are developed as feed-forward networks. Similar to their classical counterparts, this structure intakes input from one layer of qubits, and passes that input onto another layer of qubits. This layer of qubits evaluates this information and passes on the output to the next layer. Eventually the path leads to the final layer of qubits. The layers do not have to be of the same width, meaning they don't have to have the same number of qubits as the layer before or after it. This structure is trained on which path to take similar to classical artificial neural networks. This is discussed in a lower section. Quantum neural networks refer to three different categories: Quantum computer with classical data, classical computer with quantum data, and quantum computer with quantum data. == Examples == Quantum neural network research is still in its infancy, and a conglomeration of proposals and ideas of varying scope and mathematical rigor have been put forward. Most of them are based on the idea of replacing classical binary or McCulloch-Pitts neurons with a qubit (which can be called a "quron"), resulting in neural units that can be in a superposition of the state 'firing' and 'resting'. === Quantum perceptrons === A lot of proposals attempt to find a quantum equivalent for the perceptron unit from which neural nets are constructed. A problem is that nonlinear activation functions do not immediately correspond to the mathematical structure of quantum theory, since a quantum evolution is described by linear operations and leads to probabilistic observation. Ideas to imitate the perceptron activation function with a quantum mechanical formalism reach from special measurements to postulating non-linear quantum operators (a mathematical framework that is disputed). A direct implementation of the activation function using the circuit-based model of quantum computation has recently been proposed by Schuld, Sinayskiy and Petruccione based on the quantum phase estimation algorithm. === Quantum networks === At a larger scale, researchers have attempted to generalize neural networks to the quantum setting. One way of constructing a quantum neuron is to first generalise classical neurons and then generalising them further to make unitary gates. Interactions between neurons can be controlled quantumly, with unitary gates, or classically, via measurement of the network states. This high-level theoretical technique can be applied broadly, by taking different types of networks and different implementations of quantum neurons, such as photonically implemented neurons and quantum reservoir processor (quantum version of reservoir computing). Most learning algorithms follow the classical model of training an artificial neural network to learn the input-output function of a given training set and use classical feedback loops to update parameters of the quantum system until they converge to an optimal configuration. Learning as a parameter optimisation problem has also been approached by adiabatic models of quantum computing. Quantum neural networks can be applied to algorithmic design: given qubits with tunable mutual interactions, one can attempt to learn interactions following the classical backpropagation rule from a training set of desired input-output relations, taken to be the desired output algorithm's behavior. The quantum network thus 'learns' an algorithm. === Quantum associative memory === The first quantum associative memory algorithm was introduced by Dan Ventura and Tony Martinez in 1999. The authors do not attempt to translate the structure of artificial neural network models into quantum theory, but propose an algorithm for a circuit-based quantum computer that simulates associative memory. The memory states (in Hopfield neural networks saved in the weights of the neural connections) are written into a superposition, and a Grover-like quantum search algorithm retrieves the memory state closest to a given input. As such, this is not a fully content-addressable memory, since only incomplete patterns can be retrieved. The first truly content-addressable quantum memory, which can retrieve patterns also from corrupted inputs, was proposed by Carlo A. Trugenberger. Both memories can store an exponential (in terms of n qubits) number of patterns but can be used only once due to the no-cloning theorem and their destruction upon measurement. Trugenberger, however, has shown that his probabilistic model of quantum associative memory can be efficiently implemented and re-used multiples times for any polynomial number of stored patterns, a large advantage with respect to classical associative memories. === Classical neural networks inspired by quantum theory === A substantial amount of interest has been given to a "quantum-inspired" model that uses ideas from quantum theory to implement a neural network based on fuzzy logic. == Training == Quantum Neural Networks can be theoretically trained similarly to training classical/artificial neural networks. A key difference lies in communication between the layers of a neural networks. For classical neural networks, at the end of a given operation, the current perceptron copies its output to the next layer of perceptron(s) in the network. However, in a quantum neural network, where each perceptron is a qubit, this would violate the no-cloning theorem. A proposed generalized solution to this is to replace the classical fan-out method with an arbitrary unitary that spreads out, but does not copy, the output of one qubit to the next layer of qubits. Using this fan-out Unitary ( U f {\displaystyle U_{f}} ) with a dummy state qubit in a known state (Ex. | 0 ⟩ {\displaystyle |0\rangle } in the computational basis), also known as an Ancilla bit, the information from the qubit can be transferred to the next layer of qubits. This process adheres to the quantum operation requirement of reversibility. Using this quantum feed-forward network, deep neural networks can be executed and trained efficiently. A deep neural network is essentially a network with many hidden-layers, as seen in the sample model neural network above. Since the Quantum neural network being discussed uses fan-out Unitary operators, and each operator only acts on its respective input, only two layers are used at any given time. In other words, no Unitary operator is acting on the entire network at any given time, meaning the number of qubits required for a given step depends on the number of inputs in a given layer. Since Quantum Computers are notorious for their ability to run multiple iterations in a short period of time, the efficiency of a quantum neural network is solely dependent on the number of qubits in any given layer, and not on the depth of the network. === Cost functions === To determine the effectiveness of a neural network, a cost function is used, which essentially measures the proximity of the network's output to the expected or desired output. In a Classical Neural Network, the weights ( w {\displaystyle w} ) and biases ( b {\displaystyle b} ) at each step determine the outcome of the cost function C ( w , b ) {\displaystyle C(w,b)} . When training a Classical Neural network, the weights and biases are adjusted after each iteration, and given equation 1 below, where y ( x ) {\displaystyle y(x)} is the desired output and a out ( x ) {\displaystyle a^{\text{out}}(x)} is the actual output, the cost function is optimized when C ( w , b ) {\displaystyle C(w,b)} = 0. For a quantum neural network, the cost function is determined by measuring the fidelity of the outcome state ( ρ out {\displaystyle \rho ^{\text{out}}} ) with the desired outcome state ( ϕ out {\displaystyle \phi ^{\text{out}}} ), seen in Equation 2 below. In this case, the Unitary operators are adjusted after each it
Cloud printing
There are, in essence, three kinds of Cloud printing. == Benefits == 76% of IT teams have moved, or plan to move, their print workflows to the cloud due to its simplicity. Consumers can print easily to any printer from their PC, tablet or smartphone, while the Cloud print service monitors the supplies level. Many printer vendors such as Lexmark propose an automatic supplies shipment based on the real-time analysis of the printer supplies and user behavior to ensure printing will always be possible. For IT department, Cloud Printing eliminates the need for print servers and represents the only way to print from Cloud virtual desktops and servers. For consumers, cloud ready printers eliminate the need for PC connections and print drivers, enabling them to print from mobile devices. As for publishers and content owners, cloud printing allows them to "avoid the cost and complexity of buying and managing the underlying hardware, software and processes" required for the production of professional print products. Leveraging cloud print for print on demand also allows businesses to cut down on the costs associated with mass production. Moreover, cloud printing can be considered more eco-friendly, as it significantly reduces the amount of paper used (13% reduction in print jobs yearly) and lowers carbon emissions from transportation. As many companies move their IT to the Cloud, some adopting the Windows 365 and Azure Virtual Desktop services from Microsoft, the connection from the Cloud environment to the on-premise printers become an issue as opening ports for incoming print flow traffic is not an option. In 2020, at the exact same time Google discontinued its Google Print offer, Microsoft has announced its Universal Print service offer, aimed at making printing compatible with Cloud Desktop environments, making printing driver-free and simple with no client to install on PC. With Universal Print Microsoft has built a disrupting architecture with a value proposition commodifying printers, removing print servers and drivers, allowing to move printers to VLAN for security purpose and printing from anywhere. Clients are free to use any printer from any model as they all work the same, clients are not tied anymore to any printer brand and that gave a significant boost to the Cloud print market. That Microsoft Universal Print architecture provides APIs to third-party developers who can develop add-ons such as Celiveo 365 to extend Microsoft Cloud Print with added features such as access control on printers and copiers, follow-me pull print, data encryption, advanced usage reporting or charge back. == Providers of Consumer Cloud Printing Solutions == Before 2020 only a handful of providers used to work towards a professional cloud print solution, operating in their own niche or focus on mobile devices. In 2020 Microsoft has boosted that market by announcing its Universal Print Cloud printing service and since then many publishers have started to propose solutions for that growing market. The Covid pandemic also created the need for employees to be able to print at home when using the corporate IT software. Closed VPN often prevent accessing home network printers from corporate laptops and Full Public Cloud solutions are meant to be a solution to that problem. After the decision by Google to terminate Google Cloud Print service on 31 December 2020, most printer vendors released their own mobile cloud solution to fill the gap, while Hewlett-Packard implemented its own cloud print with their ePrint solution. Those solutions are often proprietary, only working on printers proposed by the vendor. Google has decided to let third-party developers develop Cloud Print solutions and to limit its scope to certifying the best Print Management offers compatible with its Chrome Enterprise Cloud ecosystem. == Providers of Corporate Cloud Printing solutions == While many print solutions claim to be "Cloud Printing", there are actually three categories: full Private Cloud, full Public Cloud, and Hybrid Cloud. Their differences are real and have an impact on the overall TCO as the more software there is on-site, the more hidden cost there are. In the Full Public Cloud category, independent SaaS vendors like Celiveo, ezeep , Printix , and Y Soft support a wide range of printer brands and models, allowing clients to buy the best printer without being locked on any brand. They are leveraging cloud computing technology to offer cloud-based print infrastructure and cloud-based printing software as a Service (SaaS). These solutions have integrations to cloud enabled printers or provide embedded printer agents. They feature allow users to print to any printer in any network, isolated network or not, even if that printer is otherwise not reachable from the user's computer. This also allows IT departments to move printers to VLAN for maximum security, like what they are doing with IP phones. Google Chrome Enterprise Cloud ecosystem has its own technical particularities and Google certifies Print Management solutions, ensuring they comply with Google technical requirement, yet letting each solution differentiate from others with specific features or security. Many of solutions for Chrome Enterprise are Hybrid, a few are Full Public Cloud. Industry experts believe that as these services become more popular, users will no longer consider printers as necessary assets but rather as devices that they can access on demand when the need to generate a printed page presents itself. == Caveats of Cloud Printing == == Security == Print jobs flow through Public Internet. It is therefore important to verify no Man-in-the-Middle attack can be performed. The only technical solution is to ensure each printer and PC uses a non-self-generated cryptographic token or certificate allowing TLS mutual authentication and specific data encryption. Self-generated printer certificates are unknown from the Cloud and prevent trusted authentication. Microsoft has implemented its Zero Trust Access security in its Universal Print service, it generates a unique certificate on printers compatible with its service. Other Cloud Printing SaaS providers have followed Microsoft on that High Security path. Print jobs data stored on the Cloud is sensitive as it contains user information as well as all information appearing on pages. Good practices require such data is encrypted at rest and in motion, using asymmetric PKI keys instead of fixed encryption keys. Some solutions require to open incoming traffic ports on the firewall to let Cloud services communicate with printers attached behind that firewall (most of the time for IPP/IPPS flows), some other solutions use a pull model where the communication is always initiated by the printer and no firewall port needs to be open. In terms of security the later is to be preferred.
Multiclass classification
In machine learning and statistical classification, multiclass classification or multinomial classification is the problem of classifying instances into one of three or more classes (classifying instances into one of two classes is called binary classification). For example, deciding on whether an image is showing a banana, peach, orange, or an apple is a multiclass classification problem, with four possible classes (banana, peach, orange, apple), while deciding on whether an image contains an apple or not is a binary classification problem (with the two possible classes being: apple, no apple). While many classification algorithms (e.g., decision trees, k-NN, neural networks and multinomial logistic regression) naturally permit the use of more than two classes, some are by nature binary algorithms (e.g., classical binary support vector machine) and require decomposition strategies such as one-vs-all, one-vs-one, or ECOC to solve multiclass problems. Multiclass classification should not be confused with multi-label classification, where multiple labels are to be predicted for each instance (e.g., predicting that an image contains both an apple and an orange, in the previous example). == Better-than-random multiclass models == From the confusion matrix of a multiclass model, we can determine whether a model does better than chance. Let K ≥ 3 {\displaystyle K\geq 3} be the number of classes, O {\displaystyle {\mathcal {O}}} a set of observations, y ^ : O → { 1 , . . . , K } {\displaystyle {\hat {y}}:{\mathcal {O}}\to \{1,...,K\}} a model of the target variable y : O → { 1 , . . . , K } {\displaystyle y:{\mathcal {O}}\to \{1,...,K\}} and n i , j {\displaystyle n_{i,j}} be the number of observations in the set { y = i } ∩ { y ^ = j } {\displaystyle \{y=i\}\cap \{{\hat {y}}=j\}} . We note n i . = ∑ j n i , j {\displaystyle n_{i.}=\sum _{j}n_{i,j}} , n . j = ∑ i n i , j {\displaystyle n_{.j}=\sum _{i}n_{i,j}} , n = ∑ j n . j = ∑ i n i . {\displaystyle n=\sum _{j}n_{.j}=\sum _{i}n_{i.}} , λ i = n i . n {\displaystyle \lambda _{i}={\frac {n_{i.}}{n}}} and μ j = n . j n {\displaystyle \mu _{j}={\frac {n_{.j}}{n}}} . It is assumed that the confusion matrix ( n i , j ) i , j {\displaystyle (n_{i,j})_{i,j}} contains at least one non-zero entry in each row, that is λ i > 0 {\displaystyle \lambda _{i}>0} for any i {\displaystyle i} . Finally we call "normalized confusion matrix" the matrix of conditional probabilities ( P ( y ^ = j ∣ y = i ) ) i , j = ( n i , j n i . ) i , j {\displaystyle (\mathbb {P} ({\hat {y}}=j\mid y=i))_{i,j}=\left({\frac {n_{i,j}}{n_{i.}}}\right)_{i,j}} . === Intuitive explanation === The lift is a way of measuring the deviation from independence of two events A {\displaystyle A} and B {\displaystyle B} : L i f t ( A , B ) = P ( A ∩ B ) P ( A ) P ( B ) = P ( A ∣ B ) P ( A ) = P ( B ∣ A ) P ( B ) {\displaystyle \mathrm {Lift} (A,B)={\frac {\mathbb {P} (A\cap B)}{\mathbb {P} (A)\mathbb {P} (B)}}={\frac {\mathbb {P} (A\mid B)}{\mathbb {P} (A)}}={\frac {\mathbb {P} (B\mid A)}{\mathbb {P} (B)}}} We have L i f t ( A , B ) > 1 {\displaystyle \mathrm {Lift} (A,B)>1} if and only if events A {\displaystyle A} and B {\displaystyle B} occur simultaneously with a greater probability than if they were independent. In other words, if one of the two events occurs, the probability of observing the other event increases. A first condition to satisfy is to have L i f t ( y = i , y ^ = i ) ≥ 1 {\displaystyle \mathrm {Lift} (y=i,{\hat {y}}=i)\geq 1} for any i {\displaystyle i} . And the quality of a model (better or worse than chance) does not change if we over- or undersample the dataset, that is if we multiply each row R i {\displaystyle R_{i}} of the confusion matrix by a constant c i {\displaystyle c_{i}} . Thus the second condition is that the necessary and sufficient conditions for doing better than chance need only depend on the normalized confusion matrix. The condition on lifts can be reformulated with One versus Rest binary models : for any i {\displaystyle i} , we define the binary target variable y i {\displaystyle y_{i}} which is the indicator of event { y = i } {\displaystyle \{y=i\}} , and the binary model y ^ i {\displaystyle {\hat {y}}_{i}} of y i {\displaystyle y_{i}} which is the indicator of event { y ^ = i } {\displaystyle \{{\hat {y}}=i\}} . Each of the y ^ i {\displaystyle {\hat {y}}_{i}} models is a "One versus Rest" model. L i f t ( y = i , y ^ = i ) {\displaystyle \mathrm {Lift} (y=i,{\hat {y}}=i)} only depends on the events { y = i } {\displaystyle \{y=i\}} and { y ^ = i } {\displaystyle \{{\hat {y}}=i\}} , so merging or not merging the other classes doesn't change its value. We therefore have L i f t ( y = i , y ^ = i ) = L i f t ( y i = 1 , y ^ i = 1 ) {\displaystyle \mathrm {Lift} (y=i,{\hat {y}}=i)=\mathrm {Lift} (y_{i}=1,{\hat {y}}_{i}=1)} and the first condition is that all binary One versus Rest models are better than chance. ==== Example ==== If K = 2 {\displaystyle K=2} and 2 is the class of interest , the normalized confusion matrix is ( s p e c i f i c i t y 1 − s p e c i f i c i t y 1 − s e n s i t i v i t y s e n s i t i v i t y ) {\displaystyle {\begin{pmatrix}\mathrm {specificity} &1-\mathrm {specificity} \\1-\mathrm {sensitivity} &\mathrm {sensitivity} \end{pmatrix}}} and we have L i f t ( y = 1 , y ^ = 1 ) − 1 = P ( y = y ^ = 1 ) λ 1 μ 1 − 1 = n 1 , 1 n n 1. n .1 − 1 {\displaystyle \mathrm {Lift} (y=1,{\hat {y}}=1)-1={\frac {\mathbb {P} (y={\hat {y}}=1)}{\lambda _{1}\mu _{1}}}-1={\frac {n_{1,1}n}{n_{1.}n_{.1}}}-1} = n 1 , 1 ( n 1 , 1 + n 1 , 2 + n 2 , 1 + n 2 , 2 ) − ( n 1 , 1 + n 1 , 2 ) ( n 1 , 1 + n 2 , 1 ) n 1. n .1 = n 1 , 1 n 2 , 2 − n 1 , 2 n 2 , 1 n 1. n .1 {\displaystyle ={\frac {n_{1,1}(n_{1,1}+n_{1,2}+n_{2,1}+n_{2,2})-(n_{1,1}+n_{1,2})(n_{1,1}+n_{2,1})}{n_{1.}n_{.1}}}={\frac {n_{1,1}n_{2,2}-n_{1,2}n_{2,1}}{n_{1.}n_{.1}}}} . Thus L i f t ( y = 1 , y ^ = 1 ) ≥ 1 ⟺ n 1 , 1 n 2 , 2 − n 1 , 2 n 2 , 1 ≥ 0 {\displaystyle \mathrm {Lift} (y=1,{\hat {y}}=1)\geq 1\iff n_{1,1}n_{2,2}-n_{1,2}n_{2,1}\geq 0} . Similarly, by swapping the roles of 1 and 2, we find that L i f t ( y = 2 , y ^ = 2 ) ≥ 1 ⟺ n 1 , 1 n 2 , 2 − n 1 , 2 n 2 , 1 ≥ 0 {\displaystyle \mathrm {Lift} (y=2,{\hat {y}}=2)\geq 1\iff n_{1,1}n_{2,2}-n_{1,2}n_{2,1}\geq 0} . Dividing by n 1. n 2. {\displaystyle n_{1.}n_{2.}} we find that the necessary and sufficient condition on the normalized confusion matrix is s e n s i t i v i t y s p e c i f i c i t y − ( 1 − s e n s i t i v i t y ) ( 1 − s p e c i f i c i t y ) ≥ 0 ⟺ s e n s i t i v i t y + s p e c i f i c i t y − 1 ≥ 0 ⟺ J ≥ 0 {\displaystyle \mathrm {sensitivity} \ \mathrm {specificity} -(1-\mathrm {sensitivity} )(1-\mathrm {specificity} )\geq 0\iff \mathrm {sensitivity} +\mathrm {specificity} -1\geq 0\iff J\geq 0} . This brings us back to the classical binary condition: Youden's J must be positive (or zero for random models). === Random models === A random model is a model that is independent of the target variable. This property is easily reformulated with the confusion matrix. This proposition shows that the model y ^ {\displaystyle {\hat {y}}} of y {\displaystyle y} is uninformative if and only if there are two families of numbers ( α i ) i {\displaystyle (\alpha _{i})_{i}} and ( β j ) j {\displaystyle (\beta _{j})_{j}} such that P ( { y = i } ∩ { y ^ = j } ) = α i β j {\displaystyle \mathbb {P} (\{y=i\}\cap \{{\hat {y}}=j\})=\alpha _{i}\beta _{j}} for any i {\displaystyle i} and j {\displaystyle j} . === Multiclass likelihood ratios and diagnostic odds ratios === We define generalized likelihood ratios calculated from the normalized confusion matrix: for any i {\displaystyle i} and j ≠ i {\displaystyle j\not =i} , let L R i , j = P ( y ^ = j ∣ y = j ) P ( y ^ = j ∣ y = i ) {\displaystyle \mathrm {LR} _{i,j}={\frac {\mathbb {P} ({\hat {y}}=j\mid y=j)}{\mathbb {P} ({\hat {y}}=j\mid y=i)}}} . When K = 2 {\displaystyle K=2} , if 2 is the class of interest,, we find the classical likelihood ratios L R 1 , 2 = L R + {\displaystyle \mathrm {LR} _{1,2}=\mathrm {LR} _{+}} and L R 2 , 1 = 1 L R − {\displaystyle \mathrm {LR} _{2,1}={\frac {1}{\mathrm {LR} _{-}}}} . Multiclass diagnostic odds ratios can also be defined using the formula D O R i , j = D O R j , i = L R i , j L R j , i = n i , i n j , j n i , j n j , i = P ( y ^ = j ∣ y = j ) / P ( y ^ = i ∣ y = j ) P ( y ^ = j ∣ y = i ) / P ( y ^ = i ∣ y = i ) {\displaystyle \mathrm {DOR} _{i,j}=\mathrm {DOR} _{j,i}=\mathrm {LR} _{i,j}\mathrm {LR} _{j,i}={\frac {n_{i,i}n_{j,j}}{n_{i,j}n_{j,i}}}={\frac {\mathbb {P} ({\hat {y}}=j\mid y=j)/\mathbb {P} ({\hat {y}}=i\mid y=j)}{\mathbb {P} ({\hat {y}}=j\mid y=i)/\mathbb {P} ({\hat {y}}=i\mid y=i)}}} We saw above that a better-than-chance model (or a random model) must verify L i f t ( y = i , y ^ = i ) ≥ 1 {\displaystyle \mathrm {Lift} (y=i,{\hat {y}}=i)\geq 1} for any i {\displaystyle i} and λ i {\displaystyle \lambda _{i}} . According to the previous corollary, likelihood ratios are thus greater