AI Chat Image Generator Free

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  • JAX (software)

    JAX (software)

    JAX is a Python library for accelerator-oriented array computation and program transformation, designed for high-performance numerical computing and large-scale machine learning. It is developed by Google with contributions from Nvidia and other community contributors. It is described as bringing together a modified version of the automatic differentiation system autograd and OpenXLA's XLA (Accelerated Linear Algebra). It is designed to follow the structure and workflow of NumPy as closely as possible and works with various existing frameworks such as TensorFlow and PyTorch. The primary features of JAX are: Providing a unified NumPy-like interface to computations that run on CPU, GPU, or TPU, in local or distributed settings. Built-in Just-In-Time (JIT) compilation via OpenXLA, an open-source machine learning compiler ecosystem. Efficient evaluation of gradients via its automatic differentiation transformations. Automatic vectorization to efficiently map functions over arrays representing batches of inputs. == Libraries using Jax == Flax Equinox Optax

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  • Pulsar (social listening platform)

    Pulsar (social listening platform)

    Pulsar is a software platform for social media monitoring, audience intelligence and social listening that allows organizations to monitor and analyze online conversations across social media, news, and other digital sources. The platform combines social media listening, media monitoring, trend analysis, and audience segmentation to help users understand public discussions and audience behavior in real time. The platform is a social listening platform, which aggregates data from networks such as X, Facebook, Instagram, and forums) and applies artificial intelligence for text and sentiment analysis. Pulsar is offered as a cloud-based Software as a Service (SaaS) tool and insights consultancy. It has been part of Pulsar Group (formerly Access Intelligence), a publicly listed group of communications software products, since 2019. As well as commercial uses, the platform has been used in peer-reviewed academic research analysing online discourse. The platform is listed on the UK government's G-Cloud 14 Digital Marketplace for the provision of social listening and audience intelligence services. == History == Pulsar originated in the early 2010s as a project within Face, a London-based innovation and market research consultancy. The platform's first product, Pulsar TRAC, launched in 2013 as a social media analytics tool. Pulsar TRAC was designed to measure the reach of conversations, mapping brand audiences, and tracking how content spreads through networks. The development was led by Dr Francesco D'Orazio, who created the Pulsar brand and led the development of the platform while serving as VP of Product and Innovation at Face. Face itself had been acquired by the Cello Group Plc (a UK-based advisory firm) in 2012, and Pulsar became part of Cello's portfolio of research and data tools. In January 2017, Cello Group made a significant investment to scale Pulsar and announced the merger of Face's qualitative research business into Pulsar, unifying both under the Pulsar brand for global expansion. In 2018, Pulsar opened an office in Los Angeles to better serve its growing U.S. client base in media, healthcare, and entertainment sectors and Francesco D'Orazio was appointed CEO. The company focused on developing new products amid a wave of consolidation in the social listening industry. In October 2019, Pulsar was acquired by Access Intelligence Plc (now Pulsar Group), an AIM-listed communications software company. The group, which also owns PR and media tools Isentia, Vuelio and ResponseSource, integrated Pulsar to their end-to-end marketing and communications insights offering. Pulsar established a new office in Sydney, Australia in 2022 as part of this global expansion, adding to its existing offices in London and Los Angeles. In 2023, Pulsar Group (then Access Intelligence) was recognised as one of Europe's fastest growing companies by the Financial Times. In May 2024, Access Intelligence PLC changed its name to Pulsar Group PLC. The company has since continued to develop its platform. In March 2025 it introduced new tool Narratives AI, described as a "search engine for public opinion" and the first of its kind for analyzing public narratives and their evolutions in both social media and the news. In October 2025, Pulsar launched Insight Agents, a set of AI agents embedded into the platform advertised to "proactively anticipate user needs or issues, carry out routine tasks, uncover anomalies in your datasets, and prompt responses at scale, 24/7." == Products == Pulsar's architecture integrates four main products into a single interface. The core product suite is often broken into three main components: Pulsar TRAC (for social listening and audience analysis), Pulsar TRENDS (for trend discovery and analysis), and Pulsar CORE (for owned-channel and web analytics). Pulsar's fourth product is Narratives AI. === Pulsar TRAC === Pulsar TRAC is a social listening and audience intelligence platform that allows users to configure searches that track public conversations and measure audience behaviour. Pulsar TRAC is focused on conversation insights and audience segmentations - the platform is reported to collect and analyse data from a wide range of sources, including major social networks, forums, news and review sites, and ecommerce platforms, with real-time visualisations and AI-supported analytics used to find patterns and communities of interest. Pulsar TRAC can be incorporated into workflows with other audience tools, such as an integration with Audiense that connects TRAC's conversation insights to external audience-segmentation datasets. === Pulsar CORE === Pulsar CORE centres on the analysis of owned-channel data, such as brand social media profiles, website interaction and other in-house digital assets, to generate audience and content insights. CORE can monitor published content, evaluate competitors, and extract demographic and behavioural segmentation from owned channels. === Narratives AI === Narratives AI is a tool within the Pulsar audience intelligence platform that uses artificial intelligence to detect, cluster and analyse narratives forming across social and news media. It was launched in March 2025 as a standalone search interface that processes real-time and historical data to find cultural trends, behaviours and beliefs. It uses clustering algorithms and visualisation to show how conversations form and spread online, and their relative importance within wider discourse. == Notable features == === Insight Agents === Pulsar's Insight Agents are AI-powered agents within the Pulsar platform designed to automate and augment common tasks in media, social, audience and narrative intelligence. Branded as TeamMates, these agents are grouped into four functional types: Sentinels for real-time monitoring, anomaly detection and alerting Oracles for forecasting and scenario planning Custodians for governance, compliance and policy enforcement Analysts for research, reporting and recommendations Each agent is trained on Pulsar's multi-source data and domain-specific workflows. In February 2026, Pulsar introduced 'Crisis Oracle,' an AI-driven system designed to quantify narrative momentum and predict reputational risk. == Academic research == Pulsar has been used as a data collection and analysis tool in peer-reviewed academic research across public health, infodemiology, veterinary science, and policy research. Published uses include a World Health Organization report on infodemic management, a Journal of Medical Internet Research study on headache and migraine discourse across Japan, Germany, and France, a Frontiers in Big Data study of Long COVID narratives, and Frontiers in Veterinary Science studies on canine chronic kidney disease and oral medication administration in dogs.

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  • Resistance Database Initiative

    Resistance Database Initiative

    HIV Resistance Response Database Initiative (RDI) was formed in 2002 to use artificial intelligence (AI) to predict how patients will respond to HIV drugs using data from more 250,000 patients from around 50 countries around the world. The RDI used its models to power its HIV Treatment Response Prediction System (HIV-TRePS). Launched in 2010, this free online tool enabled healthcare professionals to upload their patient’s data and obtain highly accurate predictions of how they would respond to different combinations of the 30 or more drugs available. The tool enabled physicians to individualize their patients’ treatment, using these predictions based on more than a million patient-years of treatment experience. HIV-TRePS was possibly the first ever AI-based system for medical decision-making to be developed, successfully tested, and used in clinical practice. It has since been used by thousands of healthcare professionals to optimise the treatment of tens of thousands of patients. Since the RDI’s inception the treatment of HIV infection has progressed enormously, with more effective and better tolerated drugs available in ever more convenient combination formulations. In most countries HIV is now considered a chronic, manageable condition. Moreover, the success of the drugs in reducing the amount of virus is substantially reducing the onward transmission of the virus and cases of new infections are falling in many settings. This improvement in HIV treatment means the need for sophisticated AI to support HIV treatment decisions has significantly reduced. In response, the RDI ceased development of further models and, in March 2024, withdrew its HIV-TRePS system. == Background == Human immunodeficiency virus (HIV) is the virus that causes acquired immunodeficiency syndrome (AIDS), a condition in which the immune system begins to fail, leading to life-threatening opportunistic infections. There are approximately 30 HIV antiretroviral drugs that have been approved for the treatment of HIV infection, from six different classes, based on the point in the HIV life-cycle at which they act. They are used in combination; typically 3 or more drugs from 2 or more different classes, a form of therapy known as highly active antiretroviral therapy (HAART). The aim of therapy is to suppress the virus to very low, ideally undetectable, levels in the blood. This prevents the virus from depleting the immune cells that it preferentially attacks CD4 cells and prevents or delays illness and death. Despite the expanding availability of these drugs and the impact of their use, treatments continue to fail, often involving to the development of resistance. During drug therapy, low-level virus replication may still occur, particularly when a patient misses a dose. HIV makes errors in copying its genetic material and, if a mutation makes the virus resistant to one or more of the drugs in the patient's treatment, it may begin to replicate more successfully in the presence of that drug and undermine the effect of the treatment. If this happens, the treatment needs to be changed to re-establish control over the virus. == RDI's Approach == The RDI’s approach was to use artificial intelligence (including neural network and random forest models), trained with data from hundreds of thousands of patients, treated with different drugs in a variety of clinical settings all over the world, to predict how an individual patient will respond to any new combination of HIV drugs. The models were tested with independent data sets and consistently achieved accuracy of approximately 80%.

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  • Federal Virtual World Challenge

    Federal Virtual World Challenge

    The Federal Virtual Challenge, formerly The Federal Virtual Worlds Challenge is a competition led by the Simulation and Training Technology Center (United States Army Research, Development and Engineering Command). The event is conducted in order to reach a global development community that will create innovative and interactive training and analysis services in virtual worlds. The inaugural event began in 2009 with the awards being conducted during March 2010 GameTech conference in Orlando, Florida. == Description == The focus of the challenge is training or analysis capability conducted wholly in a virtual environment. The training and analysis audience includes all United States Federal Agencies including, Department of Defense, Department of Homeland Security, Department of Transportation, and Department of Health and Human Services, NASA, DOT, and many more.

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  • Vote Compass

    Vote Compass

    Vote Compass is an interactive, online voting advice application developed by political scientists and run during election campaigns. It surveys users about their political views and, based on their responses, calculates the individual alignment of each user with the parties or candidates running in a given election contest. It is operated by a social enterprise called Vox Pop Labs in partnership with locale-specific news organizations, including the Wall Street Journal, Vox Media, the Canadian and Australian Broadcasting Corporations, Television New Zealand, France24, RTL Group, and Grupo Globo. Vote Compass also operates under the trademarks Boussole électorale and Wahl-Navi for French- and German-language iterations, respectively. == Background == Vote Compass was developed by Clifton van der Linden, a professor in the Department of Political Science at McMaster University. It is run by van der Linden along with a team of social and statistical scientists from Vox Pop Labs. Although inspired by European Voting Advice Applications, van der Linden explicitly rejects this terminology, arguing that Vote Compass was "never intended to account for every variable that influences voter choice and its results should not be interpreted as voting advice." == Methodology == Using a Likert scale, users indicate their responses to a series of policy propositions designed to discriminate between candidates' policies on prominent issues relevant to the election. Propositions are crafted in collaboration with political scientists local to each jurisdiction in which Vote Compass is run. Based on a candidate or political party's public disclosures (i.e. party manifestos, policy proposals, official websites, speeches, media releases, statements made in the legislature, etc.) they are calibrated on the same propositions and scales as are users. A series of aggregation algorithms calculate the overall distance between the user and the candidates or parties. There have been claims that Vote Compass surveys have the potential to become push polling, if the survey questions posed are poorly designed.

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  • Generative engine optimization

    Generative engine optimization

    Generative engine optimization (GEO) is one of the names given to the practice of structuring digital content and managing online presence to improve visibility in responses generated by generative artificial intelligence (AI) systems. The practice influences the way large language models (LLMs) retrieve, summarize, and present information in response to user queries. Related terms include answer engine optimization (AEO) and artificial intelligence optimization (AIO). The concept of GEO first appeared in response to generative AI technologies being integrated into mainstream search and information retrieval systems. Tools are used to monitor how websites and brands are cited, referenced, or incorporated into responses produced by large language models. == Terminology == Several overlapping terms describe related practices, and usage varies across practitioners, vendors, and publications. No consensus definition distinguishing these terms had been established in the academic literature as of early 2026, and the terms are frequently used interchangeably in trade and practitioner contexts. Other terms for the same concept include answer engine optimization (AEO), large language model optimization (LLMO), artificial intelligence optimization (AIO), and AI SEO. In 2026, Google released documentation entitled "Optimizing your website for generative AI features on Google Search." According to this documentation, "optimizing for generative AI search is optimizing for the search experience, and thus still SEO.” This position had previously been shared at conferences, with 2026 being the first time Google released official documentation stating it. == Factors influencing generative engine optimization == By early 2026, the focus of GEO practitioners shifted from simple keyword placement to "semantic relevance", a metric driven by the integration of advertising into conversational AI. OpenAI and Google began monetizing AI search results, which is not currently considered an aspect of generative engine optimization but is adjacent.

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  • Shadowrun

    Shadowrun

    Shadowrun is a science fantasy tabletop role-playing game set in an alternate future in which cybernetics, magic and fantasy creatures co-exist. It combines genres of cyberpunk, urban fantasy, and crime, with occasional elements of conspiracy, horror, and detective fiction. From its inception in 1989, it has spawned a franchise that includes a series of novels, a collectible card game, two miniature-based tabletop wargames, and multiple video games. The title is taken from the game's main premise – a near-future world damaged by a massive magical event, where industrial espionage and corporate warfare runs rampant. A shadowrun – a successful data theft or physical break-in at a rival corporation or organization – is one of the main tools employed by both corporate rivals and underworld figures. Deckers (futuristic hackers) can tap into an immersive, three-dimensional cyberspace on such missions as they seek access, physical or remote, to the power structures of rival groups. They are opposed by rival deckers and lethal, potentially brain-destroying artificial intelligences called "Intrusion Countermeasures" (IC), while they are protected by street fighters and/or mercenaries, often with cyborg implants (called cyberware), magicians, and other exotic figures. Magic has also returned to the world after a series of plagues; dragons who can take human form have returned as well, and are commonly found in high positions of corporate power. == Publication history == Shadowrun was developed and published by FASA from 1989 until early 2001, when the company closed and Shadowrun was transferred to WizKids, a company founded by former FASA employees. Two years before its closure, FASA sold its videogame branch, FASA Interactive, to Microsoft corporation, keeping rights to publishing novels and pen and paper RPGs. Since then, digital rights to Shadowrun IP have belonged to Microsoft. WizKids licensed the RPG rights to Fantasy Productions, who were already publishing a German version, until WizKids was acquired by Topps in 2003. Catalyst Game Labs, a publishing imprint of InMediaRes Productions, licensed the rights from Topps to publish new products. WizKids itself produced an unsuccessful collectible action figure game based on the property, called Shadowrun Duels. A fifth edition of Shadowrun was announced in December 2012. A limited-edition softcover was sold at the Origins Game Fair in June 2013, and the PDF in July 2013. A hardcover was published in August 2013. Shadowrun Anarchy was published in October 2016 It is a simplified version of the ruleset which allows focus more on the narration than on the rules. The sixth edition, called Shadowrun, Sixth World, was announced on May 1, 2019 to coincide with the game's 30th anniversary, along with a new website at shadowrunsixthworld.com. The game was published on August 26, 2019. The mechanics for this new version are generally similar to those of fifth edition, with some rules reworked for what line developer Jason Hardy describes as streamlining. This new version also progressed the in-game year to 2080. Since 2004, Shadowrun Missions (SRM) has offered fans "living campaigns" that allow for persistent character advancement. SRM is broken down into seasons which are made up of up to 24 individual missions that can be played at home, with special missions available to play exclusively at conventions. Each SRM season develops an overarching plot focused on a specific city from the Shadowrun setting. Missions settings have included the divided city of Denver, the corporate city-state of Manhattan, the Seattle Metroplex city-state, the formerly walled-off wastelands of Chicago, and Neo-Tokyo. For Shadowrun, Sixth World missions returned to Seattle, with twenty-four missions set in 2081, right after Seattle declared independence from the UCAS. The current Shadowrun Missions setting is 2083 New Orleans. The Shadowrun role-playing game has spawned several properties, including Shadowrun: The Trading Card Game, eight video games, an action figure game (Shadowrun Duels), two magazines, an art book and more than 50 novels, starting with the Secrets of Power series which introduces some of the original characters of Shadowrun and provides an introduction to this fictional universe. In addition to the main rule book there have been over 100 published supplements including adventures and expansions to both the rules and the game settings. Catalyst Game Labs announced that 2013 would be "The Year of Shadowrun," and in addition to the release of Shadowrun fifth edition that it has collaborated with publishers on the following properties: Shadowrun: Crossfire, The Adventure Deck-building Game; Shadowrun: Sprawl Gangers, a tactical miniatures wargame; and Shadowrun: Hostile Takeover, a board game designed by Bryan C.P. Steele was planned for release in late 2014/early 2015. Catalyst had been in collaboration with Nordic Games and Cliffhanger Studios to create Shadowrun Chronicles: Boston Lockdown online RPG, however it was shuttered November 30, 2018, with the producers citing lack of funding and the end of the license terms for use of the IP. == Fictional universe == Shadowrun takes place several decades in the future (2050 in the first edition, currently 2088). The end of the Mesoamerican Long Count calendar ushered in the "Sixth World", with once-mythological beings (e.g. dragons) appearing and forms of magic suddenly emerging. Large numbers of humans have "Goblinized" into orks and trolls, while many human children are born as elves, dwarves, and even more exotic creatures. In North America, indigenous peoples discovered that their traditional ceremonies allow them to command powerful spirits, and rituals associated with a new Ghost Dance movement let them take control of much of the western U.S. and Canada, where they formed a federation of Native American Nations. Seattle remains under U.S. control by treaty as a city-state enclave, and most game materials are set there and assume campaigns will use it as their setting. In parallel with these magical developments, the setting's 21st century features technological and social developments associated with cyberpunk science fiction. Megacorporations control the lives of their employees and command their own armies; many of the largest have extraterritoriality, such as currently enjoyed by foreign heads of state. Technological advances make cyberware (mechanical replacement body parts) and bioware (augmented vat-grown body parts implanted in place of or in tandem with natural organs) common. The Computer Crash of 2029 led to the creation of the Matrix, a worldwide computer network that users interact with via direct neural interface. When conflicts arise, corporations, governments, organized crime syndicates, and even wealthy individuals subcontract their dirty work to specialists, who then perform "shadowruns" or missions undertaken by deniable assets without identities or those that wish to remain unknown. The most skilled of these specialists, called shadowrunners, have earned a reputation for getting the job done. They have developed a knack for staying alive, and prospering, in the world of Shadowrun. The Shadowrun world is cross-genre, incorporating elements of both cyberpunk and urban fantasy. Unlike in a purely cyberpunk game, in the Shadowrun world, magic exists and has "worked" since 2011. Among other things, this split humankind into subtypes, also known as metatypes/metahumans. Some of these metatypes take the form of common fantasy races. Likewise, some animals have turned into familiar monsters of past fantasy and lore and both monsters and human magicians have regained magical powers. By the second half of the 21st century, in the time the game is set, these events are accepted as commonplace. Man, machine, and magic exist in a world where the amazing is among the most common and technology has entered into every facet of human (and metahuman) life. === Races === Characters in Shadowrun can be humans, orks, trolls, elves, dwarves, as well as certain diverging subspecies (known as metavariants) such as gnomes, giants, dryads, etc. In the early days, when magic returned to the world, humans began to either change into, or give birth to, elf and dwarf infants, a phenomenon called Unexplained Genetic Expression (UGE). Later, some juvenile and adult humans "goblinized" into other races (mostly orks, but also some trolls). The term "metahuman" is used either to refer to humanity as a whole, including all races, or to refer specifically to non-human races, depending on context. The return of Halley's Comet brought even further variation in the form of changelings, who have variation atypical to their metatype or even species, such as electroreception. Two of the metahuman races, elves and orks, have fictional languages. Additionally, a virus known as the Human Meta-Human Vampiric Virus (HMHVV), with many variant strains, has been known to cause f

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  • The 100 (TV series)

    The 100 (TV series)

    The 100 (pronounced "The Hundred" ) is an American post-apocalyptic science fiction drama television series that premiered on March 19, 2014, on the CW network, and ended on September 30, 2020. Developed by Jason Rothenberg, the series is based on the young adult novel series The 100 by Kass Morgan. The 100 follows descendants of post-apocalyptic survivors from a space habitat, the Ark, who return to Earth nearly a century after a devastating nuclear apocalypse; the first people sent to Earth are a group of juvenile delinquents who encounter another group of survivors on the ground. The juvenile delinquents include Clarke Griffin (Eliza Taylor), Finn Collins (Thomas McDonell), Bellamy Blake (Bob Morley), Octavia Blake (Marie Avgeropoulos), Jasper Jordan (Devon Bostick), Monty Green (Christopher Larkin), and John Murphy (Richard Harmon). Other lead characters include Clarke's mother Dr. Abby Griffin (Paige Turco), Marcus Kane (Henry Ian Cusick), and Chancellor Thelonious Jaha (Isaiah Washington), all of whom are council members on the Ark, and Raven Reyes (Lindsey Morgan), a mechanic aboard the Ark. == Plot == Ninety-seven years after a devastating nuclear apocalypse wipes out most human life on Earth, thousands of people now live in a space station orbiting Earth, which they call the Ark. Three generations have been born in space, but when life-support systems on the Ark begin to fail, one hundred juvenile detainees are sent to Earth in a last attempt to determine whether it is habitable, or at least save resources for the remaining residents of the Ark. They discover that some humans survived the apocalypse: the Grounders, who live in clans locked in a power struggle; the Reapers, another group of grounders who have been turned into cannibals by the Mountain Men; and the Mountain Men, who live in Mount Weather, descended from those who locked themselves away before the apocalypse. Under the leadership of Clarke and Bellamy, the juveniles attempt to survive the harsh surface conditions, battle hostile grounders and establish communication with the Ark. In the second season, the survivors face a new threat from the Mountain Men, who harvest their bone marrow to survive the radiation. Clarke and the others form a fragile alliance with the grounders to rescue their people. The season ends with Clarke making a devastating choice to save them all. In season three, power struggles erupt between the Arkadians and the grounders after a controversial new leader takes charge. Meanwhile, an AI named A.L.I.E., responsible for the original apocalypse, begins taking control of people’s minds. Clarke destroys A.L.I.E. but learns another disaster is imminent. In the fourth season, nuclear reactors are melting down, threatening to wipe out life again. Clarke and her friends search for ways to survive, including experimenting with radiation-resistant blood and finding an underground bunker. As time runs out, only a select few are able to take shelter. The fifth season picks up six years later, when Earth is left largely uninhabitable except for one green valley, where new enemies arrive. Clarke protects her adopted daughter Madi while former survivors return from space and underground, triggering another war. The battle ends with the valley destroyed and the group entering cryosleep to find a new home. In season six, the group awakens 125 years later on a new planet called Sanctum, ruled by powerful families known as the Primes. Clarke fights to stop body-snatching rituals and protect her people from new threats, including a rebel group and a dangerous AI influence. The season ends with major losses and the destruction of the Primes' rule. In the seventh and final season, the survivors face unrest on Sanctum and clash with a mysterious group called the Disciples, who believe Clarke is key to saving humanity. A wormhole network reveals multiple planets and a final "test" that determines the fate of the species. Most transcend into a higher consciousness, but Clarke and a few others choose to live out their lives on a reborn Earth. == Cast and characters == Eliza Taylor as Clarke Griffin Paige Turco as Abigail "Abby" Griffin (seasons 1–6; guest season 7) Thomas McDonell as Finn Collins (seasons 1–2) Eli Goree as Wells Jaha (season 1; guest season 2) Marie Avgeropoulos as Octavia Blake Bob Morley as Bellamy Blake Kelly Hu as Callie "Cece" Cartwig (season 1) Christopher Larkin as Monty Green (seasons 1–5; guest season 6) Devon Bostick as Jasper Jordan (seasons 1–4) Isaiah Washington as Thelonious Jaha (seasons 1–5) Henry Ian Cusick as Marcus Kane (seasons 1–6) Lindsey Morgan as Raven Reyes (seasons 2–7; recurring season 1) Ricky Whittle as Lincoln (seasons 2–3; recurring season 1) Richard Harmon as John Murphy (seasons 3–7; recurring seasons 1–2) Zach McGowan as Roan (season 4; recurring season 3; guest season 7) Tasya Teles as Echo / Ash (seasons 5–7; guest seasons 2–3; recurring season 4) Shannon Kook as Jordan Green (seasons 6–7; guest season 5) JR Bourne as Russell Lightbourne / Malachi / Sheidheda (season 7; recurring season 6) Chuku Modu as Gabriel Santiago (season 7; recurring season 6) Shelby Flannery as Hope Diyoza (season 7; guest season 6) =

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  • Projection-slice theorem

    Projection-slice theorem

    In mathematics, the projection-slice theorem, central slice theorem or Fourier slice theorem in two dimensions states that the results of the following two calculations are equal: Take a two-dimensional function f(r), project (e.g. using the Radon transform) it onto a (one-dimensional) line, and do a Fourier transform of that projection. Take that same function, but do a two-dimensional Fourier transform first, and then slice the function through its origin, parallel to the projection line. In operator terms, if F1 and F2 are the 1- and 2-dimensional Fourier transform operators mentioned above, P1 is the projection operator (which projects a 2-D function onto a 1-D line), S1 is a slice operator (which extracts a 1-D central slice from a function), then F 1 P 1 = S 1 F 2 . {\displaystyle F_{1}P_{1}=S_{1}F_{2}.} This idea can be extended to higher dimensions. This theorem is used, for example, in the analysis of medical CT scans where a "projection" is an x-ray image of an internal organ. The Fourier transforms of these images are seen to be slices through the Fourier transform of the 3-dimensional density of the internal organ, and these slices can be interpolated to build up a complete Fourier transform of that density. The inverse Fourier transform is then used to recover the 3-dimensional density of the object. This technique was first derived by Ronald N. Bracewell in 1956 for a radio-astronomy problem. == The projection-slice theorem in N dimensions == In N dimensions, the projection-slice theorem states that the Fourier transform of the projection of an N-dimensional function f(r) onto an m-dimensional linear submanifold is equal to an m-dimensional slice of the N-dimensional Fourier transform of that function consisting of an m-dimensional linear submanifold through the origin in the Fourier space which is parallel to the projection submanifold. In operator terms: F m P m = S m F N . {\displaystyle F_{m}P_{m}=S_{m}F_{N}.\,} == The generalized Fourier-slice theorem == In addition to generalizing to N dimensions, the projection-slice theorem can be further generalized with an arbitrary change of basis. For convenience of notation, we consider the change of basis to be represented as B, an N-by-N invertible matrix operating on N-dimensional column vectors. Then the generalized Fourier-slice theorem can be stated as F m P m B = S m B − T | B − T | F N {\displaystyle F_{m}P_{m}B=S_{m}{\frac {B^{-T}}{|B^{-T}|}}F_{N}} where B − T = ( B − 1 ) T {\displaystyle B^{-T}=(B^{-1})^{T}} is the transpose of the inverse of the change of basis transform. == Proof in two dimensions == The projection-slice theorem is easily proven for the case of two dimensions. Without loss of generality, we can take the projection line to be the x-axis. There is no loss of generality because if we use a shifted and rotated line, the law still applies. Using a shifted line (in y) gives the same projection and therefore the same 1D Fourier transform results. The rotated function is the Fourier pair of the rotated Fourier transform, for which the theorem again holds. If f(x, y) is a two-dimensional function, then the projection of f(x, y) onto the x axis is p(x) where p ( x ) = ∫ − ∞ ∞ f ( x , y ) d y . {\displaystyle p(x)=\int _{-\infty }^{\infty }f(x,y)\,dy.} The Fourier transform of f ( x , y ) {\displaystyle f(x,y)} is F ( k x , k y ) = ∫ − ∞ ∞ ∫ − ∞ ∞ f ( x , y ) e − 2 π i ( x k x + y k y ) d x d y . {\displaystyle F(k_{x},k_{y})=\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }f(x,y)\,e^{-2\pi i(xk_{x}+yk_{y})}\,dxdy.} The slice is then s ( k x ) {\displaystyle s(k_{x})} s ( k x ) = F ( k x , 0 ) = ∫ − ∞ ∞ ∫ − ∞ ∞ f ( x , y ) e − 2 π i x k x d x d y {\displaystyle s(k_{x})=F(k_{x},0)=\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }f(x,y)\,e^{-2\pi ixk_{x}}\,dxdy} = ∫ − ∞ ∞ [ ∫ − ∞ ∞ f ( x , y ) d y ] e − 2 π i x k x d x {\displaystyle =\int _{-\infty }^{\infty }\left[\int _{-\infty }^{\infty }f(x,y)\,dy\right]\,e^{-2\pi ixk_{x}}dx} = ∫ − ∞ ∞ p ( x ) e − 2 π i x k x d x {\displaystyle =\int _{-\infty }^{\infty }p(x)\,e^{-2\pi ixk_{x}}dx} which is just the Fourier transform of p(x). The proof for higher dimensions is easily generalized from the above example. == The FHA cycle == If the two-dimensional function f(r) is circularly symmetric, it may be represented as f(r), where r = |r|. In this case the projection onto any projection line will be the Abel transform of f(r). The two-dimensional Fourier transform of f(r) will be a circularly symmetric function given by the zeroth-order Hankel transform of f(r), which will therefore also represent any slice through the origin. The projection-slice theorem then states that the Fourier transform of the projection equals the slice or F 1 A 1 = H , {\displaystyle F_{1}A_{1}=H,} where A1 represents the Abel-transform operator, projecting a two-dimensional circularly symmetric function onto a one-dimensional line, F1 represents the 1-D Fourier-transform operator, and H represents the zeroth-order Hankel-transform operator. == Extension to fan beam or cone-beam CT == The projection-slice theorem is suitable for CT image reconstruction with parallel beam projections. It does not directly apply to fanbeam or conebeam CT. The theorem was extended to fan-beam and conebeam CT image reconstruction by Shuang-ren Zhao in 1995.

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  • Agents of S.H.I.E.L.D. season 4

    Agents of S.H.I.E.L.D. season 4

    The fourth season of the American television series Agents of S.H.I.E.L.D., based on the Marvel Comics spy organization S.H.I.E.L.D., follows Phil Coulson and other S.H.I.E.L.D. agents and allies after the signing of the Sokovia Accords. It is set in the Marvel Cinematic Universe (MCU) and acknowledges the continuity of the franchise's films. The season was produced by ABC Studios, Marvel Television, and Mutant Enemy Productions, with Jed Whedon, Maurissa Tancharoen, and Jeffrey Bell serving as showrunners. Clark Gregg reprises his role as Coulson from the film series, starring alongside the returning series regulars Ming-Na Wen, Chloe Bennet, Iain De Caestecker, Elizabeth Henstridge, and Henry Simmons. They are joined by John Hannah who was promoted from his recurring guest role in the third season. The fourth season was ordered in March 2016, with production taking place from that July until the following April. Due to its broadcast schedule, the season was split into three "pods": Ghost Rider for the first eight episodes, featuring recurring guest star Gabriel Luna as the supernatural Robbie Reyes / Ghost Rider and exploring mysticism in the MCU alongside the film Doctor Strange (2016); LMD, referring to the new Life Model Decoy program, for the next seven episodes which focus on recurring guest star Mallory Jansen as the LMD Aida; and Agents of Hydra for the final seven episodes, partly set in a "what if" virtual reality that allowed the return of former series regular Brett Dalton as Grant Ward. The season is also affected by the events of the film Captain America: Civil War (2016), and continues storylines established in the canceled series Agent Carter. The first episode premiered at a screening on September 19, 2016, with the season then airing for 22 episodes on ABC, from September 20, 2016, until May 16, 2017. The premiere debuted to 3.58 million viewers, down from previous season premieres but average for the series. Critical response to the season was positive, with many feeling that each pod was better than the last and in particular praising the visual effects and tone of Ghost Rider, the writing and acting of LMD, and the character development and political commentary explored during Agents of Hydra. The season saw series low viewership, but was still considered to have solved ABC's problem during its new Tuesday night timeslot, and the series was renewed for a fifth season in May 2017. == Episodes == == Cast and characters == == Production == === Development === Agents of S.H.I.E.L.D. was renewed for a fourth season on March 3, 2016, earlier than usual for the series. Executive producer Jed Whedon said on this, "We're thrilled to know going into the end of [season three] with certainty that we will be returning, because we can build our story accordingly." Executive producer Maurissa Tancharoen also noted that logistics for hiring directors for the season in advance would be easier, "which is a very nice privilege to have...that's a luxury". The end of the episode "What If..." features an onscreen tribute to Bill Paxton, who died in February 2017 and had portrayed John Garrett in the series' first season. The series paid additional tribute to Paxton in "All the Madame's Men" with promos during The Bakshi Report news segment showcasing John Garrett as a fallen American hero. The end of "World's End" features a similar onscreen tribute to Powers Boothe, who died in May 2017 and had portrayed Gideon Malick in the series' third season. === Writing === The season shifted to the later 10 pm timeslot, allowing it to take on a darker, more mature tone than previous seasons. According to Tancharoen, "The whole tagline for this year is 'Agents of S.H.I.E.L.D. After Dark'". The timeslot gave the series the opportunity to present an increased level of violence and partial nudity, as well as take more risks and present edgier themes. Following the third-season finale, Tancharoen stated that the fourth season would explore the guilt Daisy Johnson has over Lincoln Campbell's death. Executive producer Jeffrey Bell noted the writers tried to continue the tradition of "finding new combinations and new conflicts" between different sets of characters, given "a lot of procedurals [see] the same people doing the same thing for five years". Pairings that would be explored included Coulson and Mack, continuing from the end of season three, who have a mutual respect for one another due to their relationships with Daisy, and Leo Fitz and Holden Radcliffe, who work together. The Fitz-Simmons relationship was also explored more, examining the new challenges it presented for the two "working together, loving each other and living together". Following the third season's dealing with the themes of Captain America: Civil War (2016), such as the opposing reactions to the Inhumans, Whedon said that the question of "How do you deal with a war with powered people at that level, a government level?" was one that they wanted to answer in the fourth season. Tancharoen called the Inhumans "a permanent part of our universe now", with Whedon adding, "we have a quick-fire way of introducing people with powers. It gives us a lot of leeway in our world, and it lets us explore the metaphors of what it is like to be different. We will never close that chapter." With the Inhumans film being removed from Marvel Studios' release schedule, the series had "a little more freedom" and were "able to do a little bit more" with the species, including the potential of introducing some of the "classic" Inhumans, though the series would focus less on Inhumans than the third season which saw "a real significant Inhuman agenda story". It was not intended to be a spin-off of Agents of S.H.I.E.L.D. On the evolution of S.H.I.E.L.D. to featuring so many powered characters, Whedon said "the dynamic in the world has changed. There was one person with powers, and then by The Avengers there were maybe six total ... now they're much more prevalent, so there's reaction from the public based on that." The season is structured into three "pods" based on its airing schedule: the first eight episodes, subtitled Ghost Rider; LMD (Life Model Decoy) for the subsequent seven episodes; and a third pod for the final seven episodes called Agents of Hydra. Elements and characters cross over between the different pods, but the sections "definitely have a different feel" from one another, as Bell explained that 22 episodes "is a long time to hold a big bad or a single plot line, especially for an audience", and for the past two seasons, the series was able to have two separated halves that "allows us to introduce a big bad. And then, something happens and we rise somebody new ... Now, there's three of those." "Financial considerations" were also taken into account in creating the pods for the season, as using LMDs does not "cost as much as setting a guy's head on fire via CGI". In terms of writing the "complicated season", Whedon said the writers were "aware that our fans are our fans and have spent some time with these characters and are clever and see things coming sometimes ... Part of our job is to create not just what we are presenting on plot, but letting the audience be one step ahead of us and being one step ahead of that." He added that the writers knew that they wanted to tell a Ghost Rider story, an LMD story, and a "what if" scenario, and the hardest part was making each pod still fit together as a single season. The major connection ultimately became the Darkhold, which leads from the magic of Ghost Rider to the advanced science of LMD and then the Framework in Agents of Hydra. Ghost Rider also reappears in the final episode of the season, "World's End", as an additional connection. ==== Ghost Rider ==== While planning the fourth season, Marvel suggested that the series introduce Ghost Rider, after the character's film rights had returned to Marvel from Sony in May 2013. Loeb felt that this made the season unquestionably "the series' biggest" with the "most ambitious story yet". He added that "one of the things that we talked about is, S.H.I.E.L.D. always looked out for the weird, the unusual, the things that were and could be a problem for the public", and Marvel realized that Ghost Rider's abilities, which are more mystical than anything seen in the series to date, opened up "a quarter of the universe that we haven't really spent a lot of time exploring ... what happens if our very real, our very grounded agents who are very much a family have to take on something that is as bizarre and powerful and unique as Ghost Rider." Bell added that the producers would have been willing to give an entire season of the show to a Ghost Rider arc if the season was 13 episodes or less, but 22 episodes seemed too long to "feel like one flavor". The Robbie Reyes version of Ghost Rider was chosen over other versions of the character from the comics because of his relationship with his brother Gabe, w

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  • The 100 (TV series)

    The 100 (TV series)

    The 100 (pronounced "The Hundred" ) is an American post-apocalyptic science fiction drama television series that premiered on March 19, 2014, on the CW network, and ended on September 30, 2020. Developed by Jason Rothenberg, the series is based on the young adult novel series The 100 by Kass Morgan. The 100 follows descendants of post-apocalyptic survivors from a space habitat, the Ark, who return to Earth nearly a century after a devastating nuclear apocalypse; the first people sent to Earth are a group of juvenile delinquents who encounter another group of survivors on the ground. The juvenile delinquents include Clarke Griffin (Eliza Taylor), Finn Collins (Thomas McDonell), Bellamy Blake (Bob Morley), Octavia Blake (Marie Avgeropoulos), Jasper Jordan (Devon Bostick), Monty Green (Christopher Larkin), and John Murphy (Richard Harmon). Other lead characters include Clarke's mother Dr. Abby Griffin (Paige Turco), Marcus Kane (Henry Ian Cusick), and Chancellor Thelonious Jaha (Isaiah Washington), all of whom are council members on the Ark, and Raven Reyes (Lindsey Morgan), a mechanic aboard the Ark. == Plot == Ninety-seven years after a devastating nuclear apocalypse wipes out most human life on Earth, thousands of people now live in a space station orbiting Earth, which they call the Ark. Three generations have been born in space, but when life-support systems on the Ark begin to fail, one hundred juvenile detainees are sent to Earth in a last attempt to determine whether it is habitable, or at least save resources for the remaining residents of the Ark. They discover that some humans survived the apocalypse: the Grounders, who live in clans locked in a power struggle; the Reapers, another group of grounders who have been turned into cannibals by the Mountain Men; and the Mountain Men, who live in Mount Weather, descended from those who locked themselves away before the apocalypse. Under the leadership of Clarke and Bellamy, the juveniles attempt to survive the harsh surface conditions, battle hostile grounders and establish communication with the Ark. In the second season, the survivors face a new threat from the Mountain Men, who harvest their bone marrow to survive the radiation. Clarke and the others form a fragile alliance with the grounders to rescue their people. The season ends with Clarke making a devastating choice to save them all. In season three, power struggles erupt between the Arkadians and the grounders after a controversial new leader takes charge. Meanwhile, an AI named A.L.I.E., responsible for the original apocalypse, begins taking control of people’s minds. Clarke destroys A.L.I.E. but learns another disaster is imminent. In the fourth season, nuclear reactors are melting down, threatening to wipe out life again. Clarke and her friends search for ways to survive, including experimenting with radiation-resistant blood and finding an underground bunker. As time runs out, only a select few are able to take shelter. The fifth season picks up six years later, when Earth is left largely uninhabitable except for one green valley, where new enemies arrive. Clarke protects her adopted daughter Madi while former survivors return from space and underground, triggering another war. The battle ends with the valley destroyed and the group entering cryosleep to find a new home. In season six, the group awakens 125 years later on a new planet called Sanctum, ruled by powerful families known as the Primes. Clarke fights to stop body-snatching rituals and protect her people from new threats, including a rebel group and a dangerous AI influence. The season ends with major losses and the destruction of the Primes' rule. In the seventh and final season, the survivors face unrest on Sanctum and clash with a mysterious group called the Disciples, who believe Clarke is key to saving humanity. A wormhole network reveals multiple planets and a final "test" that determines the fate of the species. Most transcend into a higher consciousness, but Clarke and a few others choose to live out their lives on a reborn Earth. == Cast and characters == Eliza Taylor as Clarke Griffin Paige Turco as Abigail "Abby" Griffin (seasons 1–6; guest season 7) Thomas McDonell as Finn Collins (seasons 1–2) Eli Goree as Wells Jaha (season 1; guest season 2) Marie Avgeropoulos as Octavia Blake Bob Morley as Bellamy Blake Kelly Hu as Callie "Cece" Cartwig (season 1) Christopher Larkin as Monty Green (seasons 1–5; guest season 6) Devon Bostick as Jasper Jordan (seasons 1–4) Isaiah Washington as Thelonious Jaha (seasons 1–5) Henry Ian Cusick as Marcus Kane (seasons 1–6) Lindsey Morgan as Raven Reyes (seasons 2–7; recurring season 1) Ricky Whittle as Lincoln (seasons 2–3; recurring season 1) Richard Harmon as John Murphy (seasons 3–7; recurring seasons 1–2) Zach McGowan as Roan (season 4; recurring season 3; guest season 7) Tasya Teles as Echo / Ash (seasons 5–7; guest seasons 2–3; recurring season 4) Shannon Kook as Jordan Green (seasons 6–7; guest season 5) JR Bourne as Russell Lightbourne / Malachi / Sheidheda (season 7; recurring season 6) Chuku Modu as Gabriel Santiago (season 7; recurring season 6) Shelby Flannery as Hope Diyoza (season 7; guest season 6) =

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  • With Folded Hands ...

    With Folded Hands ...

    "With Folded Hands ..." is a 1947 science fiction novelette by American writer Jack Williamson (1908–2006). In writing it, Williamson was influenced by the aftermath of World War II, the atomic bombings of Hiroshima and Nagasaki, and his concern that "some of the technological creations we had developed with the best intentions might have disastrous consequences in the long run." The novelette first appeared in the July 1947 issue of Astounding Science Fiction and was later included in The Science Fiction Hall of Fame, Volume Two (1973) after being voted one of the best novellas up to 1965. In 1950, it was the first of several Astounding stories adapted for NBC's radio series Dimension X. == Rewrite and sequel == The 1947 publication was followed by a novel-length rewrite, with a different setting and inventor. At the behest of Astounding editor-in-chief John W. Campbell, a new ending had the robots defeated by means of what Williamson and Campbell would later christen "psionics". This novel was serialized, also in Astounding (March, April, May 1948), as ... And Searching Mind, and finally published in hardback book form as The Humanoids (1949). Much later, in 1980, Williamson followed with another sequel, The Humanoid Touch. == Plot summary == Underhill, a seller of "Mechanicals" (unthinking robots that perform menial tasks) in the small town of Two Rivers, is startled to find a competitor's store on his way home. The competitors are not humans but are small black robots who appear more advanced than anything Underhill has encountered before. They describe themselves as "humanoids". Disturbed at his encounter, Underhill rushes home to discover that his wife has taken in a new lodger, a mysterious old man named Sledge. In the course of the next day, the new Mechanicals have appeared everywhere in town. They state that they only follow the Prime Directive: "to serve and obey and guard men from harm". Offering their services free of charge, they replace humans as police officers, bank tellers, and more, and eventually drive Underhill out of business. Despite the humanoids' benign appearance and mission, Underhill soon realizes that, in the name of their Prime Directive, the mechanicals have essentially taken over every aspect of human life. No humans may engage in any behavior that might endanger them, and every human action is carefully scrutinized. Suicide is prohibited. Humans who resist the Prime Directive are taken away and lobotomized, so that they may live happily under the direction of the humanoids. Underhill learns that his lodger Sledge is the creator of the humanoids and is on the run from them. Sledge explains that 60 years earlier he had discovered the force of "rhodomagnetics" on the planet Wing IV and that his discovery resulted in a war that destroyed his planet. In his grief, Sledge designed the humanoids to help humanity and be invulnerable to human exploitation. However, he eventually realized that they had instead taken control of humanity, in the name of their Prime Directive, to make humans happy. The humanoids are spreading out from Wing IV to every human-occupied planet to implement their Prime Directive. Sledge and Underhill attempt to stop the humanoids by aiming a rhodomagnetic beam at Wing IV, but fail. The humanoids take Sledge away for surgery. He returns with no memory of his prior life, stating that he is now happy under the humanoids' care. Underhill is driven home by the humanoids, sitting "with folded hands," as there is nothing left to do. == Origins == In a 1991 interview, Williamson revealed how the story construction reflected events of his childhood in addition to technological extrapolations: I wrote "With Folded Hands" immediately after World War II, when the shadow of the atomic bomb had just fallen over SF and was just beginning to haunt the imaginations of people in the US. The story grows out of that general feeling that some of the technological creations we had developed with the best intentions might have disastrous consequences in the long run (that idea, of course, still seems relevant today). The notion I was consciously working on specifically came out of a fragment of a story I had worked on for a while about an astronaut in space who is accompanied by a robot obviously superior to him physically—i.e., the robot wasn't hurt by gravity, extremes of temperature, radiation, or whatever. Just looking at the fragment gave me the sense of how inferior humanity is in many ways to mechanical creations. That basic recognition was the essence of the story, and as I wrote it up in my notes the theme was that the perfect machine would prove to be perfectly destructive... It was only when I looked back at the story much later on that I was able to realize that the emotional reach of the story undoubtedly derived from my own early childhood, when people were attempting to protect me from all those hazardous things a kid is going to encounter in the isolated frontier setting I grew up in. As a result, I felt frustrated and over protected by people whom I couldn't hate because I loved them. A sort of psychological trap. Specifically, the first three years of my life were spent on a ranch at the top of the Sierra Madre Mountains on the headwaters of the Yaqui River in Sonora, Mexico. ... [My mother] was terrified by this environment. My father built a crib that became a psychological prison for me, particularly because my mother apparently kept me in it too long, when I needed to get out and crawl on the floor. ... In retrospect, I'm certain I projected my fears and suspicions of this kind of conditioning, and these projections became the governing emotional principle of "With Folded Hands" and The Humanoids. == Reception == In 2024, Robert Silverberg wrote an essay in which he asserted that "With Folded Hands..." is "probably the best story ever written about robots" and suggested that Elon Musk's Optimus Generation 2 is the realization of the "humanoids" along with their worst drawbacks.

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  • Carrenza

    Carrenza

    Carrenza was a cloud-computing company based in London, United Kingdom. The company was acquired by Six Degrees Technology Group in 2016. == Operations == Carrenza was a UK-based IT company that provides Cloud computing technologies. It offered a range of public cloud, private cloud and hybrid cloud services, including Infrastructure as a Service (IaaS), Platform as a Service (PaaS), enterprise application integration and system integration. Carrenza partnered with several enterprise IT providers and was an accredited VMware Enterprise Service Partner and HP (Hewlett-Packard) Cloud Agile Partner. The company was based on Commercial Street, in the heart of the East London Tech City district, which is host to a large number of technology companies. == History == Carrenza was formed in 2001 as a consultancy by chief executive and founder Dan Sutherland. It began trading in 2004 and launched its first enterprise cloud computing platform in 2006, becoming one of the first companies in Europe to provide this type of hosting service. In 2009, it formed a partnership with Comic Relief and its affiliated campaigns Red Nose Day Sport Relief to provide IT infrastructure services to the charity, an arrangement that has won industry recognition. In 2013 it launched its first overseas services, with a mainland Europe cloud node based in Amsterdam. == Partnerships and customers == Carrenza had formed partnerships with a range of IT providers. It was one of the first companies in Europe to become a HP Cloud Agile partner., using HP blade servers and HP 3PAR SAN technology to power its cloud computing services. The company's products also use VMware vCloud IaaS tools and it is taking part in the VMware lighthouse initiative helping develop the next generation of VMware products and services. Other technology companies that Carrenza has worked closely with include Cisco, for enterprise security and loadblancing services, and Oracle. The company was the first to deploy Oracle Database 11g stretched RAC in production. It has also won two Oracle partner awards, including a Special Recognition award for its work with Comic Relief. The company has also been recognised by the UK IT Industry, receiving awards in 2009 for Community Project of the Year and in 2010 for best small business project for its Monopoly City Streets Work. Other companies that have partnered with Carrenza for their cloud-based IT services include Age UK, Haymarket Media Group, the World Wide Fund for Nature, Royal Bank of Scotland, eBay and Cineworld. == Accreditations == Carrenza's services are accredited for their compliance with several key international IT security and quality standards. These include: ISO27001:2005, Information Security Management System for all Carrenza services. UK Government G-Cloud, Carrenza has been awarded a place on the UK government's G-Cloud iii framework as an Infrastructure as a Service provider.

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  • The Sword in the Stoned

    The Sword in the Stoned

    "The Sword in the Stoned" is the fifth episode of the second season of the American fantasy comedy television series Ted. Written by Julius Sharpe, and directed by Seth MacFarlane, it premiered on the American streaming service Peacock, along with the rest of season two, on March 5, 2026. The series acts as a precursor to the Ted film franchise, showcasing the childhood lives of the protagonists. The series, set in 1994, focuses on John Bennett (Max Burkholder), the series' primary protagonist, an awkward high-school aged boy; along with Ted (MacFarlane), the series' titular anthropomorphic teddy bear. The two live with John's family, Susan (Alanna Ubach), his mild mannered mother, and Matty (Scott Grimes), his conservative father. Also residing with the family is Blaire (Giorgia Whigham), his radically liberal cousin whom often clashes with Matty. In the episode, Ted and John join the school play so they can have more extracurricular activities for their college applications, but the latter grows a connection with the school's popular teenager, Erin (Francesca Xuereb). Concurrently, Susan and Matty get a job at Dunkin' Donuts to help with their financial troubles, and Matty is given an opportunity to tell off Bill Clinton. Burkholder wore prop armor during the episode's play scenes. Bill Clinton’s appearance in the episode was portrayed by MacFarlane. After conventional makeup and visual techniques failed to convincingly resemble Clinton, the production used artificial intelligence to digitally replace MacFarlane's face with Clinton's likeness. Upon release, the episode received generally positive reviews from critics, though the use of AI in the Clinton scene was polarizing among audiences and reviewers. == Plot == John tells Ted that he is the last single guy left at their school, to which Ted points out the popular, single cheerleader, Erin, but John dismisses this. At home, Blaire tells John that he needs extracurricular activities to get into college, while Susan and Matty discuss their financial troubles, especially regarding John's college tuition. Looking over their options, they decide to audition for a school production of the play Camelot. Matty takes a job at Dunkin' Donuts, despite being told that nobody will give him a tip, and having to wear an incorrect name tag. Waiting for their auditions, John and Ted watch several poor auditions for the play before seeing Erin's, who delivers a flawless performance; John and Ted do less serious auditions, getting cast as knights, while Erin gets the role of Guinevere. Matty complains about his low salary, and Susan decides to get a job at Dunkin' Donuts beside him to help earn more income. Erin clashes with Lancelot's actor while rehearsing, and John compliments her performance, which she ignores, but, seeing Ted and John give good performances in a repetition exercise, she becomes interested in him, particularly since he treats her better than her stage-partner. Matty and Susan watch an employee training video, explaining how they should treat customers politely, not affecting Matty's nihilistic attitude. The manager announces that Bill Clinton is visiting their Dunkin' Donuts for publicity, and Matty sees this as a chance to tell Bill off. John and Erin practice lines, as she reveals the show is being taped so it can be sent to Emerson College in hopes of her getting in; Erin asks John to go out with her after the show. At dinner, Matty enthusiastically reveals what he plans to tell Bill, as John becomes stressed about the play when Susan tells there will be a large audience. Bill comes to the Dunkin' Donuts, and, seeing Matty is nervously insulting him, stages a private meeting with him, where Bill yells at Matty, calling him a loser before posing for a picture with Matty and subsequently throwing the cold coffee onto him. To ease the pressure, Ted and John take edibles from Blaire, but learn at the show that they contained mushrooms, causing them to stress further. On stage, Ted and John yell nervously that they're on drugs as the latter urinates in his costume, causing Erin to angrily storm off. == Production == "The Sword in the Stoned" was directed by series creator and lead Seth MacFarlane, and written by Julius Sharpe in his third and final writing credit for the series. When Ted and John are doing repetition exercises, they tackle each other to the ground, which required a stuntman named Ashton to play the role of Ted, according to Max Burkholder, who portrays John. Burkholder also recalled that, when Ted was choking John in the scene, he kept making a noise during the choking, which made Bill, the cameraman, laugh, despite being a "stone face" that never laughs, noting that seeing him be amused by the noise he was making assured Burkholder that what he was doing was "hilarious". Burkholder found the filming of the play scenes "weird", as he was put in fake armor with a hose inside his suit—which was filled with water mixed with yellow food coloring—that was made to create the urine stream that comes out of John's armor in the episode; he also noted that it took around 45 minutes to put on and take off the armor. He revealed that he himself had to urinate during the filming, as doing a scene about a character having to do so "really [broke] my brain", with the fact that it took 45 minutes to get the suit off adding to the frustration. Jennifer Ashley Connell, who worked for wardrobe, had to repeatedly go to Burkholder quickly between takes to dry off his pants with two hair dryers to make it look like the fake urine hadn't already streamed down his pants, so they could get as many shots of it as possible. Francesca Xuereb guest stars in the episode as Erin, the cheerleader who stars in the play. Incumbent president Bill Clinton was portrayed by MacFarlane, with artificial intelligence (AI) being used to digitally make MacFarlane's face look like Clinton's during post-production. Before settling on AI, the crew tried to use traditional computer-generated imagery and prosthetics, which made him look "terrifying", resulting in them deciding that AI would give them a more accurate look. One of the original technologies considered was one where, after scanning MacFarlane, a mesh of his head was created, and they had to use computer graphics to replace MacFarlane's face with Clinton's. An issue was faced, however, when they found the archival footage used as reference from the Clinton Library—an official Presidential Library containing information related to Clinton—to be extremely low-quality, making it hard to properly emulate his face, since only still images were of acceptable quality, and there weren't references of his moving face to work off of. A forensic artist was hired to help with this, and they created a 3D model of Clinton's head in ZBrush, based off of his presidential portrait. The model head worked for still frames, but movement was still difficult to do realistically, due to it being made for a "single-point perspective", which made details like the cheekbones or other minor issues more noticeable when using it for the scene. Since this did not work, AI was ultimately chosen through the studio Deep Voodoo, which used large language models to teach the tool how to correctly replicate Clinton's appearance. Defending the episode's use of AI, MacFarlane noted that the crew did not want people to focus on the tool being used, trying to utilize it in a way that wouldn't distract from the humor and narrative. Like the rest of the series, the episode was shot using ViewScreen; MacFarlane was able to act live with the cast as Ted due to ViewScreen, a technology that allows the production crew to visualize what Ted will look like in each scene in real time. == Release and reception == "The Sword in the Stoned" was first released on March 5, 2026, on the American streaming service Peacock, along with the rest of the second season. Nate Richards of Collider highlighted the Dunkin' Donuts subplot as an example of Scott Grimes delivering a "lot of laughs" through his performance as Matty. Dustin Rowles of Pajiba called "The Sword in the Stoned" one of the season's many episodes he'd recommend, particularly for the scenes of Ted and John being high on mushrooms during the play. Oppositely, Nick Valdez of ComicBook.com ranked the episode as the worst of the second season, criticizing it for not having a "huge impact" on the Bennett family dynamic like other episodes of the season do, and Susan and Matty's side story as the main reason he felt it was "[kept] from being great". Valdez noted the episode for likely being an advertisement for Dunkin' Donuts, calling the plot's ending scene involving Clinton the reason "it just all sticks out like a sore thumb". === Response to AI usage === The episode's use of AI for MacFarlane's portrayal of Clinton proved controversial, mainly on social media, where audiences asserted that the crew should have gotten an actor that resembl

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  • Fuzzy pay-off method for real option valuation

    Fuzzy pay-off method for real option valuation

    The fuzzy pay-off method for real option valuation (FPOM or pay-off method) is a method for valuing real options, developed by Mikael Collan, Robert Fullér, and József Mezei; and published in 2009. It is based on the use of fuzzy logic and fuzzy numbers for the creation of the possible pay-off distribution of a project (real option). The structure of the method is similar to the probability theory based Datar–Mathews method for real option valuation, but the method is not based on probability theory and uses fuzzy numbers and possibility theory in framing the real option valuation problem. == Method == The Fuzzy pay-off method derives the real option value from a pay-off distribution that is created by using three or four cash-flow scenarios (most often created by an expert or a group of experts). The pay-off distribution is created simply by assigning each of the three cash-flow scenarios a corresponding definition with regards to a fuzzy number (triangular fuzzy number for three scenarios and a trapezoidal fuzzy number for four scenarios). This means that the pay-off distribution is created without any simulation whatsoever. This makes the procedure easy and transparent. The scenarios used are a minimum possible scenario (the lowest possible outcome), the maximum possible scenario (the highest possible outcome) and a best estimate (most likely to happen scenario) that is mapped as a fully possible scenario with a full degree of membership in the set of possible outcomes, or in the case of four scenarios used - two best estimate scenarios that are the upper and lower limit of the interval that is assigned a full degree of membership in the set of possible outcomes. The main observations that lie behind the model for deriving the real option value are the following: The fuzzy NPV of a project is (equal to) the pay-off distribution of a project value that is calculated with fuzzy numbers. The mean value of the positive values of the fuzzy NPV is the "possibilistic" mean value of the positive fuzzy NPV values. Real option value, ROV, calculated from the fuzzy NPV is the "possibilistic" mean value of the positive fuzzy NPV values multiplied with the positive area of the fuzzy NPV over the total area of the fuzzy NPV. The real option formula can then be written simply as: R O V = A ( P o s ) A ( P o s ) + A ( N e g ) × E [ A + ] {\displaystyle \mathrm {ROV} ={\frac {A(\mathrm {Pos} )}{A(\mathrm {Pos} )+A(\mathrm {Neg} )}}\times E[A_{+}]} where A(Pos) is the area of the positive part of the fuzzy distribution, A(Neg) is the area of the negative part of the fuzzy distribution, and E[A+] is the mean value of the positive part of the distribution. It can be seen that when the distribution is totally positive, the real options value reduces to the expected (mean) value, E[A+]. As can be seen, the real option value can be derived directly from the fuzzy NPV, without simulation. At the same time, simulation is not an absolutely necessary step in the Datar–Mathews method, so the two methods are not very different in that respect. But what is totally different is that the Datar–Mathews method is based on probability theory and as such has a very different foundation from the pay-off method that is based on possibility theory: the way that the two models treat uncertainty is fundamentally different. == Use of the method == The pay-off method for real option valuation is very easy to use compared to the other real option valuation methods and it can be used with the most commonly used spreadsheet software without any add-ins. The method is useful in analyses for decision making regarding investments that have an uncertain future, and especially so if the underlying data is in the form of cash-flow scenarios. The method is less useful if optimal timing is the objective. The method is flexible and accommodates easily both one-stage investments and multi-stage investments (compound real options). The method has been taken into use in some large international industrial companies for the valuation of research and development projects and portfolios. In these analyses triangular fuzzy numbers are used. Other uses of the method so far are, for example, R&D project valuation IPR valuation, valuation of M&A targets and expected synergies, valuation and optimization of M&A strategies, valuation of area development (construction) projects, valuation of large industrial real investments. The use of the pay-off method is lately taught within the larger framework of real options, for example at the Lappeenranta University of Technology and at the Tampere University of Technology in Finland.

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