AI Art Prints

AI Art Prints — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  Microsoft Teams

  Microsoft Teams is a team collaboration platform developed by Microsoft as part of the Microsoft 365 suite. It offers features such as workspace chat, video conferencing, file storage, and integration with both Microsoft and third-party applications and services. Teams gradually replaced earlier Microsoft messaging and collaboration platforms, including Skype for Business, Skype, Flip, and Microsoft Classroom. The platform saw significant growth during the COVID-19 pandemic, alongside competitors such as Zoom, Slack, and Google Meet, as organizations shifted to remote work and virtual meetings. As of January 2023, Microsoft reported approximately 280 million monthly active users. == History == On August 29, 2007, Microsoft acquired Parlano, the developer of the persistent group chat tool MindAlign. Years later, on March 4, 2016, Microsoft considered acquiring Slack for $8 billion. However, the proposal was reportedly opposed by Bill Gates, who advocated for focusing on enhancing Skype for Business instead. Lu Qi, then executive vice president of Applications and Services, had led the initiative to pursue the Slack acquisition. Following Lu's departure later that year, Microsoft announced Microsoft Teams on November 2, 2016, at an event in New York City, positioning it as a direct competitor to Slack. Teams launched worldwide on March 14, 2017. The service was initially led by corporate vice president Brian MacDonald. In response to the launch, Slack published a full-page advertisement in The New York Times welcoming the competition and outlining its product philosophy. Although Slack was used by 28 companies in the Fortune 100, The Verge wrote that executives would question paying for the service if Teams provides a similar function in their company's existing Office 365 subscription. However, ZDNET noted that the platforms initially served different markets, as Teams did not support external users, making it less appealing to small businesses and freelancers, a limitation Microsoft later addressed. In response to Teams' announcement, Slack deepened in-product integration with Google services. In May 2017, Microsoft announced that Teams would replace Microsoft Classroom in Office 365 Education. A free version of Teams was released on July 12, 2018, offering most core features at no cost, albeit with limits on users and storage. In January 2019, Microsoft introduced updates targeting "Firstline Workers" to improve Teams’ performance across shared or limited-access devices. In September 2019, Microsoft announced the retirement of Skype for Business in favor of Teams, which took effect on July 31, 2021. In early 2020, Microsoft introduced a push-to-talk "Walkie Talkie" feature aimed at firstline workers using smartphones and tablets over Wi-Fi or cellular networks. The COVID-19 pandemic significantly boosted usage of Teams. On March 19, 2020, Microsoft reported 44 million daily active users. In April, the platform logged 4.1 billion meeting minutes in a single day. A public preview of Microsoft Teams for Linux was released in December 2019, but the Linux client was discontinued in 2022. In July 2020, Microsoft shut down its video game livestreaming platform Mixer, and announced that some of its technologies would be repurposed for use in Teams. On February 28, 2025, Microsoft announced that Skype would be fully retired on May 5, 2025, with users given options to export their data or transition to Microsoft Teams. In October 2025, together with other Microsoft 365 suite apps, Teams had its logo updated. == Usage == == Underlying software == Microsoft Teams, as part of the Microsoft 365 suite, utilizes SharePoint and Exchange Online. Each Team, Shared Channel, and Private Channel has its own Microsoft 365 Group and SharePoint Site used for file storage. Messages are stored in Cosmos DB and are journaled to Exchange Online mailboxes. Private messages, including messages in Private Channels, are journaled to the sender and recipients' mailboxes. Public Channel messages are journaled to their corresponding Team's group mailbox, whereas, messages from Shared Channels are journaled to their own mailboxes. Contacts and voicemail are stored in Exchange Online. Microsoft Teams client is a web-based desktop app, originally developed on top of the Electron framework which combines the Chromium rendering engine and the Node.js JavaScript platform. Version 2.0 client was rebuilt using the Evergreen version of Microsoft Edge WebView2 in place of Electron. == Features == === Chats === Teams allows users to communicate in two-way persistent chats with one or multiple participants. Participants can message using text, emojis, stickers and gifs, as well as sharing links and files. In August 2022, the chat feature was updated for "chat with yourself"; allowing for the organization of files, notes, comments, images, and videos within a private chat tab. === Teams === Teams allows communities, groups, or teams to contribute in a shared workspace where messages and digital content on a specific topic are shared. Team members can join through an invitation sent by a team administrator or owner or sharing of a specific URL. Teams for Education allows admins and teachers to set up groups for classes, professional learning communities (PLCs), staff members, and everyone. === Channels === Channels allow team members to communicate without the use of email or group SMS (texting). Users can reply to posts with text, images, GIFs, and image macros. Direct messages send private messages to designated users rather than the entire channel. Connectors can be used within a channel to submit information contacted through a third-party service. Connectors include Mailchimp, Facebook Pages, Twitter, Power BI and Bing News. === Group conversations === Ad-hoc groups can be created to share instant messaging, audio calls (VoIP), and video calls inside the client software. === Telephone replacement === A feature on one of the higher cost licencing tiers allows connectivity to the public switched telephone network (PSTN) telephone system. This allows users to use Teams as if it were a telephone, making and receiving calls over the PSTN, including the ability to host "conference calls" with multiple participants. === Meeting === Meetings can be scheduled with multiple participants able to share audio, video, chat and presented content with all participants. Multiple users can connect via a meeting link. Automated minutes are possible using the recording and transcript features. Teams has a plugin for Microsoft Outlook to schedule a Teams Meeting in Outlook for a specific date and time and invite others to attend. If a meeting is scheduled within a channel, users visiting the channel are able to see if a meeting is in progress. ==== Teams Live Events ==== Teams Live Events replaces Skype Meeting Broadcast for users to broadcast to 10,000 participants on Teams, Yammer, or Microsoft Stream. ==== Breakout Rooms ==== Breakout rooms split a meeting into small groups. This is often utilized for collaboration during trainings or any environment where having all participants speak at once could be disruptive or unfeasible. Breakout rooms can be set by the hosts to a certain length of time, after which all participants will automatically rejoin the main meeting room. ==== Front Row ==== Front Row adjusts the layout of the viewer's screen, placing the speaker or content in the center of the gallery with other meeting participant's video feeds reduced in size and located below the speaker. === Education === Microsoft Teams for Education allows teachers to distribute, provide feedback, and grade student assignments turned in via Teams using the Assignments tab through Office 365 for Education subscribers. Quizzes can also be assigned to students through an integration with Office Forms. === Protocols === Microsoft Teams is based on a number of Microsoft-specific protocols. Video conferences are realized over the protocol MNP24, known from the Skype consumer version. VoIP and video conference clients based on SIP and H.323 need special gateways to connect to Microsoft Teams servers. With the help of Interactive Connectivity Establishment (ICE), clients behind Network address translation routers and restrictive firewalls are also able to connect, if peer-to-peer is not possible. === Integrations === Microsoft Teams has integrations through Microsoft AppSource, its integration marketplace. In 2020, Microsoft partnered with KUDO, a cloud-based solution with language interpretation, to allow integrated language meeting controls. In June 2022, an update was released using AI to improve call audio through the elimination of background feedback loops and cancelling non-vocal audio. == Anti-trust controversy == In July 2023, the European Commission opened an anti-trust investigation into the possibility that Microsoft unfairly used its office suite market power to increase sales of Teams and hurt

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  Artificial intelligence in spirituality

  Some users of artificial intelligence (AI) technologies, especially chatbots, may develop beliefs that AI has or can attain supernatural or spiritual powers. AI models such as ChatGPT are turned to for fortune telling, mysticism and remote viewing. Recent and sudden advances in large language models have led to folk myths about their origin or capabilities, as well as their deification or worship by some users. Tucker Carlson has made similar claims, including directly to Sam Altman. Pope Leo XIV advised priests against using LLM models when it came to the creation of sermons.

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  Virtual intelligence

  Virtual intelligence (VI) is the term given to artificial intelligence that exists within a virtual world. Many virtual worlds have options for persistent avatars that provide information, training, role-playing, and social interactions. The immersion in virtual worlds provides a platform for VI beyond the traditional paradigm of past user interfaces (UIs). What Alan Turing established as a benchmark for telling the difference between human and computerized intelligence was devoid of visual influences. With today's VI bots, virtual intelligence has evolved past the constraints of past testing into a new level of the machine's ability to demonstrate intelligence. The immersive features of these environments provide nonverbal elements that affect the realism provided by virtually intelligent agents. Virtual intelligence is the intersection of these two technologies: Virtual environments: Immersive 3D spaces provide for collaboration, simulations, and role-playing interactions for training. Many of these virtual environments are currently being used for government and academic projects, including Second Life, VastPark, Olive, OpenSim, Outerra, Oracle's Open Wonderland, Duke University's Open Cobalt, and many others. Some of the commercial virtual worlds are also taking this technology into new directions, including the high-definition virtual world Blue Mars. Artificial intelligence (AI): AI is a branch of computer science that aims to create intelligent machines capable of performing tasks that typically require human intelligence. VI is a type of AI that operates within virtual environments to simulate human-like interactions and responses. == Applications == Cutlass Bomb Disposal Robot: Northrop Grumman developed a virtual training opportunity because of the prohibitive real-world cost and dangers associated with bomb disposal. By replicating a complicated system without having to learn advanced code, the virtual robot has no risk of damage, trainee safety hazards, or accessibility constraints. MyCyberTwin: NASA is among the companies that have used the MyCyberTwin AI technologies. They used it for the Phoenix rover in the virtual world Second Life. Their MyCyberTwin used a programmed profile to relay information about what the Phoenix rover was doing and its purpose. Second China: The University of Florida developed the "Second China" project as an immersive training experience for learning how to interact with the culture and language in a foreign country. Students are immersed in an environment that provides role-playing challenges coupled with language and cultural sensitivities magnified during country-level diplomatic missions or during times of potential conflict or regional destabilization. The virtual training provides participants with opportunities to access information, take part in guided learning scenarios, communicate, collaborate, and role-play. While China was the country for the prototype, this model can be modified for use with any culture to help better understand social and cultural interactions and see how other people think and what their actions imply. Duke School of Nursing Training Simulation: Extreme Reality developed virtual training to test critical thinking with a nurse performing trained procedures to identify critical data to make decisions and performing the correct steps for intervention. Bots are programmed to respond to the nurse's actions as the patient with their conditions improving if the nurse performs the correct actions.

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  STIT logic

  STIT logic (from seeing to it that) is a family of modal and branching-time logics for reasoning about agency and choice. A typical STIT operator has the form [ i s t i t : φ ] {\displaystyle [i\ {\mathsf {stit}}:\varphi ]} , usually read as "agent i {\displaystyle i} sees to it that φ {\displaystyle \varphi } ", and is interpreted in models where agents choose between alternative possible futures. STIT logics are used in action theory, deontic logic, epistemic logic, and the theory of intelligent agents to formalise notions such as "could have done otherwise", responsibility, joint action, and strategic ability in an indeterministic world. == Etymology == The acronym STIT comes from the English phrase "seeing to it that", introduced in influential work by Nuel Belnap and Michael Perloff on the logical analysis of agentive expressions. In this tradition, "to see to it that φ {\displaystyle \varphi } " is treated as a primitive agency operator, rather than being reduced to ordinary modal necessity. == History == Modern STIT logic arose in the 1980s in the context of branching-time semantics and formal theories of agency. Belnap and Perloff's article "Seeing to it that: A canonical form for agentives" introduced the idea of treating expressions of the form "agent i sees to it that φ" as a primitive modal operator, and analysed such sentences using a branching tree of moments and histories. This approach was further developed in a series of papers on indeterminism and agency and provided the conceptual core for later STIT formalisms. In the 1990s the basic formal systems of STIT logic were worked out. Horty and Belnap's influential paper on the deliberative STIT operator distinguished between a "Chellas" STIT that merely records the result of an agent's present choice and a "deliberative" STIT that requires the agent's choice to make a difference, and connected STIT with issues of action, omission, ability and obligation. Around the same time, Ming Xu proved completeness and decidability results for basic STIT systems, including a single-agent logic with Kripke-style semantics and axiomatizations for multi-agent deliberative STIT, thereby establishing STIT as a well-behaved normal modal framework. This early work was systematised in Belnap, Perloff and Xu's monograph Facing the Future: Agents and Choices in Our Indeterminist World, which presents a general branching-time semantics for individual and group STIT operators, discusses independence-of-agents conditions and articulates the metaphysical picture of an indeterministic "tree" of moments. At roughly the same time, Horty's book Agency and Deontic Logic developed deontic STIT logics in which obligations are tied to agents' available choices rather than to static states of affairs, and used the resulting systems to analyse "ought implies can", contrary-to-duty obligations and deontic paradoxes. These works helped to position STIT at the intersection of action theory, temporal logic and deontic logic. From the late 1990s and 2000s onward, STIT logics were combined with epistemic, temporal and strategic modalities. Broersen introduced complete STIT logics for knowledge and action and deontic-epistemic STIT systems that distinguish different modes of mens rea, with applications to responsibility and the specification of multi-agent systems. Work on group and coalitional agency investigated axiomatisations and complexity results for group STIT logics, and related STIT-based analyses of agency to coalition logic and alternating-time temporal logic (ATL) by exhibiting formal embeddings between the frameworks. Explicit temporal operators were added to STIT in so-called temporal STIT logics. Lorini proposed a temporal STIT with "next" and "until" operators along histories and showed how it can be applied to normative reasoning about ongoing behaviour and commitments. Ciuni and Lorini compared different semantics for temporal STIT, clarifying the relationships between branching-time, game-based and epistemic approaches, while Boudou and Lorini gave a semantics for temporal STIT based on concurrent game structures, thus strengthening links with standard models of multi-agent interaction used for ATL and strategy logic. In parallel, complexity-theoretic work by Balbiani, Herzig and Troquard and by Schwarzentruber and co-authors investigated the satisfiability and model-checking problems for various STIT fragments, showing for instance that many expressive group STIT logics are undecidable or of high computational complexity. In the 2010s, STIT ideas were combined with justification logic, imagination operators and refined deontic notions. Justification STIT logics, developed by Olkhovikov and others, merge explicit justifications with STIT-style agency so that producing a proof can itself be treated as an action that brings about knowledge, and they come with completeness and decidability results. Olkhovikov and Wansing introduced STIT imagination logics, together with axiomatic systems and tableau calculi, to model acts of voluntary imagining and their role in doxastic control. Other authors have proposed STIT-based logics of responsibility, blameworthiness and intentionality for use in philosophical and AI settings. Xu's survey article "Combinations of STIT with Ought and Know" (2015) reviews many of these developments and emphasises the interplay between deontic and epistemic STIT logics. Current research on STIT focuses on proof theory, automated reasoning and richer expressive resources. Lyon and van Berkel, building on earlier work on labelled calculi for STIT, have developed cut-free sequent systems and proof-search algorithms that yield syntactic decision procedures for a range of deontic and non-deontic multi-agent STIT logics and support applications such as duty checking and compliance checking in autonomous systems. Sawasaki has proposed first-order cstit-based STIT logics that can distinguish de re and de dicto readings of agency statements and has proved strong completeness results for Hilbert systems over finite models, moving the STIT programme beyond the purely propositional level. Further work investigates interpreted-system and computationally grounded semantics for STIT and its extensions in order to model the behaviour of autonomous agents in multi-agent settings, and proposes STIT-based semantics for epistemic notions based on patterns of information disclosure in interactive systems. == Branching-time semantics == STIT logics are usually interpreted over branching-time models. A standard STIT frame consists of: a non-empty set of moments T {\displaystyle T} , partially ordered by < {\displaystyle <} so that ( T , < ) {\displaystyle (T,<)} forms a tree (every pair of moments with a common predecessor has a greatest lower bound); a set of histories, each history being a maximal linearly ordered subset of T {\displaystyle T} ; a non-empty set of agents A g {\displaystyle Ag} ; for each agent i ∈ A g {\displaystyle i\in Ag} and moment m {\displaystyle m} , a choice function c h o i c e i m {\displaystyle {\mathsf {choice}}_{i}^{m}} that partitions the set of histories passing through m {\displaystyle m} into choice cells. The idea is that a moment represents a time at which choices are made, and histories represent complete possible future courses of events. At each moment, each agent's choice corresponds to selecting one of the available cells of histories determined by their choice function. Formulas are evaluated at pairs ( m , h ) {\displaystyle (m,h)} of a moment and a history through that moment (sometimes written m / h {\displaystyle m/h} ). A valuation assigns truth-values to atomic propositions at such indices; Boolean connectives are interpreted pointwise as in Kripke-style modal logic. == Chellas and deliberative STIT operators == Several STIT operators have been distinguished in the literature. A common approach uses two closely related operators, often called Chellas STIT and deliberative STIT. Let H m {\displaystyle H_{m}} be the set of histories passing through a moment m {\displaystyle m} , and write H m {\displaystyle H_{m}} ⟦ φ ⟧ m = { h ∈ H m ∣ M , m / h ⊨ φ } {\displaystyle {\text{⟦}}\varphi {\text{⟧}}_{m}=\{h\in H_{m}\mid M,m/h\models \varphi \}} for the set of histories at m {\displaystyle m} where φ {\displaystyle \varphi } holds. The Chellas STIT operator, often written [ i c s t i t : φ ] {\displaystyle [i\ {\mathsf {cstit}}:\varphi ]} , is given by M , m / h ⊨ [ i c s t i t : φ ] iff c h o i c e i m ( h ) ⊆ ⟦ φ ⟧ m . {\displaystyle M,m/h\models [i\ {\mathsf {cstit}}:\varphi ]\quad {\text{iff}}\quad {\mathsf {choice}}_{i}^{m}(h)\subseteq {\text{⟦}}\varphi {\text{⟧}}_{m}.} Intuitively, agent i {\displaystyle i} sees to it that φ {\displaystyle \varphi } if φ {\displaystyle \varphi } holds at all histories compatible with their present choice. The deliberative STIT operator, [ i d s t i t : φ ] {\displaystyle [i\ {\mathsf {dstit}}:\varphi ]} , adds

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  Weibo

  Weibo (Chinese: 微博; pinyin: Wēibó), or Sina Weibo (Chinese: 新浪微博; pinyin: Xīnlàng Wēibó), is a Chinese microblogging (weibo) website. Launched by Sina Corporation on 14 August 2009, it is one of the biggest social media platforms in China, with over 582 million monthly active users (252 million daily active users) as of Q1 2022. The platform has been highly successful but has faced criticism for heavy censorship. Sina had gone public on the Nasdaq in 2000. In March 2014, Sina announced a spinoff of Weibo and filed an IPO under the symbol WB. Sina carved out 11% of Weibo in the IPO, with Alibaba owning 32% post-IPO. The company began trading publicly on 17 April 2014. In March 2017, Sina launched Sina Weibo International Version. In November 2018, Sina Weibo suspended its registration function for minors under the age of 14. In July 2019, Sina Weibo announced that it would launch a two-month campaign to clean up pornographic and vulgar information, named "Project Deep Blue" (蔚蓝计划). On 29 September 2020, the company announced it would go private again due to rising tensions between the US and China. == Name == "Weibo" (微博) is the Chinese word for "microblog". Sina Weibo launched its new domain name weibo.com on 7 April 2011, deactivating and redirecting from the old domain, t.sina.com.cn, to the new one. Due to its popularity, the media sometimes refers to the platform simply as "Weibo", despite the numerous other Chinese microblogging services including Tencent Weibo, Sohu Weibo, and NetEase Weibo. However, the latter three have stopped providing services. == Background == Sina Weibo is a platform based on fostering user relationships to share, disseminate, and receive information. Through the website or the mobile app, users can upload pictures and videos publicly for instant sharing, with other users being able to comment with text, pictures and videos, or use a multimedia instant messaging service. The company initially invited a large number of celebrities to join the platform at the beginning and has since invited many media personalities, government departments, businesses and non-governmental organizations to open accounts for the purpose of publishing and communicating information. To avoid the impersonation of celebrities, Sina Weibo uses verification symbols; celebrity accounts have an orange letter "V" and organizations' accounts have a blue letter "V". Sina Weibo has more than 500 million registered users; out of these, 313 million are monthly active users, 85% use the Weibo mobile app, 70% are college-aged, 50.10% are male and 49.90% are female. There are over 100 million messages posted by users each day. With more than 100 million followers, actress Xie Na holds the record for the most followers on the platform. Despite fierce competition among Chinese social media platforms, Sina Weibo remains the most popular. == History == After the July 2009 Ürümqi riots, China shut down most domestic microblogging services, including Fanfou, the very first weibo service. Many popular non-China-based microblogging services like Twitter, Facebook, and Plurk have since been blocked. Sina Corporation CEO Charles Chao considered this to be an opportunity, and on 14 August 2009, Sina launched the tested version of Sina Weibo. Basic functions including message, private message, comment and reposting were made available that September. A Sina Weibo–compatible API platform for developing third-party applications was launched on 28 July 2010. On 1 December 2010, the website experienced an outage, which administrators later said was due to the ever-increasing numbers of users and posts. Registered users surpassed 100 million in February 2011. Since 23 March 2011, t.cn has been used as Sina Weibo's official shortened URL in lieu of sinaurl.cn. On 7 April 2011, weibo.com replaced t.sina.com.cn as the new main domain name used by the website. The official logo was also updated. In June 2011, Sina announced an English-language version of Sina Weibo would be developed and launched, though content would still be governed by Chinese law. On 11 January 2013, Sina Weibo and Alibaba China (a subsidiary of Alibaba Group) signed a strategic cooperation agreement. With more and more foreign celebrities using Sina Weibo, language translation has become an urgent need for Chinese users who wish to communicate with their idols online, especially Korean. In January 2013, Sina Weibo and NetEase.com announced that they had reached a strategic cooperation agreement. When users browse foreign language content, they can now directly obtain translation results through the YouDao Dictionary. The Sina Weibo financial report in February 2013 showed that its total revenue was approximately US$66 million and that the number of registered users had exceeded the 500 million mark. In April 2013, Sina officially announced that Sina Weibo had signed a strategic cooperation agreement with Alibaba. The two sides conducted in-depth cooperation in areas such as user account interoperability, data exchange, online payment, and internet marketing. At the same time, Sina announced that Alibaba, through its wholly owned subsidiary, had purchased the preferred shares and common shares issued by Sina Weibo Company for US$586 million, which accounted for approximately 18% of Weibo's fully diluted and diluted total shares. === Ownership === On 9 April 2013, Alibaba Group announced that it would acquire 18% of Sina Weibo for US$586 million, with the option to buy up to 30% in the future. Alibaba exercised this option when Weibo was listed on the NASDAQ in April 2014. == Users == According to iResearch's report on 30 March 2011, Sina Weibo had 56.5% of China's microblogging market based on active users and 86.6% based on browsing time over competitors such as Tencent Weibo and Baidu. According to research by Sina Corporation, the number of active users reached over 400 million by Q1 2018, making Sina Weibo the 7th platform with at least 400 million active users, and daily usage increased by 21%. As of 2017, approximately 80% of its users were in their 20s and 30s. The top 100 users had over 485 million followers combined. More than 5,000 companies and 2,700 media organizations in China use Sina Weibo. The site is maintained by a growing microblogging department of 200 employees responsible for technology, design, operations, and marketing. Sina executives invited and persuaded many Chinese celebrities to join the platform. Users now include Asian celebrities, movie stars, singers, famous business and media figures, athletes, scholars, artists, organizations, religious figures, government departments, and officials from Hong Kong, Mainland China, Malaysia, Singapore, Taiwan, and Macau, as well as some famous foreign individuals and organizations, including Kevin Rudd, Boris Johnson, David Cameron, Narendra Modi, Toshiba, and the Germany national football team. Sina Weibo has a verification program for known people and organizations. Once an account is verified, a verification badge is added beside the account name. == Features == Many of Sina Weibo's features resemble those of Twitter. A user may post with a 140-character limit (increased to 2,000 as of January 2016 with the exception of reposts and comments). An analysis of 29 million Weibo posts found the median length was 14 characters. Users may mention or talk to other people using "@UserName" formatting, add hashtags, follow other users to make their posts appear in one's own timeline, re-post with "//@UserName" similar to Twitter's retweet function "RT @UserName", select posts for one's favorites list, and verify the account if the user is a celebrity, brand, business or otherwise of public interest. URLs are automatically shortened using the domain name t.cn, akin to Twitter's t.co. Official and third-party applications can access Sina Weibo from other websites or platforms. Users may: Submit up to 18 images/video files in every post Send personal messages to followers Follow others and be followed Post "stories" like on Instagram React to posts using different emojis Receive monetary rewards that can be used in a digital store linked to Weibo View posts identified as "hot" or popular Display the location they post from Hashtags differ slightly between Sina Weibo and Twitter, using the double-hashtag "#HashName#" format (the lack of spacing between Chinese characters necessitates a closing tag). Users can own a hashtag by requesting hashtag monitoring; the company reviews these requests and responds within one to three days. Once a user owns a hashtag, they have access to a wide variety of functions available only to them on the condition that they remain active (less than 1 post per calendar week revokes these privileges). Additionally, comments appear as a list below each post. A commenter can also choose to re-post the comment, quoting the whole original post, to their own page. Unregistered users can only browse a few post

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  Neuro-symbolic AI

  Neuro-symbolic AI is a subfield of artificial intelligence that integrates neural methods (e.g., neural networks and deep learning) with symbolic methods (e.g., formal logic, knowledge representation, and automated reasoning). The goal is to combine the strengths of both approaches, resulting in AI systems that can be trained from raw data and demonstrate robustness against outliers or errors in the base data, while preserving explainability, explicit use of expert knowledge, and explicit cognitive reasoning. As argued by Leslie Valiant and others, the effective construction of rich computational cognitive models demands the combination of symbolic reasoning and efficient machine learning. Gary Marcus argued, "We cannot construct rich cognitive models in an adequate, automated way without the triumvirate of hybrid architecture, rich prior knowledge, and sophisticated techniques for reasoning." Further, "To build a robust, knowledge-driven approach to AI we must have the machinery of symbol manipulation in our toolkit. Too much of useful knowledge is abstract to make do without tools that represent and manipulate abstraction, and to date, the only known machinery that can manipulate such abstract knowledge reliably is the apparatus of symbol manipulation." Angelo Dalli, Henry Kautz, Francesca Rossi, and Bart Selman also argued for such a synthesis. Their arguments attempt to address the two kinds of thinking, as discussed in Daniel Kahneman's book Thinking, Fast and Slow. It describes cognition as encompassing two components: System 1 is fast, reflexive, intuitive, and unconscious. System 2 is slower, step-by-step, and explicit. System 1 is used for pattern recognition. System 2 handles planning, deduction, and deliberative thinking. In this view, deep learning best handles the first kind of cognition, while symbolic reasoning best handles the second kind. Both are necessary for the development of a robust and reliable AI system capable of learning, reasoning, and interacting with humans to accept advice and answer questions. Since the 1990s, dual-process models with explicit references to the two contrasting systems have been the focus of research in both the fields of AI and cognitive science by numerous researchers. In 2025, the adoption of neurosymbolic AI, an approach that integrates neural networks with symbolic reasoning, increased in response to the need to address hallucination issues in large language models. For example, Amazon implemented Neurosymbolic AI in its Vulcan warehouse robots and Rufus shopping assistant to enhance accuracy and decision-making. == Approaches == Approaches for integration are diverse. Henry Kautz's taxonomy of neuro-symbolic architectures follows, along with some examples: Symbolic Neural symbolic is the current approach of many neural models in natural language processing, where words or subword tokens are the ultimate input and output of large language models. Examples include BERT, RoBERTa, and GPT-3. Symbolic[Neural] is exemplified by AlphaGo, where symbolic techniques are used to invoke neural techniques. In this case, the symbolic approach is Monte Carlo tree search and the neural techniques learn how to evaluate game positions. Neural | Symbolic uses a neural architecture to interpret perceptual data as symbols and relationships that are reasoned about symbolically. Neural-Concept Learner is an example. Neural: Symbolic → Neural relies on symbolic reasoning to generate or label training data that is subsequently learned by a deep learning model, e.g., to train a neural model for symbolic computation by using a Macsyma-like symbolic mathematics system to create or label examples. NeuralSymbolic uses a neural net that is generated from symbolic rules. An example is the Neural Theorem Prover, which constructs a neural network from an AND-OR proof tree generated from knowledge base rules and terms. Logic Tensor Networks also fall into this category. Neural[Symbolic] according to Kautz, this approach embeds true symbolic reasoning inside a neural network. These are tightly-coupled neural-symbolic systems, in which the logical inference rules are internal to the neural network. This way, the neural network internally computes the inference from the premises and learns to reason based on logical inference systems. Early work on connectionist modal and temporal logics by Garcez, Lamb, and Gabbay is aligned with this approach. These categories are not exhaustive, as they do not consider multi-agent systems. In 2005, Bader and Hitzler presented a more fine-grained categorization that took into account, e.g., whether the use of symbols included logic and, if so, whether the logic was propositional or first-order logic. The 2005 categorization and Kautz's taxonomy above are compared and contrasted in a 2021 article. Sepp Hochreiter argued that Graph Neural Networks "...are the predominant models of neural-symbolic computing" since "[t]hey describe the properties of molecules, simulate social networks, or predict future states in physical and engineering applications with particle-particle interactions." == Artificial general intelligence == Gary Marcus argues that "...hybrid architectures that combine learning and symbol manipulation are necessary for robust intelligence, but not sufficient", and that there are ...four cognitive prerequisites for building robust artificial intelligence: hybrid architectures that combine large-scale learning with the representational and computational powers of symbol manipulation, large-scale knowledge bases—likely leveraging innate frameworks—that incorporate symbolic knowledge along with other forms of knowledge, reasoning mechanisms capable of leveraging those knowledge bases in tractable ways, and rich cognitive models that work together with those mechanisms and knowledge bases. This echoes earlier calls for hybrid models as early as the 1990s. == History == Garcez and Lamb described research in this area as ongoing, at least since the 1990s. During that period, the terms symbolic and sub-symbolic AI were popular. A series of workshops on neuro-symbolic AI has been held annually since 2005 Neuro-Symbolic Artificial Intelligence. In the early 1990s, an initial set of workshops on this topic were organized. == Research == Key research questions remain, such as: What is the best way to integrate neural and symbolic architectures? How should symbolic structures be represented within neural networks and extracted from them? How should common-sense knowledge be learned and reasoned about? How can abstract knowledge that is hard to encode logically be handled? == Implementations == Implementations of neuro-symbolic approaches include: AllegroGraph: an integrated Knowledge Graph based platform for neuro-symbolic application development. Scallop: a language based on Datalog that supports differentiable logical and relational reasoning. Scallop can be integrated in Python and with a PyTorch learning module. Logic Tensor Networks: encode logical formulas as neural networks and simultaneously learn term encodings, term weights, and formula weights. DeepProbLog: combines neural networks with the probabilistic reasoning of ProbLog. Abductive Learning: integrates machine learning and logical reasoning in a balanced-loop via abductive reasoning, enabling them to work together in a mutually beneficial way. SymbolicAI: a compositional differentiable programming library.

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  Audio inpainting

  Audio inpainting (also known as audio interpolation) is an audio restoration task which deals with the reconstruction of missing or corrupted portions of a digital audio signal. Inpainting techniques are employed when parts of the audio have been lost due to various factors such as transmission errors, data corruption or errors during recording. The goal of audio inpainting is to fill in the gaps (i.e., the missing portions) in the audio signal seamlessly, making the reconstructed portions indistinguishable from the original content and avoiding the introduction of audible distortions or alterations. Many techniques have been proposed to solve the audio inpainting problem and this is usually achieved by analyzing the temporal and spectral information surrounding each missing portion of the considered audio signal. Classic methods employ statistical models or digital signal processing algorithms to predict and synthesize the missing or damaged sections. Recent solutions, instead, take advantage of deep learning models, thanks to the growing trend of exploiting data-driven methods in the context of audio restoration. Depending on the extent of the lost information, the inpainting task can be divided in three categories. Short inpainting refers to the reconstruction of few milliseconds (approximately less than 10) of missing signal, that occurs in the case of short distortions such as clicks or clipping. In this case, the goal of the reconstruction is to recover the lost information exactly. In long inpainting instead, with gaps in the order of hundreds of milliseconds or even seconds, this goal becomes unrealistic, since restoration techniques cannot rely on local information. Therefore, besides providing a coherent reconstruction, the algorithms need to generate new information that has to be semantically compatible with the surrounding context (i.e., the audio signal surrounding the gaps). The case of medium duration gaps lays between short and long inpainting. It refers to the reconstruction of tens of millisecond of missing data, a scale where the non-stationary characteristic of audio already becomes important. == Definition == Consider a digital audio signal x {\displaystyle \mathbf {x} } . A corrupted version of x {\displaystyle \mathbf {x} } , which is the audio signal presenting missing gaps to be reconstructed, can be defined as x ~ = m ∘ x {\displaystyle \mathbf {\tilde {x}} =\mathbf {m} \circ \mathbf {x} } , where m {\displaystyle \mathbf {m} } is a binary mask encoding the reliable or missing samples of x {\displaystyle \mathbf {x} } , and ∘ {\displaystyle \circ } represents the element-wise product. Audio inpainting aims at finding x ^ {\displaystyle \mathbf {\hat {x}} } (i.e., the reconstruction), which is an estimation of x {\displaystyle \mathbf {x} } . This is an ill-posed inverse problem, which is characterized by a non-unique set of solutions. For this reason, similarly to the formulation used for the inpainting problem in other domains, the reconstructed audio signal can be found through an optimization problem that is formally expressed as x ^ ∗ = argmin X ^ L ( m ∘ x ^ , x ~ ) + R ( x ^ ) {\displaystyle \mathbf {\hat {x}} ^{}={\underset {\hat {\mathbf {X} }}{\text{argmin}}}~L(\mathbf {m} \circ \mathbf {\hat {x}} ,\mathbf {\tilde {x}} )+R(\mathbf {\hat {x}} )} . In particular, x ^ ∗ {\displaystyle \mathbf {\hat {x}} ^{}} is the optimal reconstructed audio signal and L {\displaystyle L} is a distance measure term that computes the reconstruction accuracy between the corrupted audio signal and the estimated one. For example, this term can be expressed with a mean squared error or similar metrics. Since L {\displaystyle L} is computed only on the reliable frames, there are many solutions that can minimize L ( m ∘ x ^ , x ~ ) {\displaystyle L(\mathbf {m} \circ \mathbf {\hat {x}} ,\mathbf {\tilde {x}} )} . It is thus necessary to add a constraint to the minimization, in order to restrict the results only to the valid solutions. This is expressed through the regularization term R {\displaystyle R} that is computed on the reconstructed audio signal x ^ {\displaystyle \mathbf {\hat {x}} } . This term encodes some kind of a-priori information on the audio data. For example, R {\displaystyle R} can express assumptions on the stationarity of the signal, on the sparsity of its representation or can be learned from data. == Techniques == There exist various techniques to perform audio inpainting. These can vary significantly, influenced by factors such as the specific application requirements, the length of the gaps and the available data. In the literature, these techniques are broadly divided in model-based techniques (sometimes also referred as signal processing techniques) and data-driven techniques. === Model-based techniques === Model-based techniques involve the exploitation of mathematical models or assumptions about the underlying structure of the audio signal. These models can be based on prior knowledge of the audio content or statistical properties observed in the data. By leveraging these models, missing or corrupted portions of the audio signal can be inferred or estimated. An example of a model-based techniques are autoregressive models. These methods interpolate or extrapolate the missing samples based on the neighboring values, by using mathematical functions to approximate the missing data. In particular, in autoregressive models the missing samples are completed through linear prediction. The autoregressive coefficients necessary for this prediction are learned from the surrounding audio data, specifically from the data adjacent to each gap. Some more recent techniques approach audio inpainting by representing audio signals as sparse linear combinations of a limited number of basis functions (as for example in the Short Time Fourier Transform). In this context, the aim is to find the sparse representation of the missing section of the signal that most accurately matches the surrounding, unaffected signal. The aforementioned methods exhibit optimal performance when applied to filling in relatively short gaps, lasting only a few tens of milliseconds, and thus they can be included in the context of short inpainting. However, these signal-processing techniques tend to struggle when dealing with longer gaps. The reason behind this limitation lies in the violation of the stationarity condition, as the signal often undergoes significant changes after the gap, making it substantially different from the signal preceding the gap. As a way to overcome these limitations, some approaches add strong assumptions also about the fundamental structure of the gap itself, exploiting sinusoidal modeling or similarity graphs to perform inpainting of longer missing portions of audio signals. === Data-driven techniques === Data-driven techniques rely on the analysis and exploitation of the available audio data. These techniques often employ deep learning algorithms that learn patterns and relationships directly from the provided data. They involve training models on large datasets of audio examples, allowing them to capture the statistical regularities present in the audio signals. Once trained, these models can be used to generate missing portions of the audio signal based on the learned representations, without being restricted by stationarity assumptions. Data-driven techniques also offer the advantage of adaptability and flexibility, as they can learn from diverse audio datasets and potentially handle complex inpainting scenarios. As of today, such techniques constitute the state-of-the-art of audio inpainting, being able to reconstruct gaps of hundreds of milliseconds or even seconds. These performances are made possible by the use of generative models that have the capability to generate novel content to fill in the missing portions. For example, generative adversarial networks, which are the state-of-the-art of generative models in many areas, rely on two competing neural networks trained simultaneously in a two-player minmax game: the generator produces new data from samples of a random variable, the discriminator attempts to distinguish between generated and real data. During the training, the generator's objective is to fool the discriminator, while the discriminator attempts to learn to better classify real and fake data. In GAN-based inpainting methods the generator acts as a context encoder and produces a plausible completion for the gap only given the available information surrounding it. The discriminator is used to train the generator and tests the consistency of the produced inpainted audio. Recently, also diffusion models have established themselves as the state-of-the-art of generative models in many fields, often beating even GAN-based solutions. For this reason they have also been used to solve the audio inpainting problem, obtaining valid results. These models generate new data instances by inverting the

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  Neurorobotics

  Neurorobotics is the combined study of neuroscience, robotics, and artificial intelligence. It is the science and technology of embodied autonomous neural systems. Neural systems include brain-inspired algorithms (e.g. connectionist networks), computational models of biological neural networks (e.g. artificial spiking neural networks, large-scale simulations of neural microcircuits) and actual biological systems (e.g. in vivo and in vitro neural nets). Such neural systems can be embodied in machines with mechanic or any other forms of physical actuation. This includes robots, prosthetic or wearable systems but also, at smaller scale, micro-machines and, at the larger scales, furniture and infrastructures. Neurorobotics is that branch of neuroscience with robotics, which deals with the study and application of science and technology of embodied autonomous neural systems like brain-inspired algorithms. It is based on the idea that the brain is embodied and the body is embedded in the environment. Therefore, most neurorobots are required to function in the real world, as opposed to a simulated environment. Beyond brain-inspired algorithms for robots neurorobotics may also involve the design of brain-controlled robot systems. == Major classes of models == Neurorobots can be divided into various major classes based on the robot's purpose. Each class is designed to implement a specific mechanism of interest for study. Common types of neurorobots are those used to study motor control, memory, action selection, and perception. === Locomotion and motor control === Neurorobots are often used to study motor feedback and control systems, and have proved their merit in developing controllers for robots. Locomotion is modeled by a number of neurologically inspired theories on the action of motor systems. Locomotion control has been mimicked using models or central pattern generators, clumps of neurons capable of driving repetitive behavior, to make four-legged walking robots. Other groups have expanded the idea of combining rudimentary control systems into a hierarchical set of simple autonomous systems. These systems can formulate complex movements from a combination of these rudimentary subsets. This theory of motor action is based on the organization of cortical columns, which progressively integrate from simple sensory input into a complex afferent signals, or from complex motor programs to simple controls for each muscle fiber in efferent signals, forming a similar hierarchical structure. Another method for motor control uses learned error correction and predictive controls to form a sort of simulated muscle memory. In this model, awkward, random, and error-prone movements are corrected for using error feedback to produce smooth and accurate movements over time. The controller learns to create the correct control signal by predicting the error. Using these ideas, robots have been designed which can learn to produce adaptive arm movements or to avoid obstacles in a course. === Learning and memory systems === Robots designed to test theories of animal memory systems. Many studies examine the memory system of rats, particularly the rat hippocampus, dealing with place cells, which fire for a specific location that has been learned. Systems modeled after the rat hippocampus are generally able to learn mental maps of the environment, including recognizing landmarks and associating behaviors with them, allowing them to predict the upcoming obstacles and landmarks. Another study has produced a robot based on the proposed learning paradigm of barn owls for orientation and localization based on primarily auditory, but also visual stimuli. The hypothesized method involves synaptic plasticity and neuromodulation, a mostly chemical effect in which reward neurotransmitters such as dopamine or serotonin affect the firing sensitivity of a neuron to be sharper. The robot used in the study adequately matched the behavior of barn owls. Furthermore, the close interaction between motor output and auditory feedback proved to be vital in the learning process, supporting active sensing theories that are involved in many of the learning models. Neurorobots in these studies are presented with simple mazes or patterns to learn. Some of the problems presented to the neurorobot include recognition of symbols, colors, or other patterns and execute simple actions based on the pattern. In the case of the barn owl simulation, the robot had to determine its location and direction to navigate in its environment. === Action selection and value systems === Action selection studies deal with negative or positive weighting to an action and its outcome. Neurorobots can and have been used to study simple ethical interactions, such as the classical thought experiment where there are more people than a life raft can hold, and someone must leave the boat to save the rest. However, more neurorobots used in the study of action selection contend with much simpler persuasions such as self-preservation or perpetuation of the population of robots in the study. These neurorobots are modeled after the neuromodulation of synapses to encourage circuits with positive results. In biological systems, neurotransmitters such as dopamine or acetylcholine positively reinforce neural signals that are beneficial. One study of such interaction involved the robot Darwin VII, which used visual, auditory, and a simulated taste input to "eat" conductive metal blocks. The arbitrarily chosen good blocks had a striped pattern on them while the bad blocks had a circular shape on them. The taste sense was simulated by conductivity of the blocks. The robot had positive and negative feedbacks to the taste based on its level of conductivity. The researchers observed the robot to see how it learned its action selection behaviors based on the inputs it had. Other studies have used herds of small robots which feed on batteries strewn about the room, and communicate its findings to other robots. === Sensory perception === Neurorobots have also been used to study sensory perception, particularly vision. These are primarily systems that result from embedding neural models of sensory pathways in automatas. This approach gives exposure to the sensory signals that occur during behavior and also enables a more realistic assessment of the degree of robustness of the neural model. It is well known that changes in the sensory signals produced by motor activity provide useful perceptual cues that are used extensively by organisms. For example, researchers have used the depth information that emerges during replication of human head and eye movements to establish robust representations of the visual scene. == Biological robots == Biological robots are not officially neurorobots in that they are not neurologically inspired AI systems, but actual neuron tissue wired to a robot. This employs the use of cultured neural networks to study brain development or neural interactions. These typically consist of a neural culture raised on a multielectrode array (MEA), which is capable of both recording the neural activity and stimulating the tissue. In some cases, the MEA is connected to a computer which presents a simulated environment to the brain tissue and translates brain activity into actions in the simulation, as well as providing sensory feedback The ability to record neural activity gives researchers a window into a brain, which they can use to learn about a number of the same issues neurorobots are used for. An area of concern with the biological robots is ethics. Many questions are raised about how to treat such experiments. The central question concerns consciousness and whether or not the rat brain experiences it. There are many theories about how to define consciousness. == Implications for neuroscience == Neuroscientists benefit from neurorobotics because it provides a blank slate to test various possible methods of brain function in a controlled and testable environment. While robots are more simplified versions of the systems they emulate, they are more specific, allowing more direct testing of the issue at hand. They also have the benefit of being accessible at all times, while it is more difficult to monitor large portions of a brain while the human or animal is active, especially individual neurons. The development of neuroscience has produced neural treatments. These include pharmaceuticals and neural rehabilitation. Progress is dependent on an intricate understanding of the brain and how exactly it functions. It is difficult to study the brain, especially in humans, due to the danger associated with cranial surgeries. Neurorobots can improved the range of tests and experiments that can be performed in the study of neural processes.

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  Super-resolution optical fluctuation imaging

  Super-resolution optical fluctuation imaging (SOFI) is a post-processing method for the calculation of super-resolved images from recorded image time series that is based on the temporal correlations of independently fluctuating fluorescent emitters. SOFI has been developed for super-resolution of biological specimen that are labelled with independently fluctuating fluorescent emitters (organic dyes, fluorescent proteins). In comparison to other super-resolution microscopy techniques such as STORM or PALM that rely on single-molecule localization and hence only allow one active molecule per diffraction-limited area (DLA) and timepoint, SOFI does not necessitate a controlled photoswitching and/ or photoactivation as well as long imaging times. Nevertheless, it still requires fluorophores that are cycling through two distinguishable states, either real on-/off-states or states with different fluorescence intensities. In mathematical terms SOFI-imaging relies on the calculation of cumulants, for what two distinguishable ways exist. For one thing an image can be calculated via auto-cumulants that by definition only rely on the information of each pixel itself, and for another thing an improved method utilizes the information of different pixels via the calculation of cross-cumulants. Both methods can increase the final image resolution significantly although the cumulant calculation has its limitations. Actually SOFI is able to increase the resolution in all three dimensions. == Principle == Likewise to other super-resolution methods SOFI is based on recording an image time series on a CCD- or CMOS camera. In contrary to other methods the recorded time series can be substantially shorter, since a precise localization of emitters is not required and therefore a larger quantity of activated fluorophores per diffraction-limited area is allowed. The pixel values of a SOFI-image of the n-th order are calculated from the values of the pixel time series in the form of a n-th order cumulant, whereas the final value assigned to a pixel can be imagined as the integral over a correlation function. The finally assigned pixel value intensities are a measure of the brightness and correlation of the fluorescence signal. Mathematically, the n-th order cumulant is related to the n-th order correlation function, but exhibits some advantages concerning the resulting resolution of the image. Since in SOFI several emitters per DLA are allowed, the photon count at each pixel results from the superposition of the signals of all activated nearby emitters. The cumulant calculation now filters the signal and leaves only highly correlated fluctuations. This provides a contrast enhancement and therefore a background reduction for good measure. As it is implied in the figure on the left the fluorescence source distribution: ∑ k = 1 N δ ( r → − r → k ) ⋅ ε k ⋅ s k ( t ) {\displaystyle \sum _{k=1}^{N}\delta ({\vec {r}}-{\vec {r}}_{k})\cdot \varepsilon _{k}\cdot s_{k}(t)} is convolved with the system's point spread function (PSF) U(r). Hence the fluorescence signal at time t and position r → {\displaystyle {\vec {r}}} is given by F ( r → , t ) = ∑ k = 1 N U ( r → − r → k ) ⋅ ε k ⋅ s k ( t ) . {\displaystyle F({\vec {r}},t)=\sum _{k=1}^{N}U({\vec {r}}-{\vec {r}}_{k})\cdot \varepsilon _{k}\cdot s_{k}(t).} Within the above equations N is the amount of emitters, located at the positions r → k {\displaystyle {\vec {r}}_{k}} with a time-dependent molecular brightness ε k ⋅ s k {\displaystyle \varepsilon _{k}\cdot s_{k}} where ε k {\displaystyle \varepsilon _{k}} is a variable for the constant molecular brightness and s k ( t ) {\displaystyle s_{k}(t)} is a time-dependent fluctuation function. The molecular brightness is just the average fluorescence count-rate divided by the number of molecules within a specific region. For simplification it has to be assumed that the sample is in a stationary equilibrium and therefore the fluorescence signal can be expressed as a zero-mean fluctuation: δ F ( r → , t ) = F ( r → , t ) − ⟨ F ( r → , t ) ⟩ t {\displaystyle \delta F({\vec {r}},t)=F({\vec {r}},t)-\langle F({\vec {r}},t)\rangle _{t}} where ⟨ ⋯ ⟩ t {\displaystyle \langle \cdots \rangle _{t}} denotes time-averaging. The auto-correlation here e.g. the second-order can then be described deductively as follows for a certain time-lag τ {\displaystyle \tau } : δ F ( r → , t ) = ⟨ δ F ( r → , t + τ ) ⋅ δ F ( r → , t ) ⟩ t {\displaystyle \delta F({\vec {r}},t)=\langle \delta F({\vec {r}},t+\tau )\cdot \delta F({\vec {r}},t)\rangle _{t}} From these equations it follows that the PSF of the optical system has to be taken to the power of the order of the correlation. Thus in a second-order correlation the PSF would be reduced along all dimensions by a factor of 2 {\displaystyle {\sqrt {2}}} . As a result, the resolution of the SOFI-images increases according to this factor. === Cumulants versus correlations === Using only the simple correlation function for a reassignment of pixel values, would ascribe to the independency of fluctuations of the emitters in time in a way that no cross-correlation terms would contribute to the new pixel value. Calculations of higher-order correlation functions would suffer from lower-order correlations for what reason it is superior to calculate cumulants, since all lower-order correlation terms vanish. == Cumulant-calculation == === Auto-cumulants === For computational reasons it is convenient to set all time-lags in higher-order cumulants to zero so that a general expression for the n-th order auto-cumulant can be found: A C n ( r → , τ 1 … n − 1 = 0 ) = ∑ k = 1 N U n ( r → − r → k ) ε k n w k ( 0 ) {\displaystyle AC_{n}({\vec {r}},\tau _{1\ldots n-1}=0)=\sum _{k=1}^{N}U^{n}({\vec {r}}-{\vec {r}}_{k})\varepsilon _{k}^{n}w_{k}(0)} w k {\displaystyle w_{k}} is a specific correlation based weighting function influenced by the order of the cumulant and mainly depending on the fluctuation properties of the emitters. Albeit there is no fundamental limitation in calculating very high orders of cumulants and thereby shrinking the FWHM of the PSF there are practical limitations according to the weighting of the values assigned to the final image. Emitters with a higher molecular brightness will show a strong increase in terms of the pixel cumulant value assigned at higher-orders as well as this performance can be expected from a diverse appearance of fluctuations of different emitters. A wide intensity range of the resulting image can therefore be expected and as a result dim emitters can get masked by bright emitters in higher-order images:. The calculation of auto-cumulants can be realized in a very attractive way in a mathematical sense. The n-th order cumulant can be calculated with a basic recursion from moments K n ( r → ) = μ n ( r → ) − ∑ i = 1 n − 1 ( n − 1 i ) K n − i ( r → ) μ i ( r → ) {\displaystyle K_{n}({\vec {r}})=\mu _{n}({\vec {r}})-\sum _{i=1}^{n-1}{\begin{pmatrix}n-1\\i\end{pmatrix}}K_{n-i}({\vec {r}})\mu _{i}({\vec {r}})} where K is a cumulant of the index's order, likewise μ {\displaystyle \mu } represents the moments. The term within the brackets indicates a binomial coefficient. This way of computation is straightforward in comparison with calculating cumulants with standard formulas. It allows for the calculation of cumulants with only little time of computing and is, as it is well implemented, even suitable for the calculation of high-order cumulants on large images. === Cross-cumulants === In a more advanced approach cross-cumulants are calculated by taking the information of several pixels into account. Cross-cumulants can be described as follows: C C n ( r → , τ 1 … n − 1 = 0 ) = ∏ j < l n U ( r → j − r → l n ) ⋅ ∑ i = 1 N U n ( r → i − ∑ k n r → k n ) ε i n w i ( 0 ) {\displaystyle CC_{n}({\vec {r}},\tau _{1\ldots n-1}=0)=\prod _{j Read more →

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  Gödel machine

  A Gödel machine is a hypothetical self-improving computer program that solves problems in an optimal way. It uses a recursive self-improvement protocol in which it rewrites its own code when it can prove the new code provides a better strategy. The machine was invented by Jürgen Schmidhuber (first proposed in 2003), but is named after Kurt Gödel who inspired the mathematical theories. The Gödel machine is often discussed when dealing with issues of meta-learning, also known as "learning to learn." Applications include automating human design decisions and transfer of knowledge between multiple related tasks, and may lead to design of more robust and general learning architectures. Though theoretically possible, no full implementation has been created. The Gödel machine is often compared with Marcus Hutter's AIXI, another formal specification for an artificial general intelligence. Schmidhuber points out that the Gödel machine could start out by implementing AIXItl as its initial sub-program, and self-modify after it finds proof that another algorithm for its search code will be better. == Limitations == Traditional problems solved by a computer only require one input and provide some output. Computers of this sort had their initial algorithm hardwired. This does not take into account the dynamic natural environment, and thus was a goal for the Gödel machine to overcome. The Gödel machine has limitations of its own, however. According to Gödel's First Incompleteness Theorem, any formal system that encompasses arithmetic is either flawed or allows for statements that cannot be proved in the system. Hence even a Gödel machine with unlimited computational resources must ignore those self-improvements whose effectiveness it cannot prove. == Variables of interest == There are three variables that are particularly useful in the run time of the Gödel machine. At some time t {\displaystyle t} , the variable time {\displaystyle {\text{time}}} will have the binary equivalent of t {\displaystyle t} . This is incremented steadily throughout the run time of the machine. Any input meant for the Gödel machine from the natural environment is stored in variable x {\displaystyle x} . It is likely the case that x {\displaystyle x} will hold different values for different values of variable time {\displaystyle {\text{time}}} . The outputs of the Gödel machine are stored in variable y {\displaystyle y} , where y ( t ) {\displaystyle y(t)} would be the output bit-string at some time t {\displaystyle t} . At any given time t {\displaystyle t} , where ( 1 ≤ t ≤ T ) {\displaystyle (1\leq t\leq T)} , the goal is to maximize future success or utility. A typical utility function follows the pattern u ( s , E n v ) : S × E → R {\displaystyle u(s,\mathrm {Env} ):S\times E\rightarrow \mathbb {R} } : u ( s , E n v ) = E μ [ ∑ τ = time T r ( τ ) ∣ s , E n v ] {\displaystyle u(s,\mathrm {Env} )=E_{\mu }{\Bigg [}\sum _{\tau ={\text{time}}}^{T}r(\tau )\mid s,\mathrm {Env} {\Bigg ]}} where r ( t ) {\displaystyle r(t)} is a real-valued reward input (encoded within s ( t ) {\displaystyle s(t)} ) at time t {\displaystyle t} , E μ [ ⋅ ∣ ⋅ ] {\displaystyle E_{\mu }[\cdot \mid \cdot ]} denotes the conditional expectation operator with respect to some possibly unknown distribution μ {\displaystyle \mu } from a set M {\displaystyle M} of possible distributions ( M {\displaystyle M} reflects whatever is known about the possibly probabilistic reactions of the environment), and the above-mentioned time = time ⁡ ( s ) {\displaystyle {\text{time}}=\operatorname {time} (s)} is a function of state s {\displaystyle s} which uniquely identifies the current cycle. Note that we take into account the possibility of extending the expected lifespan through appropriate actions. == Instructions used by proof techniques == The nature of the six proof-modifying instructions below makes it impossible to insert an incorrect theorem into proof, thus trivializing proof verification. === get-axiom(n) === Appends the n-th axiom as a theorem to the current theorem sequence. Below is the initial axiom scheme: Hardware Axioms formally specify how components of the machine could change from one cycle to the next. Reward Axioms define the computational cost of hardware instruction and the physical cost of output actions. Related Axioms also define the lifetime of the Gödel machine as scalar quantities representing all rewards/costs. Environment Axioms restrict the way new inputs x are produced from the environment, based on previous sequences of inputs y. Uncertainty Axioms/String Manipulation Axioms are standard axioms for arithmetic, calculus, probability theory, and string manipulation that allow for the construction of proofs related to future variable values within the Gödel machine. Initial State Axioms contain information about how to reconstruct parts or all of the initial state. Utility Axioms describe the overall goal in the form of utility function u. === apply-rule(k, m, n) === Takes in the index k of an inference rule (such as Modus tollens, Modus ponens), and attempts to apply it to the two previously proved theorems m and n. The resulting theorem is then added to the proof. === delete-theorem(m) === Deletes the theorem stored at index m in the current proof. This helps to mitigate storage constraints caused by redundant and unnecessary theorems. Deleted theorems can no longer be referenced by the above apply-rule function. === set-switchprog(m, n) === Replaces switchprog S pm:n, provided it is a non-empty substring of S p. === check() === Verifies whether the goal of the proof search has been reached. A target theorem states that given the current axiomatized utility function u (Item 1f), the utility of a switch from p to the current switchprog would be higher than the utility of continuing the execution of p (which would keep searching for alternative switchprogs). === state2theorem(m, n) === Takes in two arguments, m and n, and attempts to convert the contents of Sm:n into a theorem. == Example applications == === Time-limited NP-hard optimization === The initial input to the Gödel machine is the representation of a connected graph with a large number of nodes linked by edges of various lengths. Within given time T it should find a cyclic path connecting all nodes. The only real-valued reward will occur at time T. It equals 1 divided by the length of the best path found so far (0 if none was found). There are no other inputs. The by-product of maximizing expected reward is to find the shortest path findable within the limited time, given the initial bias. === Fast theorem proving === Prove or disprove as quickly as possible that all even integers > 2 are the sum of two primes (Goldbach’s conjecture). The reward is 1/t, where t is the time required to produce and verify the first such proof. === Maximizing expected reward with bounded resources === A cognitive robot that needs at least 1 liter of gasoline per hour interacts with a partially unknown environment, trying to find hidden, limited gasoline depots to occasionally refuel its tank. It is rewarded in proportion to its lifetime, and dies after at most 100 years or as soon as its tank is empty or it falls off a cliff, and so on. The probabilistic environmental reactions are initially unknown but assumed to be sampled from the axiomatized Speed Prior, according to which hard-to-compute environmental reactions are unlikely. This permits a computable strategy for making near-optimal predictions. One by-product of maximizing expected reward is to maximize expected lifetime.

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  Something Big Is Happening

  "Something Big Is Happening" is an essay by Matt Shumer, an AI entrepreneur, about the impact of artificial intelligence, published in February 2026, that has since been reportedly viewed more than 80 million times and widely discussed. Shumer noted that the technology has crossed an important threshold, where AI has become capable of creating self-improving systems. Referring to one the most recent AI models, he wrote: "It was making intelligent decisions. It had something that felt, for the first time, like judgment. Like taste." Speaking to CNBC's Power Lunch, Shumer said that his "core message" is "people in the workforce should start to use and experiment with AI tools so they can understand what’s coming". Even as the essay was widely shared and discussed, the essay also elicited criticism. Paulo Carvao, in an essay published by the Forbes Magazine stated that some of his advice is sound, but added: "It reads at times like a sales pitch. He urges readers to subscribe to the most advanced AI tools. He implies that those with access to premium models will outpace those without. He frames paid AI subscriptions as a form of insurance against obsolescence." Writing in The Guardian, Dan Milmo and Aisha Down mentioned Shumer as having a history of AI hype and stated, "He previously excited the internet by announcing the release of the world's "top open-source model", which it was not". Many workers in the technology sector criticized the article in blog posts shared on Hacker News; Edward Zitron commented that "while coding LLMs can test products, or scan/fix some bugs, this suggests they A) do this autonomously without human input, B) they do this correctly every time (or ever!)." In an article alluding to Shumer's original post, Ari Colaprete wrote "the LLM is fundamentally a writing machine, it does everything via text, and if you make it produce writing that exists purely to serve some sort of mechanical function, and you train it to succeed in that task, then it will tend to do so, even with vast intricacy."

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  Neuro-symbolic AI

  Neuro-symbolic AI is a subfield of artificial intelligence that integrates neural methods (e.g., neural networks and deep learning) with symbolic methods (e.g., formal logic, knowledge representation, and automated reasoning). The goal is to combine the strengths of both approaches, resulting in AI systems that can be trained from raw data and demonstrate robustness against outliers or errors in the base data, while preserving explainability, explicit use of expert knowledge, and explicit cognitive reasoning. As argued by Leslie Valiant and others, the effective construction of rich computational cognitive models demands the combination of symbolic reasoning and efficient machine learning. Gary Marcus argued, "We cannot construct rich cognitive models in an adequate, automated way without the triumvirate of hybrid architecture, rich prior knowledge, and sophisticated techniques for reasoning." Further, "To build a robust, knowledge-driven approach to AI we must have the machinery of symbol manipulation in our toolkit. Too much of useful knowledge is abstract to make do without tools that represent and manipulate abstraction, and to date, the only known machinery that can manipulate such abstract knowledge reliably is the apparatus of symbol manipulation." Angelo Dalli, Henry Kautz, Francesca Rossi, and Bart Selman also argued for such a synthesis. Their arguments attempt to address the two kinds of thinking, as discussed in Daniel Kahneman's book Thinking, Fast and Slow. It describes cognition as encompassing two components: System 1 is fast, reflexive, intuitive, and unconscious. System 2 is slower, step-by-step, and explicit. System 1 is used for pattern recognition. System 2 handles planning, deduction, and deliberative thinking. In this view, deep learning best handles the first kind of cognition, while symbolic reasoning best handles the second kind. Both are necessary for the development of a robust and reliable AI system capable of learning, reasoning, and interacting with humans to accept advice and answer questions. Since the 1990s, dual-process models with explicit references to the two contrasting systems have been the focus of research in both the fields of AI and cognitive science by numerous researchers. In 2025, the adoption of neurosymbolic AI, an approach that integrates neural networks with symbolic reasoning, increased in response to the need to address hallucination issues in large language models. For example, Amazon implemented Neurosymbolic AI in its Vulcan warehouse robots and Rufus shopping assistant to enhance accuracy and decision-making. == Approaches == Approaches for integration are diverse. Henry Kautz's taxonomy of neuro-symbolic architectures follows, along with some examples: Symbolic Neural symbolic is the current approach of many neural models in natural language processing, where words or subword tokens are the ultimate input and output of large language models. Examples include BERT, RoBERTa, and GPT-3. Symbolic[Neural] is exemplified by AlphaGo, where symbolic techniques are used to invoke neural techniques. In this case, the symbolic approach is Monte Carlo tree search and the neural techniques learn how to evaluate game positions. Neural | Symbolic uses a neural architecture to interpret perceptual data as symbols and relationships that are reasoned about symbolically. Neural-Concept Learner is an example. Neural: Symbolic → Neural relies on symbolic reasoning to generate or label training data that is subsequently learned by a deep learning model, e.g., to train a neural model for symbolic computation by using a Macsyma-like symbolic mathematics system to create or label examples. NeuralSymbolic uses a neural net that is generated from symbolic rules. An example is the Neural Theorem Prover, which constructs a neural network from an AND-OR proof tree generated from knowledge base rules and terms. Logic Tensor Networks also fall into this category. Neural[Symbolic] according to Kautz, this approach embeds true symbolic reasoning inside a neural network. These are tightly-coupled neural-symbolic systems, in which the logical inference rules are internal to the neural network. This way, the neural network internally computes the inference from the premises and learns to reason based on logical inference systems. Early work on connectionist modal and temporal logics by Garcez, Lamb, and Gabbay is aligned with this approach. These categories are not exhaustive, as they do not consider multi-agent systems. In 2005, Bader and Hitzler presented a more fine-grained categorization that took into account, e.g., whether the use of symbols included logic and, if so, whether the logic was propositional or first-order logic. The 2005 categorization and Kautz's taxonomy above are compared and contrasted in a 2021 article. Sepp Hochreiter argued that Graph Neural Networks "...are the predominant models of neural-symbolic computing" since "[t]hey describe the properties of molecules, simulate social networks, or predict future states in physical and engineering applications with particle-particle interactions." == Artificial general intelligence == Gary Marcus argues that "...hybrid architectures that combine learning and symbol manipulation are necessary for robust intelligence, but not sufficient", and that there are ...four cognitive prerequisites for building robust artificial intelligence: hybrid architectures that combine large-scale learning with the representational and computational powers of symbol manipulation, large-scale knowledge bases—likely leveraging innate frameworks—that incorporate symbolic knowledge along with other forms of knowledge, reasoning mechanisms capable of leveraging those knowledge bases in tractable ways, and rich cognitive models that work together with those mechanisms and knowledge bases. This echoes earlier calls for hybrid models as early as the 1990s. == History == Garcez and Lamb described research in this area as ongoing, at least since the 1990s. During that period, the terms symbolic and sub-symbolic AI were popular. A series of workshops on neuro-symbolic AI has been held annually since 2005 Neuro-Symbolic Artificial Intelligence. In the early 1990s, an initial set of workshops on this topic were organized. == Research == Key research questions remain, such as: What is the best way to integrate neural and symbolic architectures? How should symbolic structures be represented within neural networks and extracted from them? How should common-sense knowledge be learned and reasoned about? How can abstract knowledge that is hard to encode logically be handled? == Implementations == Implementations of neuro-symbolic approaches include: AllegroGraph: an integrated Knowledge Graph based platform for neuro-symbolic application development. Scallop: a language based on Datalog that supports differentiable logical and relational reasoning. Scallop can be integrated in Python and with a PyTorch learning module. Logic Tensor Networks: encode logical formulas as neural networks and simultaneously learn term encodings, term weights, and formula weights. DeepProbLog: combines neural networks with the probabilistic reasoning of ProbLog. Abductive Learning: integrates machine learning and logical reasoning in a balanced-loop via abductive reasoning, enabling them to work together in a mutually beneficial way. SymbolicAI: a compositional differentiable programming library.

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  AIOps

  AIOps (Artificial Intelligence for IT Operations) refers to the use of artificial intelligence, machine learning, and big data analytics to automate and enhance data center management. It helps organizations manage complex IT environments by detecting, diagnosing, and resolving issues more efficiently than traditional methods. == History == AIOps was first defined by Gartner in 2016, combining "artificial intelligence" and "IT operations" to describe the application of AI and machine learning to enhance IT operations. This concept was introduced to address the increasing complexity and data volume in IT environments, aiming to automate processes such as event correlation, anomaly detection, and causality determination. == Definition == AIOps refers to multi-layered, complex technology platforms that enhance and automate IT operations by using machine learning and analytics to analyze the large amounts of data collected from various DevOps devices and tools, automatically identifying and responding to issues in real-time. AIOps represents a shift from isolated IT data to aggregated observational data (e.g., job logs and monitoring systems) and interaction data (such as ticketing, events, or incident records) within a big data platform. AIOps applies machine learning and analytics to this data, resulting in continuous visibility that, when combined with automation, can lead to ongoing improvements. AIOps connects three IT disciplines (automation, service management, and performance management) to achieve continuous visibility and improvement. This new approach in modern, accelerated, and hyper-scaled IT environments leverages advances in machine learning and big data to overcome previous limitations. == Components == AIOps includes, but is not limited to, the following processes and techniques: Anomaly Detection Log Analysis Root Cause Analysis Cohort Analysis Event Correlation Predictive Analytics Hardware Failure Prediction Automated Remediation Performance Prediction Incident Management Causality Determination Queue Management Resource Scheduling and Optimization Predictive Capacity Management Resource Allocation Service Quality Monitoring Deployment and Integration Testing System Configuration Auto-diagnosis and Problem Localization Efficient ML Training and Inferencing Using LLMs for Cloud Ops Auto Service Healing Data Center Management Customer Support Security and Privacy in Cloud Operations == Comparison with DevOps == AIOps is increasingly compared with DevOps in terms of impact on operational efficiency. While DevOps focuses on collaboration between development and operations teams to accelerate software delivery, AIOps integrates artificial intelligence to enhance monitoring, automation, and predictive capabilities. Various industry analyses have explored the similarities and differences between the two approaches, including discussions on how organizations can combine them to improve incident management and resource optimization. == Results == AI optimizes IT operations in five ways: First, intelligent monitoring powered by AI helps identify potential issues before they cause outages, improving metrics like Mean Time to Detect (MTTD) by 15-20%. Second, performance data analysis and insights enable quick decision-making by ingesting and analyzing large data sets in real time. Third, AI-driven automated infrastructure optimization efficiently allocates resources and thereby reducing cloud costs. Fourth, enhanced IT service management reduces critical incidents by over 50% through AI-driven end-to-end service management. Lastly, intelligent task automation accelerates problem resolution and automates remedial actions with minimal human intervention. In 2025, Atera Networks was identified as a leader in AIOps by the software review platform G2. == AIOps vs. MLOps == AIOps tools use big data analytics, machine learning algorithms, and predictive analytics to detect anomalies, correlate events, and provide proactive insights. This automation reduces the burden on IT teams, allowing them to focus on strategic tasks rather than routine operational issues. AIOps is widely used by IT operations teams, DevOps, network administrators, and IT service management (ITSM) teams to enhance visibility and enable quicker incident resolution in hybrid cloud environments, data centers, and other IT infrastructures. In contrast to MLOps (Machine Learning Operations), which focuses on the lifecycle management and operational aspects of machine learning models, AIOps focuses on optimizing IT operations using a variety of analytics and AI-driven techniques. While both disciplines rely on AI and data-driven methods, AIOps primarily targets IT operations, whereas MLOps is concerned with the deployment, monitoring, and maintenance of ML models. == Conferences == There are several conferences that are specific to AIOps: AIOps Summit AI Dev Summit IBM Think conference

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  Labeled data

  Labeled data is a group of samples that have been tagged with one or more labels. Labeling typically takes a set of unlabeled data and augments each piece of it with informative tags called judgments. For example, a data label might indicate whether a photo contains a horse or a cow, which words were uttered in an audio recording, what type of action is being performed in a video, what the topic of a news article is, what the overall sentiment of a tweet is, or whether a dot in an X-ray is a tumor. Labels can be obtained by having humans make judgments about a given piece of unlabeled data. Labeled data is significantly more expensive to obtain than the raw unlabeled data. The quality of labeled data directly influences the performance of supervised machine learning models in operation, as these models learn from the provided labels. == Crowdsourced labeled data == In 2006, Fei-Fei Li, the co-director of the Stanford Human-Centered AI Institute, initiated research to improve the artificial intelligence models and algorithms for image recognition by significantly enlarging the training data. The researchers downloaded millions of images from the World Wide Web and a team of undergraduates started to apply labels for objects to each image. In 2007, Li outsourced the data labeling work on Amazon Mechanical Turk, an online marketplace for digital piece work. The 3.2 million images that were labeled by more than 49,000 workers formed the basis for ImageNet, one of the largest hand-labeled database for outline of object recognition. == Automated data labelling == After obtaining a labeled dataset, machine learning models can be applied to the data so that new unlabeled data can be presented to the model and a likely label can be guessed or predicted for that piece of unlabeled data. == Challenges == === Data-driven bias === Algorithmic decision-making is subject to programmer-driven bias as well as data-driven bias. Training data that relies on bias labeled data will result in prejudices and omissions in a predictive model, despite the machine learning algorithm being legitimate. The labeled data used to train a specific machine learning algorithm needs to be a statistically representative sample to not bias the results. For example, in facial recognition systems underrepresented groups are subsequently often misclassified if the labeled data available to train has not been representative of the population,. In 2018, a study by Joy Buolamwini and Timnit Gebru demonstrated that two facial analysis datasets that have been used to train facial recognition algorithms, IJB-A and Adience, are composed of 79.6% and 86.2% lighter skinned humans respectively. === Human error and inconsistency === Human annotators are prone to errors and biases when labeling data. This can lead to inconsistent labels and affect the quality of the data set. The inconsistency can affect the machine learning model's ability to generalize well. === Domain expertise === Certain fields, such as legal document analysis or medical imaging, require annotators with specialized domain knowledge. Without the expertise, the annotations or labeled data may be inaccurate, negatively impacting the machine learning model's performance in a real-world scenario.

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  Labeled data

  Labeled data is a group of samples that have been tagged with one or more labels. Labeling typically takes a set of unlabeled data and augments each piece of it with informative tags called judgments. For example, a data label might indicate whether a photo contains a horse or a cow, which words were uttered in an audio recording, what type of action is being performed in a video, what the topic of a news article is, what the overall sentiment of a tweet is, or whether a dot in an X-ray is a tumor. Labels can be obtained by having humans make judgments about a given piece of unlabeled data. Labeled data is significantly more expensive to obtain than the raw unlabeled data. The quality of labeled data directly influences the performance of supervised machine learning models in operation, as these models learn from the provided labels. == Crowdsourced labeled data == In 2006, Fei-Fei Li, the co-director of the Stanford Human-Centered AI Institute, initiated research to improve the artificial intelligence models and algorithms for image recognition by significantly enlarging the training data. The researchers downloaded millions of images from the World Wide Web and a team of undergraduates started to apply labels for objects to each image. In 2007, Li outsourced the data labeling work on Amazon Mechanical Turk, an online marketplace for digital piece work. The 3.2 million images that were labeled by more than 49,000 workers formed the basis for ImageNet, one of the largest hand-labeled database for outline of object recognition. == Automated data labelling == After obtaining a labeled dataset, machine learning models can be applied to the data so that new unlabeled data can be presented to the model and a likely label can be guessed or predicted for that piece of unlabeled data. == Challenges == === Data-driven bias === Algorithmic decision-making is subject to programmer-driven bias as well as data-driven bias. Training data that relies on bias labeled data will result in prejudices and omissions in a predictive model, despite the machine learning algorithm being legitimate. The labeled data used to train a specific machine learning algorithm needs to be a statistically representative sample to not bias the results. For example, in facial recognition systems underrepresented groups are subsequently often misclassified if the labeled data available to train has not been representative of the population,. In 2018, a study by Joy Buolamwini and Timnit Gebru demonstrated that two facial analysis datasets that have been used to train facial recognition algorithms, IJB-A and Adience, are composed of 79.6% and 86.2% lighter skinned humans respectively. === Human error and inconsistency === Human annotators are prone to errors and biases when labeling data. This can lead to inconsistent labels and affect the quality of the data set. The inconsistency can affect the machine learning model's ability to generalize well. === Domain expertise === Certain fields, such as legal document analysis or medical imaging, require annotators with specialized domain knowledge. Without the expertise, the annotations or labeled data may be inaccurate, negatively impacting the machine learning model's performance in a real-world scenario.

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