AI Face Paint

AI Face Paint — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

  • Exposure Notification

    Exposure Notification

    The (Google/Apple) Exposure Notification System (GAEN) is a framework and protocol specification developed by Apple Inc. and Google to facilitate digital contact tracing during the COVID-19 pandemic. When used by health authorities, it augments more traditional contact tracing techniques by automatically logging close approaches among notification system users using Android or iOS smartphones. Exposure Notification is a decentralized reporting protocol built on a combination of Bluetooth Low Energy technology and privacy-preserving cryptography. It is an opt-in feature within COVID-19 apps developed and published by authorized health authorities. Unveiled on April 10, 2020, it was made available on iOS on May 20, 2020, as part of the iOS 13.5 update and on December 14, 2020, as part of the iOS 12.5 update for older iPhones. On Android, it was added to devices via a Google Play Services update, supporting all versions since Android Marshmallow. The Apple/Google protocol is similar to the Decentralized Privacy-Preserving Proximity Tracing (DP-3T) protocol created by the European DP-3T consortium and the Temporary Contact Number (TCN) protocol by Covid Watch, but is implemented at the operating system level, which allows for more efficient operation as a background process. Since May 2020, a variant of the DP-3T protocol is supported by the Exposure Notification Interface. Other protocols are constrained in operation because they are not privileged over normal apps. This leads to issues, particularly on iOS devices where digital contact tracing apps running in the background experience significantly degraded performance. The joint approach is also designed to maintain interoperability between Android and iOS devices, which constitute nearly all of the market. The ACLU stated the approach "appears to mitigate the worst privacy and centralization risks, but there is still room for improvement". In late April, Google and Apple shifted the emphasis of the naming of the system, describing it as an "exposure notification service", rather than "contact tracing" system. == Technical specification == Digital contact tracing protocols typically have two major responsibilities: encounter logging and infection reporting. Exposure Notification only involves encounter logging which is a decentralized architecture. The majority of infection reporting is centralized in individual app implementations. To handle encounter logging, the system uses Bluetooth Low Energy to send tracking messages to nearby devices running the protocol to discover encounters with other people. The tracking messages contain unique identifiers that are encrypted with a secret daily key held by the sending device. These identifiers change every 15–20 minutes as well as Bluetooth MAC address in order to prevent tracking of clients by malicious third parties through observing static identifiers over time. The sender's daily encryption keys are generated using a random number generator. Devices record received messages, retaining them locally for 14 days. If a user tests positive for infection, the last 14 days of their daily encryption keys can be uploaded to a central server, where it is then broadcast to all devices on the network. The method through which daily encryption keys are transmitted to the central server and broadcast is defined by individual app developers. The Google-developed reference implementation calls for a health official to request a one-time verification code (VC) from a verification server, which the user enters into the encounter logging app. This causes the app to obtain a cryptographically signed certificate, which is used to authorize the submission of keys to the central reporting server. The received keys are then provided to the protocol, where each client individually searches for matches in their local encounter history. If a match meeting certain risk parameters is found, the app notifies the user of potential exposure to the infection. Google and Apple intend to use the received signal strength (RSSI) of the beacon messages as a source to infer proximity. RSSI and other signal metadata will also be encrypted to resist deanonymization attacks. === Version 1.0 === To generate encounter identifiers, first a persistent 32-byte private Tracing Key ( t k {\displaystyle tk} ) is generated by a client. From this a 16 byte Daily Tracing Key is derived using the algorithm d t k i = H K D F ( t k , N U L L , 'CT-DTK' | | D i , 16 ) {\displaystyle dtk_{i}=HKDF(tk,NULL,{\text{'CT-DTK'}}||D_{i},16)} , where H K D F ( Key, Salt, Data, OutputLength ) {\displaystyle HKDF({\text{Key, Salt, Data, OutputLength}})} is a HKDF function using SHA-256, and D i {\displaystyle D_{i}} is the day number for the 24-hour window the broadcast is in starting from Unix Epoch Time. These generated keys are later sent to the central reporting server should a user become infected. From the daily tracing key a 16-byte temporary Rolling Proximity Identifier is generated every 10 minutes with the algorithm R P I i , j = Truncate ( H M A C ( d t k i , 'CT-RPI' | | T I N j ) , 16 ) {\displaystyle RPI_{i,j}={\text{Truncate}}(HMAC(dtk_{i},{\text{'CT-RPI'}}||TIN_{j}),16)} , where H M A C ( Key, Data ) {\displaystyle HMAC({\text{Key, Data}})} is a HMAC function using SHA-256, and T I N j {\displaystyle TIN_{j}} is the time interval number, representing a unique index for every 10 minute period in a 24-hour day. The Truncate function returns the first 16 bytes of the HMAC value. When two clients come within proximity of each other they exchange and locally store the current R P I i , j {\displaystyle RPI_{i,j}} as the encounter identifier. Once a registered health authority has confirmed the infection of a user, the user's Daily Tracing Key for the past 14 days is uploaded to the central reporting server. Clients then download this report and individually recalculate every Rolling Proximity Identifier used in the report period, matching it against the user's local encounter log. If a matching entry is found, then contact has been established and the app presents a notification to the user warning them of potential infection. === Version 1.1 === Unlike version 1.0 of the protocol, version 1.1 does not use a persistent tracing key, rather every day a new random 16-byte Temporary Exposure Key ( t e k i {\displaystyle tek_{i}} ) is generated. This is analogous to the daily tracing key from version 1.0. Here i {\displaystyle i} denotes the time is discretized in 10 minute intervals starting from Unix Epoch Time. From this two 128-bit keys are calculated, the Rolling Proximity Identifier Key ( R P I K i {\displaystyle RPIK_{i}} ) and the Associated Encrypted Metadata Key ( A E M K i {\displaystyle AEMK_{i}} ). R P I K i {\displaystyle RPIK_{i}} is calculated with the algorithm R P I K i = H K D F ( t e k i , N U L L , 'EN-RPIK' , 16 ) {\displaystyle RPIK_{i}=HKDF(tek_{i},NULL,{\text{'EN-RPIK'}},16)} , and A E M K i {\displaystyle AEMK_{i}} using the algorithm A E M K i = H K D F ( t e k i , N U L L , 'EN-AEMK' , 16 ) {\displaystyle AEMK_{i}=HKDF(tek_{i},NULL,{\text{'EN-AEMK'}},16)} . From these values a temporary Rolling Proximity Identifier ( R P I i , j {\displaystyle RPI_{i,j}} ) is generated every time the BLE MAC address changes, roughly every 15–20 minutes. The following algorithm is used: R P I i , j = A E S 128 ( R P I K i , 'EN-RPI' | | 0 x 000000000000 | | E N I N j ) {\displaystyle RPI_{i,j}=AES128(RPIK_{i},{\text{'EN-RPI'}}||{\mathtt {0x000000000000}}||ENIN_{j})} , where A E S 128 ( Key, Data ) {\displaystyle AES128({\text{Key, Data}})} is an AES cryptography function with a 128-bit key, the data is one 16-byte block, j {\displaystyle j} denotes the Unix Epoch Time at the moment the roll occurs, and E N I N j {\displaystyle ENIN_{j}} is the corresponding 10-minute interval number. Next, additional Associated Encrypted Metadata is encrypted. What the metadata represents is not specified, likely to allow the later expansion of the protocol. The following algorithm is used: Associated Encrypted Metadata i , j = A E S 128 _ C T R ( A E M K i , R P I i , j , Metadata ) {\displaystyle {\text{Associated Encrypted Metadata}}_{i,j}=AES128\_CTR(AEMK_{i},RPI_{i,j},{\text{Metadata}})} , where A E S 128 _ C T R ( Key, IV, Data ) {\displaystyle AES128\_CTR({\text{Key, IV, Data}})} denotes AES encryption with a 128-bit key in CTR mode. The Rolling Proximity Identifier and the Associated Encrypted Metadata are then combined and broadcast using BLE. Clients exchange and log these payloads. Once a registered health authority has confirmed the infection of a user, the user's Temporary Exposure Keys t e k i {\displaystyle tek_{i}} and their respective interval numbers i {\displaystyle i} for the past 14 days are uploaded to the central reporting server. Clients then download this report and individually recalculate every Rolling Proximity Identifier starting from interval number i {\displaystyle i} ,

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  • Asian Digital Finance Forum & Awards

    Asian Digital Finance Forum & Awards

    Asian Digital Finance Forum & Awards (also known as Asian Digital Finance Forum and Awards) is a forum and honorary awards platform convened in Colombo, Sri Lanka. It has been hosted in a hybrid format (virtual and in-person), with editions reported in 2022, 2023 and 2025. The event is organised by the Asian FinTech Academy (AFTA) in collaboration with a number of local and international institutions. == Overview == The forum has featured international academic, industry, and policy speakers and has recognised institutions and individuals for contributions related to digital finance and fintech innovation. Media coverage has described participation and recognition at the forum as spanning multiple regions, with institutions and individuals from South Asia, Southeast Asia, East Asia, the Middle East, Europe, and North America featured across different editions. == Awards and recognition == The forum and awards were held in a hybrid format with virtual and in-person proceedings at Hilton Colombo in the 2022 and 2023 editions. The Asian Digital Finance Forum & Awards presents honorary recognitions to institutions and individuals for contributions to digital finance, financial inclusion, and related regulatory, technological, and policy developments. Media coverage has described the recognitions as non-competitive and based on demonstrated leadership and impact rather than open nominations. In 2025, the forum and awards served as an anchor initiative associated with the Asia International Digital Economy & AI in Finance Summit at Port City Colombo, with an emphasis on artificial intelligence in finance, financial inclusion, and governance-related themes. === 2022 === According to reporting by Daily FT, institutions recognised at the 2022 edition included Sri Lanka’s Bank of Ceylon, Commercial Bank of Ceylon, Hatton National Bank, and People’s Bank, alongside international organisations and fintech-sector contributors. === 2023 === Coverage of the 2023 forum described recognitions awarded to India’s International Financial Services Centres Authority (IFSCA) for regulatory innovation, as well as to digital finance and payments platforms including Dialog Genie and SLT-Mobitel mCash. IDEMIA’s Asia–Pacific operations were also recognised for contributions related to biometric and digital identity technologies in financial services. === 2025 === For the 2025 edition, institutional honourees reported in the media included Nium (Singapore), recognised for cross-border payments optimisation, and Paytm (India), recognised for AI-powered financial inclusion initiatives. A Visionary Award for Next-Generation Financial Hub Development was presented to Port City Colombo in recognition of its fintech- and AI-oriented development strategy. Individual honourees reported for 2025 included Sopnendu Mohanty (Singapore), Neil Tan (Hong Kong), Purvi Munot (United Arab Emirates), and Amira Abdelaziz (Egypt), recognised for contributions spanning fintech governance, ecosystem development, inclusive wealth technology, and AI-driven financial policy and regulation. In 2025, media reports described the awards as being subject to an independent validation framework. The process was led by Dr. Sivaguru S. Sritharan, appointed as Global Validation Chair, and involved independent research, analytical review, and benchmarking against international standards, with recognitions characterised as honorary and non-competitive.

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  • Oxa

    Oxa

    Oxa (formerly Oxbotica) is an autonomous vehicle software company, headquartered in Oxfordshire, England, and founded by Paul Newman and Ingmar Posner. == History == In 2013, Newman and Posner led the RobotCar UK project as part of Oxford University's Department of Engineering Science Mobile Robotics Group. RobotCar became the first autonomous vehicle on UK roads. In 2014, the pair used the newly developed technology to found Oxbotica. Oxbotica has raised over $18 million to date and is backed by the IP Group, Parkwalk Advisors and AXA XL. In 2018, Uber's former EMEA business head, Fraser Robinson, was appointed to the board of directors. In May 2019, Ozgur Tohumcu replaced Dr Graeme Smith as Oxbotica's CEO. Also in 2019, the company opened an office in Toronto, Canada. In January 2021, Oxbotica announced it had raised $47 million in a Series B round. In August 2021, the company achieved a safety landmark as the first company to have its autonomy safety case assessed by BSI (British Standards Institution) against the requirements of the UK Code of Practice 2019, PAS 1881:2020 and PAS 1883:2020, certifying the safety conformity of its autonomous vehicle trials and testing. The assessment was completed as part of Project Endeavour, the UK's first multi-city demonstration of autonomous vehicle services and capability. In December 2021, Gavin Jackson was named CEO. In January 2023, the company raised $140 million in a Series C round. In May 2023, the company changed its name to Oxa. Oxa raised $103 million (£77 million) in March 2026, including $50 million from the UK National Wealth Fund. Nvidia's venture capital division, NVentures, also invested in the Series D funding round, along with existing Oxa shareholders IP Group, Australian pension fund Hostplus, and BP Ventures, a division of the UK oil company. == Technology == Oxa designs software and hardware for the conversion of industrial vehicles into autonomous ones. Its full stack, end-to-end Universal Autonomy software is both vehicle and platform-agnostic, with no dependence on external infrastructure such as GPS. It can be deployed in any environment and on any terrain. In addition to underground uses, the technology is also useful in natural canyons and forests, where GPS signals are weak or non-existent, but also in "urban canyons" — cities with tall buildings that obstruct GPS signals for proper navigation. == Public deployments == The LUTZ Pathfinder pod had its first public demonstration in February 2015 in Milton Keynes. The Government-funded project was designed to ensure that autonomous vehicles would comply with the Highway Code. The pod featured autonomous control software from Oxbotica, including 19 sensors, cameras, radar and Lidar. As part of the GATEway Project in 2017, Oxbotica trialled seven autonomous shuttle buses in Greenwich, navigating a two-mile riverside path near London's O2 Arena on a route that is also used by pedestrians and cyclists. Oxbotica ran the UK's first trial of autonomous grocery deliveries that year, with British online supermarket Ocado in London, as the next step in the GATEway Project. In 2018, Oxbotica deployed its autonomous vehicle software at London's Gatwick Airport, which subsequently became the first airport in the world to trial an autonomous shuttle service. The electric-powered vehicles transported staff via airside roads between the airport's North and South terminals. An airside trial of Oxbotica's autonomous driving technology was then successfully completed at Heathrow Airport in partnership with IAG Cargo, the first airside trial of an autonomous vehicle at a UK airport. The Oxbotica-designed CargoPod ran autonomously along a cargo route around the airside perimeter for three weeks. As part of the UK Centre for Connected and Autonomous Vehicles-funded DRIVEN project, Oxbotica is developing and deploying a fleet of Ford Fusion autonomous vehicles running in both London and Oxford on public roads, and in conjunction with its consortium partners, running real-time insurance. AXA XL is partnering with Oxbotica on the development of smart insurance products using Oxbotica's autonomy technology to improve road safety. In 2018, Oxbotica announced a partnership with London private taxi firm Addison Lee to develop and deploy autonomous taxis in the city of London by 2021. A 3D street mapping exercise was conducted in London's Canary Wharf. In 2019, Oxbotica deployed a fleet of their autonomous technology within Ford Mondeo cars on public roads in Stratford, London to test their use in city environments. The £13.2 million project is in collaboration with The DRIVEN Project to develop self-driving cars. == Awards == 2019 Royal Academy of Engineering Silver Medal - Paul Newman 2017 Financial Times ArcelorMittal Boldness in Business Award Barclays Award for Innovation 2016 Frost & Sullivan Award, Technology Leadership for Autonomous Driving Software

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  • 2023 Bilderberg Conference

    2023 Bilderberg Conference

    The 2023 Bilderberg Conference or Bilderberg Club was held between May 18–21, 2023 at the Pestana Palace hotel in Lisbon, Portugal. The 2023 meeting was the 69th edition of the event. A Bilderberg Group press release stated that there were approximately 130 participants from 23 countries. Established in 1954 by Prince Bernhard of the Netherlands, Bilderberg conferences (or meetings) are an annual private gathering of the European and North American political and business elite. Events are attended by between 120 and 150 people each year invited by the Bilderberg Group's steering committee; including prominent politicians, CEOs, national security experts, academics and journalists. The 2023 conference received some media attention due to the participation of several major players in the artificial intelligence space, such as OpenAI CEO Sam Altman, Microsoft CEO Satya Nadella, Google DeepMind chief Demis Hassabis and former Google CEO Eric Schmidt. Bilderberg conferences operate under Chatham House Rule, meaning that participants are cannot disclose the identity or affiliation of any particular speaker. There were no press conferences during or after the event, as is customary. According to The Guardian, the paper's journalists were able to approach one high-ranking attendee, economist Victor Halberstadt, in a Lisbon pharmacy, but he denied his identity before jumping into a car and heading back to his hotel. == Agenda == The key topics for discussion at the 2023 Bilderberg Conference were announced on the Bilderberg website shortly before the meeting. These topics included: == Participants == A list of 128 participants was published on the Bilderberg website. This list may not be complete, as a source connected to the Bilderberg group told The Daily Telegraph in 2013 that some attendees do not have their names publicized. Oscar Stenström, Sweden’s chief negotiator for NATO membership, was reported to have been seen at the venue despite his name not being on the list.

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  • Automated storage and retrieval system

    Automated storage and retrieval system

    An automated storage and retrieval system (ASRS or AS/RS) consists of a variety of computer-controlled systems for automatically placing and retrieving loads from defined storage locations. Automated storage and retrieval systems (AS/RS) are typically used in applications where: There is a very high volume of loads being moved into and out of storage Storage density is important because of space constraints No value is added in this process (no processing, only storage and transport) Accuracy is critical because of potential expensive damages to the load An AS/RS can be used with standard loads as well as nonstandard loads, meaning that each standard load can fit in a uniformly-sized volume; for example, the film canisters in the image of the Defense Visual Information Center are each stored as part of the contents of the uniformly sized metal boxes, which are shown in the image. Standard loads simplify the handling of a request of an item. In addition, audits of the accuracy of the inventory of contents can be restricted to the contents of an individual metal box, rather than undergoing a top-to-bottom search of the entire facility, for a single item. They can also be used in self storage places. == Overview == AS/RS systems are designed for automated storage and retrieval of parts and items in manufacturing, distribution, retail, wholesale and institutions. They first originated in the 1960s, initially focusing on heavy pallet loads but with the evolution of the technology the handled loads have become smaller. The systems operate under computerized control, maintaining an inventory of stored items. Retrieval of items is accomplished by specifying the item type and quantity to be retrieved. The computer determines where in the storage area the item can be retrieved from and schedules the retrieval. It directs the proper automated storage and retrieval machine (SRM) to the location where the item is stored and directs the machine to deposit the item at a location where it is to be picked up. A system of conveyors and or automated guided vehicles is sometimes part of the AS/RS system. These take loads into and out of the storage area and move them to the manufacturing floor or loading docks. To store items, the pallet or tray is placed at an input station for the system, the information for inventory is entered into a computer terminal and the AS/RS system moves the load to the storage area, determines a suitable location for the item, and stores the load. As items are stored into or retrieved from the racks, the computer updates its inventory accordingly. The benefits of an AS/RS system include reduced labor for transporting items into and out of inventory, reduced inventory levels, more accurate tracking of inventory, and space savings. Items are often stored more densely than in systems where items are stored and retrieved manually. Within the storage, items can be placed on trays or hang from bars, which are attached to chains/drives in order to move up and down. The equipment required for an AS/RS include a storage & retrieval machine (SRM) that is used for rapid storage and retrieval of material. SRMs are used to move loads vertically or horizontally, and can also move laterally to place objects in the correct storage location. The trend towards Just In Time production often requires sub-pallet level availability of production inputs, and AS/RS is a much faster way of organizing the storage of smaller items next to production lines. The Material Handling Institute of America (MHIA), the non-profit trade association for the material handling world, and its members have categorised AS/RS into two primary segments: Fixed Aisle and Carousels/Vertical Lift Modules (VLMs). Both sets of technologies provide automated storage and retrieval for parts and items, but use different technologies. Each technology has its unique set of benefits and disadvantages. Fixed Aisle systems are characteristically larger systems whereas carousels and Vertical Lift Modules are used individually or grouped, but in small to medium-sized applications. A fixed-aisle AS/R machine (stacker crane) is one of two main designs: single-masted or double masted. Most are supported on a track and ceiling guided at the top by guide rails or channels to ensure accurate vertical alignment, although some are suspended from the ceiling. The 'shuttles' that make up the system travel between fixed storage shelves to deposit or retrieve a requested load (ranging from a single book in a library system to a several ton pallet of goods in a warehouse system). The entire unit moves horizontally within an aisle, while the shuttles are able to elevate up to the necessary height to reach the load, and can extend and retract to store or retrieve loads that are several positions deep in the shelving. A semi-automated system can be achieved by utilizing only specialized shuttles within an existing rack system. Another AS/RS technology is known as shuttle technology. In this technology the horizontal movement is made by independent shuttles each operating on one level of the rack while a lift at a fixed position within the rack is responsible for the vertical movement. By using two separate machines for these two axes the shuttle technology is able to provide higher throughput rates than stacker cranes. Storage and Retrieval Machines pick up or drop off loads to the rest of the supporting transportation system at specific stations, where inbound and outbound loads are precisely positioned for proper handling. In addition, there are several types of Automated Storage & Retrieval Systems (AS/RS) devices called Unit-load AS/RS, Mini-load AS/RS, Mid-Load AS/RS, Vertical Lift Modules (VLMs), Horizontal Carousels and Vertical Carousels. These systems are used either as stand-alone units or in integrated workstations called pods or systems. These units are usually integrated with various types of pick to light systems and use either a microprocessor controller for basic usage or inventory management software. These systems are ideal for increasing space utilization up to 90%, productivity levels by 90%, accuracy to 99.9%+ levels and throughput up to 750 lines per hour/per operator or more depending on the configuration of the system. == Horizontal carousels == Robotic Inserter/Extractor devices can be used for horizontal carousels. The robotic device is positioned in the front or rear of up to three horizontal carousels tiered high. The robot grabs the tote required in the order and often replenishes at the same time to speed up throughput. The tote(s) are then delivered to a conveyor, which routes it to a work station for picking or replenishing. Up to eight transactions per minute per unit can be done. Totes or containers up to 36" x 36" x 36" can be used in a system. On a simplistic level, horizontal carousels are also often used as "rotating shelving". With simple "fetch" command, items are brought to the operator and otherwise wasted space is eliminated. AS/RS Applications: Most applications of AS/RS technology have been associated with warehousing and distribution operations. An AS/RS can also be used to store raw materials and work in process in manufacturing. Three application areas can be distinguished for AS/RS: (1) Unit load storage and handling, (2) Order picking, and (3) Work in process storage. Unit load storage and retrieval applications are represented by unit load AS/RS and deep-lane storage systems. These kinds of applications are commonly found in warehousing for finishing goods in a distribution center, rarely in manufacturing. Deep-lane systems are used in the food industry. As described above, order picking involves retrieving materials in less than full unit load quantities. Minilpass, man-on board, and items retrieval systems are used for this second application area. Work in process storage is a more recent application of automated storage technology. While it is desirable to minimize the amount of work in process, WIP is unavoidable and must be effectively managed. Automated storage systems, either automated storage/retrieval systems or carousel systems, represent an efficient way to store materials between processing steps, particularly in batch and job shop production. In high production, work in process is often carried between operations by conveyor system, which this serve both storage and transport functions. === Inventory Category-specific AS/RS === Each inventory category—raw materials, work-in-process, and finished goods—requires its own specialized Automated Storage and Retrieval System (AS/RS). Particularly for work-in-process (WIP) inventories, due to variations in manufacturing processes, the AS/RS systems are significantly different in design and function, tailored specifically to match unique handling, storage, and retrieval requirements === Installed applications === Installed applications of this technology can be wide-ranging. In some librarie

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  • Autonomic computing

    Autonomic computing

    Autonomic computing (AC) is distributed computing resources with self-managing characteristics, adapting to unpredictable changes while hiding intrinsic complexity to operators and users. Initiated by IBM in 2001, this initiative ultimately aimed to develop computer systems capable of self-management, to overcome the rapidly growing complexity of computing systems management, and to reduce the barrier that complexity poses to further growth. == Description == The AC system concept is designed to make adaptive decisions, using high-level policies. It will constantly check and optimize its status and automatically adapt itself to changing conditions. An autonomic computing framework is composed of autonomic components (AC) interacting with each other. An AC can be modeled in terms of two main control schemes (local and global) with sensors (for self-monitoring), effectors (for self-adjustment), knowledge and planner/adapter for exploiting policies based on self- and environment awareness. This architecture is sometimes referred to as Monitor-Analyze-Plan-Execute (MAPE). Driven by such vision, a variety of architectural frameworks based on "self-regulating" autonomic components has been recently proposed. A similar trend has recently characterized significant research in the area of multi-agent systems. However, most of these approaches are typically conceived with centralized or cluster-based server architectures in mind and mostly address the need of reducing management costs rather than the need of enabling complex software systems or providing innovative services. Some autonomic systems involve mobile agents interacting via loosely coupled communication mechanisms. Autonomy-oriented computation is a paradigm proposed by Jiming Liu in 2001 that uses artificial systems imitating social animals' collective behaviours to solve difficult computational problems. For example, ant colony optimization could be studied in this paradigm. == Problem of growing complexity == Forecasts suggested that the computing devices in use would grow at 38% per year and the average complexity of each device was increasing. This volume and complexity was managed by highly skilled humans; but the demand for skilled IT personnel was already outstripping supply, with labour costs exceeding equipment costs by a ratio of up to 18:1. Computing systems have brought great benefits of speed and automation but there is now an overwhelming economic need to automate their maintenance. In a 2003 IEEE Computer article, Kephart and Chess warn that the dream of interconnectivity of computing systems and devices could become the "nightmare of pervasive computing" in which architects are unable to anticipate, design and maintain the complexity of interactions. They state the essence of autonomic computing is system self-management, freeing administrators from low-level task management while delivering better system behavior. A general problem of modern distributed computing systems is that their complexity, and in particular the complexity of their management, is becoming a significant limiting factor in their further development. Large companies and institutions are employing large-scale computer networks for communication and computation. The distributed applications running on these computer networks are diverse and deal with multiple tasks, ranging from internal control processes to presenting web content to customer support. Additionally, mobile computing is pervading these networks at an increasing speed: employees need to communicate with their companies while they are not in their office. They do so by using laptops, personal digital assistants, or mobile phones with diverse forms of wireless technologies to access their companies' data. This creates an enormous complexity in the overall computer network which is hard to control manually by human operators. Manual control is time-consuming, expensive, and error-prone. The manual effort needed to control a growing networked computer-system tends to increase quickly. 80% of such problems in infrastructure happen at the client specific application and database layer. Most 'autonomic' service providers guarantee only up to the basic plumbing layer (power, hardware, operating system, network and basic database parameters). == Characteristics of autonomic systems == A possible solution could be to enable modern, networked computing systems to manage themselves without direct human intervention. The Autonomic Computing Initiative (ACI) aims at providing the foundation for autonomic systems. It is inspired by the autonomic nervous system of the human body. This nervous system controls important bodily functions (e.g. respiration, heart rate, and blood pressure) without any conscious intervention. In a self-managing autonomic system, the human operator takes on a new role: instead of controlling the system directly, he/she defines general policies and rules that guide the self-management process. For this process, IBM defined the following four types of property referred to as self-star (also called self-, self-x, or auto-) properties. Self-configuration: Automatic configuration of components; Self-healing: Automatic discovery, and correction of faults; Self-optimization: Automatic monitoring and control of resources to ensure the optimal functioning with respect to the defined requirements; Self-protection: Proactive identification and protection from arbitrary attacks. Others such as Poslad and Nami and Sharifi have expanded on the set of self-star as follows: Self-regulation: A system that operates to maintain some parameter, e.g., Quality of service, within a reset range without external control; Self-learning: Systems use machine learning techniques such as unsupervised learning which does not require external control; Self-awareness (also called Self-inspection and Self-decision): System must know itself. It must know the extent of its own resources and the resources it links to. A system must be aware of its internal components and external links in order to control and manage them; Self-organization: System structure driven by physics-type models without explicit pressure or involvement from outside the system; Self-creation (also called Self-assembly, Self-replication): System driven by ecological and social type models without explicit pressure or involvement from outside the system. A system's members are self-motivated and self-driven, generating complexity and order in a creative response to a continuously changing strategic demand; Self-management (also called self-governance): A system that manages itself without external intervention. What is being managed can vary dependent on the system and application. Self -management also refers to a set of self-star processes such as autonomic computing rather than a single self-star process; Self-description (also called self-explanation or Self-representation): A system explains itself. It is capable of being understood (by humans) without further explanation. IBM has set forth eight conditions that define an autonomic system: The system must know itself in terms of what resources it has access to, what its capabilities and limitations are and how and why it is connected to other systems; be able to automatically configure and reconfigure itself depending on the changing computing environment; be able to optimize its performance to ensure the most efficient computing process; be able to work around encountered problems by either repairing itself or routing functions away from the trouble; detect, identify and protect itself against various types of attacks to maintain overall system security and integrity; adapt to its environment as it changes, interacting with neighboring systems and establishing communication protocols; rely on open standards and cannot exist in a proprietary environment; anticipate the demand on its resources while staying transparent to users. Even though the purpose and thus the behaviour of autonomic systems vary from system to system, every autonomic system should be able to exhibit a minimum set of properties to achieve its purpose: Automatic: This essentially means being able to self-control its internal functions and operations. As such, an autonomic system must be self-contained and able to start-up and operate without any manual intervention or external help. Again, the knowledge required to bootstrap the system (Know-how) must be inherent to the system. Adaptive: An autonomic system must be able to change its operation (i.e., its configuration, state and functions). This will allow the system to cope with temporal and spatial changes in its operational context either long term (environment customisation/optimisation) or short term (exceptional conditions such as malicious attacks, faults, etc.). Aware: An autonomic system must be able to monitor (sense) its operational context as well as its internal state in order to be able to asses

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  • Predicate (logic)

    Predicate (logic)

    In logic, a predicate is a non-logical symbol that represents a property or a relation, though, formally, does not need to represent anything at all. For instance, in the first-order formula P ( a ) {\displaystyle P(a)} , the symbol P {\displaystyle P} is a predicate that applies to the individual constant a {\displaystyle a} which evaluates to either true or false. Similarly, in the formula R ( a , b ) {\displaystyle R(a,b)} , the symbol R {\displaystyle R} is a predicate that applies to the individual constants a {\displaystyle a} and b {\displaystyle b} . Predicates are considered a primitive notion of first-order, and higher-order logic and are therefore not defined in terms of other more basic concepts. The term derives from the grammatical term "predicate", meaning a word or phrase that represents a property or relation. In the semantics of logic, predicates are interpreted as relations. For instance, in a standard semantics for first-order logic, the formula R ( a , b ) {\displaystyle R(a,b)} would be true on an interpretation if the entities denoted by a {\displaystyle a} and b {\displaystyle b} stand in the relation denoted by R {\displaystyle R} . Since predicates are non-logical symbols, they can denote different relations depending on the interpretation given to them. While first-order logic only includes predicates that apply to individual objects, other logics may allow predicates that apply to collections of objects defined by other predicates. Strictly speaking, a predicate does not need to be given any interpretation, so long as its syntactic properties are well-defined. For example, equality may be understood solely through its reflexive and substitution properties (cf. Equality (mathematics) § Axioms). Other properties can be derived from these, and they are sufficient for proving theorems in mathematics. Similarly, set membership can be understood solely through the axioms of Zermelo–Fraenkel set theory. == Predicates in different systems == A predicate is a statement or mathematical assertion that contains variables, sometimes referred to as predicate variables, and may be true or false depending on those variables’ value or values. In propositional logic, atomic formulas are sometimes regarded as zero-place predicates. In a sense, these are nullary (i.e. 0-arity) predicates. In first-order logic, a predicate is a non-logical relation symbol, which forms an atomic formula when applied to an appropriate number of terms. In set theory with the law of excluded middle, predicates are understood to be characteristic functions or set indicator functions (i.e., functions from a set element to a truth value). Set-builder notation makes use of predicates to define sets. In autoepistemic logic, which rejects the law of excluded middle, predicates may be true, false, or simply unknown. In particular, a given collection of facts may be insufficient to determine the truth or falsehood of a predicate. In fuzzy logic, the strict true/false valuation of the predicate is replaced by a quantity interpreted as the degree of truth.

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  • Polyworld

    Polyworld

    Polyworld is a cross-platform (Linux, Mac OS X) program written by Larry Yaeger to evolve Artificial Intelligence through natural selection and evolutionary algorithms. It uses the Qt graphics toolkit and OpenGL to display a graphical environment in which a population of trapezoid agents search for food, mate, have offspring, and prey on each other. The population is typically only in the hundreds, as each individual is rather complex and the environment consumes considerable computer resources. The graphical environment is necessary since the individuals actually move around the 2-D plane and must be able to "see." Since some basic abilities, like eating carcasses or randomly generated food, seeing other individuals, mating or fighting with them, etc., are possible, a number of interesting behaviours have been observed to spontaneously arise after prolonged evolution, such as cannibalism, predators and prey, and mimicry. Each individual makes decisions based on a neural net using Hebbian learning; the neural net is derived from each individual's genome. The genome does not merely specify the wiring of the neural nets, but also determines their size, speed, color, mutation rate and a number of other factors. The genome is randomly mutated at a set probability, which are also changed in descendant organisms.

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  • Bright Computing

    Bright Computing

    Bright Computing, Inc. was a developer of software for deploying and managing high-performance (HPC) clusters, Kubernetes clusters, and OpenStack private clouds in on-premises data centers as well as in the public cloud. In 2022, it was acquired by Nvidia. == History == Bright Computing was founded by Matthijs van Leeuwen in 2009, who spun the company out of ClusterVision, which he had co-founded with Alex Ninaber and Arijan Sauer. Alex and Matthijs had worked together at UK’s Compusys, which was one of the first companies to commercially build HPC clusters. They left Compusys in 2002 to start ClusterVision in the Netherlands, after determining there was a growing market for building and managing supercomputer clusters using off-the-shelf hardware components and open source software, tied together with their own customized scripts. ClusterVision also provided delivery and installation support services for HPC clusters at universities and government entities. In 2004, Martijn de Vries joined ClusterVision and began development of cluster management software. The software was made available to customers in 2008, under the name ClusterVisionOS v4. In 2009, Bright Computing was spun out of ClusterVision. ClusterVisionOS was renamed Bright Cluster Manager, and van Leeuwen was named Bright Computing’s CEO. In February 2016, Bright appointed Bill Wagner as chief executive officer. Matthijs van Leeuwen became chief strategy officer, and then left the company and board of directors in 2018. In January 2022 Bright was acquired by Nvidia. Nvidia cited using Bright's Amsterdam facility as a development center. The acquisition occurred after several layoffs under Bill Wagner. == Customers == Early customers included Boeing, Sandia National Laboratories, Virginia Tech, Hewlett Packard, NSA, and Drexel University. Many early customers were introduced through resellers, including SICORP, Cray, Dell, and Advanced HPC. As of 2019, the company had more than 700 customers, including more than fifty Fortune 500 Companies. == Products and services == Bright Cluster Manager for HPC lets customers deploy and manage complete clusters. It provides management for the hardware, the operating system, the HPC software, and users. In 2014, the company announced Bright OpenStack, software to deploy, provision, and manage OpenStack-based private cloud infrastructures. In 2016, Bright started bundling several machine learning frameworks and associated tools and libraries with the product, to make it very easy to get machine learning workload up and running on a Bright cluster. In December 2018, version 8.2 was released, which introduced support for the ARM64 architecture, edge capabilities to build clusters spread out over many different geographical locations, improved workload accounting & reporting features, as well as many improvements to Bright's integration with Kubernetes. Bright Cluster Manager software was frequently sold through original equipment manufacturer (OEM) resellers, including Dell and HPE. In version 10, Bright Cluster Manager was merged into the NVIDIA Base Command Manager. Bright Computing was covered by Software Magazine and Yahoo! Finance, among other publications. == Awards == In 2016, Bright Computing was awarded a €1.5M Horizon 2020 SME Instrument grant from the European Commission. Bright Computing was one of only 33 grant recipients from 960 submitted proposals. In its category only 5 out of 260 grants were awarded. 2015 HPCwire Editor’s Choice Award for “Best HPC Cluster Solution or Technology" Main Software 50 “Highest Growth” award winner, 2013 Deloitte Technology Fast50 “Rising Star 2013” award winner Bio-IT World Conference & Expo ‘13, Boston, MA, winner of “IT Hardware & Infrastructure” category of the “Best of Show Award” program Red Herring Top 100 Global Award, 2013

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  • Construction of t-norms

    Construction of t-norms

    In mathematics, t-norms are a special kind of binary operations on the real unit interval [0, 1]. Various constructions of t-norms, either by explicit definition or by transformation from previously known functions, provide a plenitude of examples and classes of t-norms. This is important, e.g., for finding counter-examples or supplying t-norms with particular properties for use in engineering applications of fuzzy logic. The main ways of construction of t-norms include using generators, defining parametric classes of t-norms, rotations, or ordinal sums of t-norms. Relevant background can be found in the article on t-norms. == Generators of t-norms == The method of constructing t-norms by generators consists in using a unary function (generator) to transform some known binary function (most often, addition or multiplication) into a t-norm. In order to allow using non-bijective generators, which do not have the inverse function, the following notion of pseudo-inverse function is employed: Let f: [a, b] → [c, d] be a monotone function between two closed subintervals of extended real line. The pseudo-inverse function to f is the function f (−1): [c, d] → [a, b] defined as f ( − 1 ) ( y ) = { sup { x ∈ [ a , b ] ∣ f ( x ) < y } for f non-decreasing sup { x ∈ [ a , b ] ∣ f ( x ) > y } for f non-increasing. {\displaystyle f^{(-1)}(y)={\begin{cases}\sup\{x\in [a,b]\mid f(x)y\}&{\text{for }}f{\text{ non-increasing.}}\end{cases}}} === Additive generators === The construction of t-norms by additive generators is based on the following theorem: Let f: [0, 1] → [0, +∞] be a strictly decreasing function such that f(1) = 0 and f(x) + f(y) is in the range of f or in [f(0+), +∞] for all x, y in [0, 1]. Then the function T: [0, 1]2 → [0, 1] defined as T(x, y) = f (-1)(f(x) + f(y)) is a t-norm. Alternatively, one may avoid using the notion of pseudo-inverse function by having T ( x , y ) = f − 1 ( min ( f ( 0 + ) , f ( x ) + f ( y ) ) ) {\displaystyle T(x,y)=f^{-1}\left(\min \left(f(0^{+}),f(x)+f(y)\right)\right)} . The corresponding residuum can then be expressed as ( x ⇒ y ) = f − 1 ( max ( 0 , f ( y ) − f ( x ) ) ) {\displaystyle (x\Rightarrow y)=f^{-1}\left(\max \left(0,f(y)-f(x)\right)\right)} . And the biresiduum as ( x ⇔ y ) = f − 1 ( | f ( x ) − f ( y ) | ) {\displaystyle (x\Leftrightarrow y)=f^{-1}\left(\left|f(x)-f(y)\right|\right)} . If a t-norm T results from the latter construction by a function f which is right-continuous in 0, then f is called an additive generator of T. Examples: The function f(x) = 1 – x for x in [0, 1] is an additive generator of the Łukasiewicz t-norm. The function f defined as f(x) = –log(x) if 0 < x ≤ 1 and f(0) = +∞ is an additive generator of the product t-norm. The function f defined as f(x) = 2 – x if 0 ≤ x < 1 and f(1) = 0 is an additive generator of the drastic t-norm. Basic properties of additive generators are summarized by the following theorem: Let f: [0, 1] → [0, +∞] be an additive generator of a t-norm T. Then: T is an Archimedean t-norm. T is continuous if and only if f is continuous. T is strictly monotone if and only if f(0) = +∞. Each element of (0, 1) is a nilpotent element of T if and only if f(0) < +∞. The multiple of f by a positive constant is also an additive generator of T. T has no non-trivial idempotents. (Consequently, e.g., the minimum t-norm has no additive generator.) === Multiplicative generators === The isomorphism between addition on [0, +∞] and multiplication on [0, 1] by the logarithm and the exponential function allow two-way transformations between additive and multiplicative generators of a t-norm. If f is an additive generator of a t-norm T, then the function h: [0, 1] → [0, 1] defined as h(x) = e−f (x) is a multiplicative generator of T, that is, a function h such that h is strictly increasing h(1) = 1 h(x) · h(y) is in the range of h or equal to 0 or h(0+) for all x, y in [0, 1] h is right-continuous in 0 T(x, y) = h (−1)(h(x) · h(y)). Vice versa, if h is a multiplicative generator of T, then f: [0, 1] → [0, +∞] defined by f(x) = −log(h(x)) is an additive generator of T. == Parametric classes of t-norms == Many families of related t-norms can be defined by an explicit formula depending on a parameter p. This section lists the best known parameterized families of t-norms. The following definitions will be used in the list: A family of t-norms Tp parameterized by p is increasing if Tp(x, y) ≤ Tq(x, y) for all x, y in [0, 1] whenever p ≤ q (similarly for decreasing and strictly increasing or decreasing). A family of t-norms Tp is continuous with respect to the parameter p if lim p → p 0 T p = T p 0 {\displaystyle \lim _{p\to p_{0}}T_{p}=T_{p_{0}}} for all values p0 of the parameter. === Schweizer–Sklar t-norms === The family of Schweizer–Sklar t-norms, introduced by Berthold Schweizer and Abe Sklar in the early 1960s, is given by the parametric definition T p S S ( x , y ) = { T min ( x , y ) if p = − ∞ ( x p + y p − 1 ) 1 / p if − ∞ < p < 0 T p r o d ( x , y ) if p = 0 ( max ( 0 , x p + y p − 1 ) ) 1 / p if 0 < p < + ∞ T D ( x , y ) if p = + ∞ . {\displaystyle T_{p}^{\mathrm {SS} }(x,y)={\begin{cases}T_{\min }(x,y)&{\text{if }}p=-\infty \\(x^{p}+y^{p}-1)^{1/p}&{\text{if }}-\infty −∞ Continuous if and only if p < +∞ Strict if and only if −∞ < p ≤ 0 (for p = −1 it is the Hamacher product) Nilpotent if and only if 0 < p < +∞ (for p = 1 it is the Łukasiewicz t-norm). The family is strictly decreasing for p ≥ 0 and continuous with respect to p in [−∞, +∞]. An additive generator for T p S S {\displaystyle T_{p}^{\mathrm {SS} }} for −∞ < p < +∞ is f p S S ( x ) = { − log ⁡ x if p = 0 1 − x p p otherwise. {\displaystyle f_{p}^{\mathrm {SS} }(x)={\begin{cases}-\log x&{\text{if }}p=0\\{\frac {1-x^{p}}{p}}&{\text{otherwise.}}\end{cases}}} === Hamacher t-norms === The family of Hamacher t-norms, introduced by Horst Hamacher in the late 1970s, is given by the following parametric definition for 0 ≤ p ≤ +∞: T p H ( x , y ) = { T D ( x , y ) if p = + ∞ 0 if p = x = y = 0 x y p + ( 1 − p ) ( x + y − x y ) otherwise. {\displaystyle T_{p}^{\mathrm {H} }(x,y)={\begin{cases}T_{\mathrm {D} }(x,y)&{\text{if }}p=+\infty \\0&{\text{if }}p=x=y=0\\{\frac {xy}{p+(1-p)(x+y-xy)}}&{\text{otherwise.}}\end{cases}}} The t-norm T 0 H {\displaystyle T_{0}^{\mathrm {H} }} is called the Hamacher product. Hamacher t-norms are the only t-norms which are rational functions. The Hamacher t-norm T p H {\displaystyle T_{p}^{\mathrm {H} }} is strict if and only if p < +∞ (for p = 1 it is the product t-norm). The family is strictly decreasing and continuous with respect to p. An additive generator of T p H {\displaystyle T_{p}^{\mathrm {H} }} for p < +∞ is f p H ( x ) = { 1 − x x if p = 0 log ⁡ p + ( 1 − p ) x x otherwise. {\displaystyle f_{p}^{\mathrm {H} }(x)={\begin{cases}{\frac {1-x}{x}}&{\text{if }}p=0\\\log {\frac {p+(1-p)x}{x}}&{\text{otherwise.}}\end{cases}}} === Frank t-norms === The family of Frank t-norms, introduced by M.J. Frank in the late 1970s, is given by the parametric definition for 0 ≤ p ≤ +∞ as follows: T p F ( x , y ) = { T m i n ( x , y ) if p = 0 T p r o d ( x , y ) if p = 1 T L u k ( x , y ) if p = + ∞ log p ⁡ ( 1 + ( p x − 1 ) ( p y − 1 ) p − 1 ) otherwise. {\displaystyle T_{p}^{\mathrm {F} }(x,y)={\begin{cases}T_{\mathrm {min} }(x,y)&{\text{if }}p=0\\T_{\mathrm {prod} }(x,y)&{\text{if }}p=1\\T_{\mathrm {Luk} }(x,y)&{\text{if }}p=+\infty \\\log _{p}\left(1+{\frac {(p^{x}-1)(p^{y}-1)}{p-1}}\right)&{\text{otherwise.}}\end{cases}}} The Frank t-norm T p F {\displaystyle T_{p}^{\mathrm {F} }} is strict if p < +∞. The family is strictly decreasing and continuous with respect to p. An additive generator for T p F {\displaystyle T_{p}^{\mathrm {F} }} is f p F ( x ) = { − log ⁡ x if p = 1 1 − x if p = + ∞ log ⁡ p − 1 p x − 1 otherwise. {\displaystyle f_{p}^{\mathrm {F} }(x)={\begin{cases}-\log x&{\text{if }}p=1\\1-x&{\text{if }}p=+\infty \\\log {\frac {p-1}{p^{x}-1}}&{\text{otherwise.}}\end{cases}}} === Yager t-norms === The family of Yager t-norms, introduced in the early 1980s by Ronald R. Yager, is given for 0 ≤ p ≤ +∞ by T p Y ( x , y ) = { T D ( x , y ) if p = 0 max ( 0 , 1 − ( ( 1 − x ) p + ( 1 − y ) p ) 1 / p ) if 0 < p < + ∞ T m i n ( x , y ) if p = + ∞ {\displaystyle T_{p}^{\mathrm {Y} }(x,y)={\begin{cases}T_{\mathrm {D} }(x,y)&{\text{if }}p=0\\\max \left(0,1-((1-x)^{p}+(1-y)^{p})^{1/p}\right)&{\text{if }}0 Read more →

  • BL (logic)

    BL (logic)

    In mathematical logic, basic fuzzy logic (or shortly BL), the logic of the continuous t-norms, is one of the t-norm fuzzy logics. It belongs to the broader class of substructural logics, or logics of residuated lattices; it extends the logic MTL of all left-continuous t-norms. == Syntax == === Language === The language of the propositional logic BL consists of countably many propositional variables and the following primitive logical connectives: Implication → {\displaystyle \rightarrow } (binary) Strong conjunction ⊗ {\displaystyle \otimes } (binary). The sign & is a more traditional notation for strong conjunction in the literature on fuzzy logic, while the notation ⊗ {\displaystyle \otimes } follows the tradition of substructural logics. Bottom ⊥ {\displaystyle \bot } (nullary — a propositional constant); 0 {\displaystyle 0} or 0 ¯ {\displaystyle {\overline {0}}} are common alternative signs and zero a common alternative name for the propositional constant (as the constants bottom and zero of substructural logics coincide in MTL). The following are the most common defined logical connectives: Weak conjunction ∧ {\displaystyle \wedge } (binary), also called lattice conjunction (as it is always realized by the lattice operation of meet in algebraic semantics). Unlike MTL and weaker substructural logics, weak conjunction is definable in BL as A ∧ B ≡ A ⊗ ( A → B ) {\displaystyle A\wedge B\equiv A\otimes (A\rightarrow B)} Negation ¬ {\displaystyle \neg } (unary), defined as ¬ A ≡ A → ⊥ {\displaystyle \neg A\equiv A\rightarrow \bot } Equivalence ↔ {\displaystyle \leftrightarrow } (binary), defined as A ↔ B ≡ ( A → B ) ∧ ( B → A ) {\displaystyle A\leftrightarrow B\equiv (A\rightarrow B)\wedge (B\rightarrow A)} As in MTL, the definition is equivalent to ( A → B ) ⊗ ( B → A ) . {\displaystyle (A\rightarrow B)\otimes (B\rightarrow A).} (Weak) disjunction ∨ {\displaystyle \vee } (binary), also called lattice disjunction (as it is always realized by the lattice operation of join in algebraic semantics), defined as A ∨ B ≡ ( ( A → B ) → B ) ∧ ( ( B → A ) → A ) {\displaystyle A\vee B\equiv ((A\rightarrow B)\rightarrow B)\wedge ((B\rightarrow A)\rightarrow A)} Top ⊤ {\displaystyle \top } (nullary), also called one and denoted by 1 {\displaystyle 1} or 1 ¯ {\displaystyle {\overline {1}}} (as the constants top and zero of substructural logics coincide in MTL), defined as ⊤ ≡ ⊥ → ⊥ {\displaystyle \top \equiv \bot \rightarrow \bot } Well-formed formulae of BL are defined as usual in propositional logics. In order to save parentheses, it is common to use the following order of precedence: Unary connectives (bind most closely) Binary connectives other than implication and equivalence Implication and equivalence (bind most loosely) === Axioms === A Hilbert-style deduction system for BL has been introduced by Petr Hájek (1998). Its single derivation rule is modus ponens: from A {\displaystyle A} and A → B {\displaystyle A\rightarrow B} derive B . {\displaystyle B.} The following are its axiom schemata: ( B L 1 ) : ( A → B ) → ( ( B → C ) → ( A → C ) ) ( B L 2 ) : A ⊗ B → A ( B L 3 ) : A ⊗ B → B ⊗ A ( B L 4 ) : A ⊗ ( A → B ) → B ⊗ ( B → A ) ( B L 5 a ) : ( A → ( B → C ) ) → ( A ⊗ B → C ) ( B L 5 b ) : ( A ⊗ B → C ) → ( A → ( B → C ) ) ( B L 6 ) : ( ( A → B ) → C ) → ( ( ( B → A ) → C ) → C ) ( B L 7 ) : ⊥ → A {\displaystyle {\begin{array}{ll}{\rm {(BL1)}}\colon &(A\rightarrow B)\rightarrow ((B\rightarrow C)\rightarrow (A\rightarrow C))\\{\rm {(BL2)}}\colon &A\otimes B\rightarrow A\\{\rm {(BL3)}}\colon &A\otimes B\rightarrow B\otimes A\\{\rm {(BL4)}}\colon &A\otimes (A\rightarrow B)\rightarrow B\otimes (B\rightarrow A)\\{\rm {(BL5a)}}\colon &(A\rightarrow (B\rightarrow C))\rightarrow (A\otimes B\rightarrow C)\\{\rm {(BL5b)}}\colon &(A\otimes B\rightarrow C)\rightarrow (A\rightarrow (B\rightarrow C))\\{\rm {(BL6)}}\colon &((A\rightarrow B)\rightarrow C)\rightarrow (((B\rightarrow A)\rightarrow C)\rightarrow C)\\{\rm {(BL7)}}\colon &\bot \rightarrow A\end{array}}} The axioms (BL2) and (BL3) of the original axiomatic system were shown to be redundant (Chvalovský, 2012) and (Cintula, 2005). All the other axioms were shown to be independent (Chvalovský, 2012). == Semantics == Like in other propositional t-norm fuzzy logics, algebraic semantics is predominantly used for BL, with three main classes of algebras with respect to which the logic is complete: General semantics, formed of all BL-algebras — that is, all algebras for which the logic is sound Linear semantics, formed of all linear BL-algebras — that is, all BL-algebras whose lattice order is linear Standard semantics, formed of all standard BL-algebras — that is, all BL-algebras whose lattice reduct is the real unit interval [0, 1] with the usual order; they are uniquely determined by the function that interprets strong conjunction, which can be any continuous t-norm.

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  • KitKat (cat)

    KitKat (cat)

    KitKat was a bodega cat from the Mission District of San Francisco who was killed by a Waymo car on October 27, 2025. Locals built altars and the death has raised comments about the safety of self-driving cars. == Life == Mike Zeidan, the owner of Randa's Market, adopted KitKat as a stray to help keep rodents out of his store. KitKat lived in Randa's Market for six years and was well-loved by the neighborhood, including an appearance on a shop cats map that went viral in 2022 as a "particularly friendly cat". After KitKat arrived at the bodega, customers were said to come more often, and regularly brought the cat food and gifts. == Death == At around 11:40 pm on October 27, 2025, witnesses saw KitKat sitting in front of a stopped Waymo car for seven seconds. He walked under the car as the car pulled out, and the right rear tire ran over the back half of his body. A bartender who was taking a cigarette break used a sandwich board sign as a stretcher and took KitKat to an emergency animal clinic. An hour later, KitKat was pronounced dead. Waymo confirmed that the cat was killed by one of its vehicles on October 30. Surveillance footage of the incident was released in December. From Waymo's report to the National Highway Traffic Safety Administration (NHTSA): The Waymo AV was stopped next to the curb for a passenger pickup facing east on 16th Street. As the passengers were boarding the Waymo AV, a cat approached the Waymo AV from the southern sidewalk of 16th Street and sat in the roadway partially under the front right corner of the Waymo AV. A pedestrian approached the Waymo AV from the east on the southern sidewalk of 16th Street and began crouching near the front of the Waymo AV, stepping partially into the roadway, appearing to reach for the cat. As they did so, the cat moved farther from the sidewalk under the Waymo AV and the pedestrian stepped back onto the sidewalk. The Waymo AV then departed the pickup location and the rear right tire made contact with the cat. At the time of impact, the Waymo AV's Level 4 ADS was engaged in autonomous mode. Waymo later received notice that the cat did not survive. The passengers in the Waymo AV did not have seatbelts fastened at the time, having just boarded the Waymo AV. Prior to KitKat's death, the NHTSA had logged 14 collisions between Waymo cars and animals, of which 5 were confirmed fatalities. == Aftermath == After KitKat's death, an altar was created outside Randa's Market. People left flowers, candles, cat food, written notes, and Kit Kat candy bars in the cat's honor. A city worker took down the memorial for fire safety reasons, but neighbors built it again. Local supervisor Jackie Fielder held a rally called "Justice for KitKat" in support of a non-binding San Francisco resolution to shift decision-making about the operation of self-driving cars from the state to individual counties. Critics say that the resolution is performative because it is non-binding, that local control would make autonomous vehicle operation impractical, and that Waymo is still far less dangerous to animals than human drivers. Elon Musk commented that "many pets will be saved by autonomy". There are multiple meme coins inspired by KitKat.

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  • Intrinsic dimension

    Intrinsic dimension

    In mathematics, the intrinsic dimension of a subset can be thought of as the minimal number of variables needed to represent the subset. The concept has widespread applications in geometry, dynamical systems, signal processing, statistics, and other fields. Due to its widespread applications and vague conceptualization, there are many different ways to define it rigorously. Consequently, the same set might have different intrinsic dimensions according to different definitions. The intrinsic dimension can be used as a lower bound of what dimension it is possible to compress a data set into through dimension reduction, but it can also be used as a measure of the complexity of the data set or signal. For a data set or signal of N variables, its intrinsic dimension M satisfies 0 ≤ M ≤ N, although estimators may yield higher values. == Exact dimension == === Differential === In differential geometry, given a differentiable manifold N and a submanifold M, the intrinsic dimension of M is its dimension. Suppose N has n dimensions and M has m dimensions, then that means around any point in M, there exists a local coordinate system ( x 1 , … , x m , x m + 1 , … , x n ) {\displaystyle (x_{1},\dots ,x_{m},x_{m+1},\dots ,x_{n})} of N, such that the manifold M is simply the subset of N defined by x m + 1 = 0 , … , x n = 0 {\displaystyle x_{m+1}=0,\dots ,x_{n}=0} . === Metric === Given a mere metric space, we can still define its intrinsic dimension. The most general case is the Hausdorff dimension, though for metric spaces occurring in practice, the box-counting dimension and the packing dimension often are identical to the Hausdorff dimension. Let X , d {\textstyle X,d} be a metric space and A ⊂ X {\textstyle A\subset X} be totally bounded. Define the covering number N ( A , ε ) = min { k : A ⊂ ⋃ i = 1 k B ( x i , ε ) } . {\displaystyle N(A,\varepsilon )=\min \left\{k:A\subset \bigcup _{i=1}^{k}B\left(x_{i},\varepsilon \right)\right\}.} The metric entropy is H ( A , ε ) = log ⁡ N ( A , ε ) {\textstyle H(A,\varepsilon )=\log N(A,\varepsilon )} (any log base). The upper and lower metric entropy dimensions are dim ¯ E A = lim sup ε ↓ 0 H ( A , ε ) log ⁡ ( 1 / ε ) , dim _ E A = lim inf ε ↓ 0 H ( A , ε ) log ⁡ ( 1 / ε ) . {\displaystyle {\overline {\dim }}_{E}A=\limsup _{\varepsilon \downarrow 0}{\frac {H(A,\varepsilon )}{\log(1/\varepsilon )}},\quad {\underline {\dim }}_{E}A=\liminf _{\varepsilon \downarrow 0}{\frac {H(A,\varepsilon )}{\log(1/\varepsilon )}}.} If they are equal, then dim E ⁡ A {\textstyle \operatorname {dim} _{E}A} is that common value, called the metric entropy dimension. The entropy dimensions are usually used in information theory, and especially coding theory, since entropy is involved in its definition. === Topological === If X {\displaystyle X} is merely a topological space, then we can still define its intrinsic dimension, using the topological dimension or Lebesgue covering dimension. An open cover of a topological space X is a family of open sets Uα such that their union is the whole space, ∪ α {\displaystyle \cup _{\alpha }} Uα = X. The order or ply of an open cover A {\displaystyle {\mathfrak {A}}} = {Uα} is the smallest number m (if it exists) for which each point of the space belongs to at most m open sets in the cover: in other words Uα1 ∩ ⋅⋅⋅ ∩ Uαm+1 = ∅ {\displaystyle \emptyset } for α1, ..., αm+1 distinct. A refinement of an open cover A {\displaystyle {\mathfrak {A}}} = {Uα} is another open cover B {\displaystyle {\mathfrak {B}}} = {Vβ}, such that each Vβ is contained in some Uα. The covering dimension of a topological space X is defined to be the minimum value of n such that every finite open cover A {\displaystyle {\mathfrak {A}}} of X has an open refinement B {\displaystyle {\mathfrak {B}}} with order n + 1. The refinement B {\displaystyle {\mathfrak {B}}} can always be chosen to be finite. Thus, if n is finite, Vβ1 ∩ ⋅⋅⋅ ∩ Vβn+2 = ∅ {\displaystyle \emptyset } for β1, ..., βn+2 distinct. If no such minimal n exists, the space is said to have infinite covering dimension. == Introductory example == Let f ( x 1 , x 2 ) {\textstyle f(x_{1},x_{2})} be a two-variable function (or signal) which is of the form f ( x 1 , x 2 ) = g ( x 1 ) {\textstyle f(x_{1},x_{2})=g(x_{1})} for some one-variable function g which is not constant. This means that f varies, in accordance to g, with the first variable or along the first coordinate. On the other hand, f is constant with respect to the second variable or along the second coordinate. It is only necessary to know the value of one, namely the first, variable in order to determine the value of f. Hence, it is a two-variable function but its intrinsic dimension is one. A slightly more complicated example is f ( x 1 , x 2 ) = g ( x 1 + x 2 ) {\textstyle f(x_{1},x_{2})=g(x_{1}+x_{2})} . f is still intrinsic one-dimensional, which can be seen by making a variable transformation y 1 = x 1 + x 2 {\textstyle y_{1}=x_{1}+x_{2}} and y 2 = x 1 − x 2 {\textstyle y_{2}=x_{1}-x_{2}} which gives f ( y 1 + y 2 2 , y 1 − y 2 2 ) = g ( y 1 ) {\textstyle f\left({\frac {y_{1}+y_{2}}{2}},{\frac {y_{1}-y_{2}}{2}}\right)=g\left(y_{1}\right)} . Since the variation in f can be described by the single variable y1 its intrinsic dimension is one. For the case that f is constant, its intrinsic dimension is zero since no variable is needed to describe variation. For the general case, when the intrinsic dimension of the two-variable function f is neither zero or one, it is two. In the literature, functions which are of intrinsic dimension zero, one, or two are sometimes referred to as i0D, i1D or i2D, respectively. == Signal processing == In signal processing of multidimensional signals, the intrinsic dimension of the signal describes how many variables are needed to generate a good approximation of the signal. For an N-variable function f, the set of variables can be represented as an N-dimensional vector x: f = f ( x ) where x = ( x 1 , … , x N ) {\textstyle f=f\left(\mathbf {x} \right){\text{ where }}\mathbf {x} =\left(x_{1},\dots ,x_{N}\right)} . If for some M-variable function g and M × N matrix A it is the case that for all x; f ( x ) = g ( A x ) , {\textstyle f(\mathbf {x} )=g(\mathbf {Ax} ),} M is the smallest number for which the above relation between f and g can be found, then the intrinsic dimension of f is M. The intrinsic dimension is a characterization of f, it is not an unambiguous characterization of g nor of A. That is, if the above relation is satisfied for some f, g, and A, it must also be satisfied for the same f and g′ and A′ given by g ′ ( y ) = g ( B y ) {\textstyle g'\left(\mathbf {y} \right)=g\left(\mathbf {By} \right)} and A ′ = B − 1 A {\textstyle \mathbf {A'} =\mathbf {B} ^{-1}\mathbf {A} } where B is a non-singular M × M matrix, since f ( x ) = g ′ ( A ′ x ) = g ( B A ′ x ) = g ( A x ) {\textstyle f\left(\mathbf {x} \right)=g'\left(\mathbf {A'x} \right)=g\left(\mathbf {BA'x} \right)=g\left(\mathbf {Ax} \right)} . == The Fourier transform of signals of low intrinsic dimension == An N variable function which has intrinsic dimension M < N has a characteristic Fourier transform. Intuitively, since this type of function is constant along one or several dimensions its Fourier transform must appear like an impulse (the Fourier transform of a constant) along the same dimension in the frequency domain. === A simple example === Let f be a two-variable function which is i1D. This means that there exists a normalized vector n ∈ R 2 {\textstyle \mathbf {n} \in \mathbb {R} ^{2}} and a one-variable function g such that f ( x ) = g ( n T x ) {\textstyle f(\mathbf {x} )=g(\mathbf {n} ^{\operatorname {T} }\mathbf {x} )} for all x ∈ R 2 {\textstyle \mathbf {x} \in \mathbb {R} ^{2}} . If F is the Fourier transform of f (both are two-variable functions) it must be the case that F ( u ) = G ( n T u ) ⋅ δ ( m T u ) {\textstyle F\left(\mathbf {u} \right)=G\left(\mathbf {n} ^{\mathrm {T} }\mathbf {u} \right)\cdot \delta \left(\mathbf {m} ^{\mathrm {T} }\mathbf {u} \right)} . Here G is the Fourier transform of g (both are one-variable functions), δ is the Dirac impulse function and m is a normalized vector in R 2 {\textstyle \mathbb {R} ^{2}} perpendicular to n. This means that F vanishes everywhere except on a line which passes through the origin of the frequency domain and is parallel to m. Along this line F varies according to G. === The general case === Let f be an N-variable function which has intrinsic dimension M, that is, there exists an M-variable function g and M × N matrix A such that f ( x ) = g ( A x ) ∀ x {\textstyle f(\mathbf {x} )=g(\mathbf {Ax} )\quad \forall \mathbf {x} } . Its Fourier transform F can then be described as follows: F vanishes everywhere except for a subspace of dimension M The subspace M is spanned by the rows of the matrix A In the subspace, F varies according to G the Fourier transform of g == Generalizations == The type of intrinsic dimension described above assume

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  • Tales from the Loop (role-playing game)

    Tales from the Loop (role-playing game)

    Tales from the Loop (Swedish: Ur Varselklotet), subtitled "Roleplaying in the '80s That Never Was", is an alternative history science fiction tabletop role-playing game published in 2017 by Free League Publishing, the international arm of Swedish game and book publisher Fria Ligan AB, and Modiphius Entertainment. The game, based on the art of Simon Stålenhag, envisions an alternative world where a group of bored and ignored preteens and teens solve mysteries caused by new technology near their hometown. == Description == === Setting === Tales from the Loop is set in an alternative history world taken from the artwork of Simon Stålenhag. According to this alternative timeline, back in the 1940s, research began on particle accelerators. In the 1960s, two massive underground particle accelerators were built in Sweden and Colorado with the promise of a harvest of technological marvels that would change everyone's lives. Tales from the Loop is set twenty years later, in the late 1980s, and the better life has not materialized. Although the particle accelerators have created robots and large skyships, the detritus of failed experiments and the ruins of abandoned high tech company buildings litter the landscape. Generally the life of the average family has not changed for the better. A campaign can either be set in the Mälaren Islands, west of the Swedish capital of Stockholm, or in a city in the Southwest United States that resembles Boulder City, Nevada. There is also a step-by-step guide for the gamemaster to use their own hometown. === Character generation === Player characters are preteens and young teenagers age 10–15 who live in a society where they are bored and largely left to themselves. Players can choose archetypes for their characters including Bookworm, Jock, Troublemaker, Popular Kid and Weirdo. Unlike most role-playing games, characters in Tales from the Loop cannot be killed, although in an ongoing campaign or due to an in-game effect, they are removed from the game if they reach the age of sixteen. === Game system === The game uses the Year Zero Engine first developed by Tomas Härenstam for the post-apocalyptic role-playing game Mutant: Year Zero. (Härenstam served as the editor and project manager for Tales from the Loop.) Problems are resolved by rolling a pool of six-sided dice, with any 6 rolled marking success. Attributes and skills (Sneak, Force, Move, Build, Tinker, Calculate, Contact, Charm, Lead, Investigate, Comprehend, and Empathize) may allow the player to add more dice to the dice pool, increasing the chances of success. However, if a character has earned a condition such as Scared or Injured, dice are removed from the dice pool. === Gameplay === The game principles are that life for the characters is dull and boring, but the area around the town is full of wonderful, mysterious things. An adventure is set up as a Mystery, and in order to successfully resolve the Mystery, characters must overcome a series of Troubles, which can range from having to be home by a certain time to dealing with a bully to disarming or otherwise overcoming a booby-trap on a door that must be opened. Each Mystery is played as a series of scenes, much like a TV drama. Although the gamemaster leads the players into the Mystery, each scene is set collaboratively with the players before action continues. As critic Jukka Kauppinen noted, "The players and the gamemaster take turns verbally staging a new scene — where we are, what it's like there — and only then what we do." === Campaign === The book presents a chronologically-linked set of four Mysteries called "The Four Seasons of Mad Science" that take place over a calendar year: "Summer Break and Killer Birds": The Kids hears pigeons having a conversation and investigate "Grown-Up Attraction": Adults start disappearing without any sign of struggle. "Creatures from the Cretaceous": The search for a missing dog leads to the discovery of creatures that don't belong in our time "I, Wagner": The Kids discover a body in a stream, and are drawn into a Mystery with robots and humans that may affect them closely. == Publication history == In 2017, Swedish artist Simon Stålenhag was raising money on Kickstarter to publish a book of his art titled Tales from the Loop. One of the stretch goals offered was the creation of a role-playing game. A second Kickstarter campaign to publish the role-playing game was initiated by Fria Ligan AB, who surpassed their crowdfunding goal and raised a total of 3,745,896 kr from 5,600 backers. The role-playing game Tales from the Loop was subsequently published as a 184-page hardcover book in 2017 by Free League Publishing, the international arm of Swedish game and book publisher Fria Ligan AB, and Modiphius Entertainment. Cover art and interior art were by Stålenhag, and cartography was by Christian Granath. A stand-alone expansion, Things from the Flood (Swedish: Flodskörden), based on Stålenhag's art book of the same name, was created by Nils Hintze, Rickard Antroia, and Tomas Härenstam. The 216-page hardcover book was published in 2019 with cover art by Stålenhag, interior art by Stålenhag and Reine Rosenberg, and cartography by Christian Granath. In 2020, the setting of the role-playing game was transferred to the TV series Tales from the Loop developed by Nathanial Halpern and Simon Stålenhag. The series tells eight stories of children's encounters with strange technology. == Reception == Shut Up & Sit Down praised Tales from the Loop for its comfortable, contemporary setting, simple rules that make the game easy to run, and the alternation between sci-fi and the kids' lives, but criticized the Type system for characters, noting "a suggested 'Pride' for the Weirdo involved being homosexual –– the only mention of queerness in the entire game. Those of us who identify as GLBTQ bristled at that: why was only the Weirdo queer, with queerness as a (possibly secret) Pride? Why not more fully address being a GLBTQ kid in the 1980s?" The review concluded, "For new RPG players, Tales is a decent game that you'll enjoy and that will make your heart burst. But you need an experienced GM who’s able to either alter the book’s mysteries or create their own, and who can put in work when poor dice rolls hold the players back." Rob Weiland of Geek & Sundry named Tales from the Loop 2017's best RPG release and praised Stålenhag's art, the collaborative nature between the GM and players, and the simplicity of running the game. Weiland concluded, "It has a simple system that is easy to explain but holds up under several plays. It has a setting that’s immediately evocative but also leaves plenty of room for GMs to build out their own world. It offers players a chance to experience the rush of memory, the pain of childhood and the wonder of movies." In a review of Tales from the Loop in Black Gate, Andrew Zimmerman Jones said, "Though not based directly on an established franchise, it draws richly from elements of popular culture that will make it resonate with many players. The focus on narrative play also means it’s a good game for people who aren’t necessarily big into learning a ton of new rules." Jukka Kauppinen, writing for the Finnish games magazine Skrolli, called the game, "downright delicious in its diversity. The science fiction world created by the Swedish artist Simon Stälenhag is, after all, both delightful vintage and tickling novelty." Kauppinen concluded, "This mutual storytelling and interaction makes this game more of a campfire circle than a traditional role-playing game. At the same time, its setting in the real world, tinged with science fiction and even horror, creates a delicious and unique adventure environment." In his 2023 book Monsters, Aliens, and Holes in the Ground, RPG historian Stu Horvath noted that the game system "pushes the players to constantly reevaluate their characters' relationships with the everyday world, for better or worse. It won't be long before navigating entanglements with parents, teachers, siblings and bullies proves just as risky to the characters, and central to the players' experience, as trying to find out what happened with the time portal or dealing with a rampaging robot." Horvath concluded, "The appeal of Tales from the Loop is Stålenhag's deep shadows and purple dusks. They hide the dangers and mysteries that often act [as] an escape hatch, a way to avoid prosaic problems." == Awards == At the 2017 Golden Geek Awards, Tales of the Loop won "RPG of the Year", and was a finalist for " Best RPG Artwork/Presentation" At the 2017 ENnie Awards, Tales from the Loops won five Gold Medals: Product of the Year Best Writing Best Setting Best Game Best Art, Interior

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  • Fuzzy differential equation

    Fuzzy differential equation

    Fuzzy differential equation are general concept of ordinary differential equation in mathematics defined as differential inclusion for non-uniform upper hemicontinuity convex set with compactness in fuzzy set. d x ( t ) / d t = F ( t , x ( t ) , α ) , {\displaystyle dx(t)/dt=F(t,x(t),\alpha ),} for all α ∈ [ 0 , 1 ] {\displaystyle \alpha \in [0,1]} . == First order fuzzy differential equation == A first order fuzzy differential equation with real constant or variable coefficients x ′ ( t ) + p ( t ) x ( t ) = f ( t ) {\displaystyle x'(t)+p(t)x(t)=f(t)} where p ( t ) {\displaystyle p(t)} is a real continuous function and f ( t ) : [ t 0 , ∞ ) → R F {\displaystyle f(t)\colon [t_{0},\infty )\rightarrow R_{F}} is a fuzzy continuous function y ( t 0 ) = y 0 {\displaystyle y(t_{0})=y_{0}} such that y 0 ∈ R F {\displaystyle y_{0}\in R_{F}} . == Linear systems of fuzzy differential equations == A system of equations of the form x ( t ) n ′ = a n 1 ( t ) x 1 ( t ) + . . . . . . + a n n ( t ) x n ( t ) + f n ( t ) {\displaystyle x(t)'_{n}=a_{n}1(t)x_{1}(t)+......+a_{n}n(t)x_{n}(t)+f_{n}(t)} where a i j {\displaystyle a_{i}j} are real functions and f i {\displaystyle f_{i}} are fuzzy functions x n ′ ( t ) = ∑ i = 0 1 a i j x i . {\displaystyle x'_{n}(t)=\sum _{i=0}^{1}a_{ij}x_{i}.} == Fuzzy partial differential equations == A fuzzy differential equation with partial differential operator is ∇ x ( t ) = F ( t , x ( t ) , α ) , {\displaystyle \nabla x(t)=F(t,x(t),\alpha ),} for all α ∈ [ 0 , 1 ] {\displaystyle \alpha \in [0,1]} . == Fuzzy fractional differential equation == A fuzzy differential equation with fractional differential operator is d n x ( t ) d t n = F ( t , x ( t ) , α ) , {\displaystyle {\frac {d^{n}x(t)}{dt^{n}}}=F(t,x(t),\alpha ),} for all α ∈ [ 0 , 1 ] {\displaystyle \alpha \in [0,1]} where n {\displaystyle n} is a rational number.

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