AI For Business Microsoft

AI For Business Microsoft — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

Wave Financial

Wave is a Canadian company that provides financial services and software for small businesses. Wave is headquartered in the East Bayfront neighbourhood in Toronto, Canada. The company's first product was free online accounting software designed for businesses with 1–9 employees, followed by invoicing, personal finance and receipt-scanning software (OCR). In 2012, Wave began branching into financial services, initially with Payments by Wave (credit card processing) and Payroll by Wave, followed in February 2017 by Lending by Wave, which has since been discontinued. == History == CEO Kirk Simpson and CPO James Lochrie launched Wave Accounting Inc. in July 2009, Wave Accounting launched to the public on November 16, 2010. In June 2011, Series A funding led by OMERS Ventures was closed. In September 2011, FedDev Ontario invested one million dollars in funding. In October 2011, a $5-million investment led by U.S. venture capital firm Charles River Ventures was announced. In May 2012, Wave Accounting closed its series B financing round led by The Social+Capital Partnership, with follow-on participation from Charles River Ventures and OMERS Ventures. Wave acquired a company called Small Payroll in November 2011, which was later launched as a payroll product called Wave Payroll. In February 2012, Wave officially launched Wave Payroll to the public in Canada, followed by the American release in November of the same year. In August, 2012, the company announced the acquisition of Vuru.co, an online stock-tracking service. Terms of the deal were not disclosed. In December 2012, the company rebranded itself as Wave to emphasize its broadened spectrum of services. On March 14, 2019, the company acquired Every, a Toronto-based fintech company that provides business accounts and debit cards to small businesses. On June 11, 2019, the company announced it was being acquired by tax preparation company, H&R Block, for $537 million. On June 15, 2022, Wave announced that Kirk Simpson would be leaving and being replaced as CEO by Zahir Khoja. In May 2025, US customers of Wave were transitioned to a new Payroll processing system supported by CheckHQ. The new integration improved support for US employers by handling employer tax withholding and payments in all 50 US States. == Products == The company's initial product, Accounting by Wave, is a double entry accounting tool. Services include direct bank data imports, invoicing and expense tracking, customizable chart of accounts, and journal transactions. Accounting by Wave integrates with expense tracking software Shoeboxed and e-commerce website Etsy. The next product launched was Payroll by Wave, which was launched in 2012 after the acquisition of SmallPayroll.ca. Payroll by Wave is only available in the US and Canada. Invoicing by Wave is an offshoot of the company's earlier accounting tools. Additional products launched on or shortly after the company's rebrand in December 2012 include: a credit card processing tool, Payments by Wave, built initially on integration with Stripe credit card processing. However, Wave does not report merchant fees correctly for countries where Stripe charges a tax such as GST. In these cases, the merchant fees are reported without tax and do not match your Stripe account. a receipt scanning tool, Receipts by Wave. In 2017, Wave signed an agreement to provide its platform on RBC's online business banking site. The RBC-Wave service will be co-branded. == Taxes supported == The company's software supports tax-exclusive pricing, such as U.S. sales tax, where taxes are added on top of prices quoted. This has two effects: When scanning receipts users must manually add the tax, and input the amount. When making an invoice, users must put in a price before tax, and the system will add the tax on top. This makes Wave unable to handle taxes in countries like Australia where prices must be quoted inclusive of all taxes, such as GST. There is no way to set an invoice total and have Wave calculate the tax portion as a percentage. == Pricing and business model == As of June 10, 2024, Wave offers two tiers for its software: a free Starter plan with limitations on some features, and a paid Pro plan. In addition to its paid plan, revenue from the company comes from other paid financial services the company offers: Payments by Wave: Card processing which includes debit, credit and prepaid cards as well as ACH (bank payments) in the United States. Fees are a percentage of the transaction. Payroll by Wave: Monthly subscription fee plus usage fees. Wave previously included advertising on its pages as a source of revenue. Advertising was removed in January 2017. In 2017, Wave raised $24m (USD) in funding led by NAB Ventures. In 2019, H&R Block announced the acquisition of Wave in a cash deal worth $405 million USD.
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SAP BTP

SAP Business Technology Platform (SAP BTP) is a platform as a service developed by SAP SE that offers a suite of services including database and data management, AI, analytics, application development, automation and integration all running on one unified platform. == Overview == SAP BTP is made up of four components: Application development and automation: to create applications or extend existing applications. Data and analytics: to access and analyze data across SAP and third-party systems using multi-cloud architecture. Integration: to integrate and connect applications and data. Artificial Intelligence (AI): to access large language models (LLMs) to develop AI. == History == SAP BTP was introduced as part of the SAP strategy to unify its portfolio and cloud offerings under a single platform. The platform was evolved from earlier initiatives such as SAP Cloud Platform and now serves as the central hub for cloud, data, analytics, integration and AI technologies. Initially unveiled as "SAP NetWeaver Cloud" belonging to the SAP HANA Cloud portfolio on October 16, 2012 the cloud platform was reintroduced with the new name "SAP HANA Cloud Platform" on May 13, 2013 as the foundation for SAP cloud products, including the SAP BusinessObjects Cloud. Adoption of the SAP HANA Cloud Platform in 2015 stood at over 4000 customers and 500 partners. In 2016, SAP and Apple Inc. partnered to develop mobile applications on iOS using cloud-based software development kits (SDKs) for the SAP Cloud Platform. On February 27, 2017, SAP HANA Cloud Platform was renamed "SAP Cloud Platform" at the Mobile World Congress. On January 18, 2021, the name "SAP Cloud Platform" was retired from the SAP product portfolio to support SAP BTP. As of October 2024, SAP states that SAP BTP is used by more than 27,000 customers and more than 2,800 partners. Recently, SAP Business One has worked on improving the functionalities of BTP to cater for the demands of digital transformation. The platform offers comprehensive services in AI, application development, automation, integration, data management, and analytics.
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Clean Email

Clean Email is an automated software as a service email management application which identifies and clears junk mail from inboxes. The service uses a subscription business model with a free trial for the first 1,000 emails. and is available on macOS, iOS, Android, and on the web. == History == Clean Email is a self-funded company headquartered in Los Angeles, California. Initially developed by the founder for personal use, the service was designed to address the growing issue of inbox clutter and privacy concerns. In 2017, John Gruber recognized Clean Email as a trustworthy alternative to Unroll.me after the latter was found to be selling user data. == Features == Clean Email uses algorithms to identify and categorize emails, enabling users to group, remove, label, and archive email messages in bulk. Its Unsubscriber tool consolidates all subscriptions and newsletters into a single view for quick management, allowing users to bulk unsubscribe or temporarily pause mail. Its Screener feature transforms the inbox into an "opt-in" system, enabling users to pre-approve mail from new senders. Cleaning Suggestions identifies frequently cleaned mail, recommending actions accordingly. Additional functionalities include automatic deletion of aging emails, delivery of messages to specified folders, and options to mute or block senders.
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GNU Binutils

The GNU Binary Utilities, or binutils, is a collection of programming tools maintained by the GNU Project for working with executable code including assembly, linking and many other development operations. The tools are originally from Cygnus Solutions. The tools are typically used along with other GNU tools such as GNU Compiler Collection, and the GNU Debugger. == Tools == The tools include: == elfutils == Ulrich Drepper wrote elfutils, to partially replace GNU Binutils, purely for Linux and with support only for ELF and DWARF. It distributes three libraries with it for programmatic access.
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Label noise

Label noise refers to errors or inaccuracies in the class labels of data instances. This is a widespread issue in machine learning datasets, arising from human annotator mistakes, unclear labeling instructions, automated labeling methods, or adversarial attacks in supervised learning. Label noise can be roughly divided into random noise, where labels are flipped independently of input features, and systematic noise, where mislabeling is dependent on certain patterns or biases in the data. Label noise can be damaging to model performance, especially for complex models that may overfit to noisy labels rather than generalizable patterns. Many approaches have been proposed to deal with the effects of label noise, including robust loss functions, noise-tolerant algorithms, data cleaning methods, and semi-supervised learning approaches. To reduce the impact of wrong labels during training, techniques like label smoothing, sample reweighting and using trusted validation sets are used. The role of noise-robust training paradigms and curriculum learning strategies to improve resilience against mislabeled data is also explored in recent research.
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Rclone

Rclone is an open source, multi threaded, command line computer program to manage or migrate content on cloud and other high latency storage. Its capabilities include sync, transfer, crypt, cache, union, compress and mount. The rclone website lists supported backends including S3 and Google Drive. Descriptions of rclone often carry the strapline "Rclone syncs your files to cloud storage". Those prior to 2020 include the alternative "Rsync for Cloud Storage". Rclone is well known for its rclone sync and rclone mount commands. It provides further management functions analogous to those ordinarily used for files on local disks, but which tolerate some intermittent and unreliable service. Rclone is commonly used with media servers such as Plex, Emby or Jellyfin to stream content direct from consumer file storage services. Official Ubuntu, Debian, Fedora, Gentoo, Arch, Brew, Chocolatey, and other package managers include rclone. == History == Nick Craig-Wood was inspired by rsync. Concerns about the noise and power costs arising from home computer servers prompted him to embrace cloud storage and he began developing rclone as open source software in 2012 under the name swiftsync. Rclone was promoted to stable version 1.00 in July 2014. In May 2017, Amazon Drive barred new users of rclone and other upload utilities, citing security concerns. Amazon Drive had been advertised as offering unlimited storage for £55 per year. Amazon's AWS S3 service continues to support new rclone users. The original rclone logo was updated in September 2018. In March 2020, Nick Craig-Wood resigned from Memset Ltd, a cloud hosting company he founded, to focus on open source software. Amazon's AWS April 2020 public sector blog explained how the Fred Hutch Cancer Research Center were using rclone in their Motuz tool to migrate very large biomedical research datasets in and out of AWS S3 object stores. In November 2020, rclone was updated to correct a weakness in the way it generated passwords. Passwords for encrypted remotes can be generated randomly by rclone or supplied by the user. In all versions of rclone from 1.49.0 to 1.53.2 the seed value for generated passwords was based on the number of seconds elapsed in the day, and therefore not truly random. CVE-2020-28924 recommended users upgrade to the latest version of rclone and check the passwords protecting their encrypted remotes. Release 1.55 of rclone in March 2021 included features sponsored by CERN and their CS3MESH4EOSC project. The work was EU funded to promote vendor-neutral application programming interfaces and protocols for synchronisation and sharing of academic data on cloud storage. == Backends and commands == Rclone supports the following services as backends. There are others, built on standard protocols such as WebDAV or S3, that work. WebDAV backends do not support rclone functionality dependent on server side checksum or modtime. Remotes are usually defined interactively from these backends, local disk, or memory (as S3), with rclone config. Rclone can further wrap those remotes with one or more of alias, chunk, compress, crypt or union, remotes. Once defined, the remotes are referenced by other rclone commands interchangeably with the local drive. Remote names are followed by a colon to distinguish them from local drives. For example, a remote example_remote containing a folder, or pseudofolder, myfolder is referred to within a command as a path example_remote:/myfolder. Rclone commands directly apply to remotes, or mount them for file access or streaming. With appropriate cache options the mount can be addressed as if a conventional, block level disk. Commands are provided to serve remotes over SFTP, HTTP, WebDAV, FTP and DLNA. Commands can have sub-commands and flags. Filters determine which files on a remote that rclone commands are applied to. rclone rc passes commands or new parameters to existing rclone sessions and has an experimental web browser interface. === Crypt remotes === Rclone's crypt implements encryption of files at rest in cloud storage. It layers an encrypted remote over a pre-existing, cloud or other remote. Crypt is commonly used to encrypt / decrypt media, for streaming, on consumer storage services such as Google Drive. Rclone's configuration file contains the crypt password. The password can be lightly obfuscated, or the whole rclone.conf file can be encrypted. Crypt can either encrypt file content and name, or additionally full paths. In the latter case there is a potential clash with encryption for cloud backends, such as Microsoft OneDrive, having limited path lengths. Crypt remotes do not encrypt object modification time or size. The encryption mechanism for content, name and path is available, for scrutiny, on the rclone website. Key derivation is with scrypt. === Example syntax (Linux) === These examples describe paths and file names but object keys behave similarly. To recursively copy files from directory remote_stuff, at the remote xmpl, to directory stuff in the home folder:- -v enables logging and -P, progress information. By default rclone checks the file integrity (hash) after copy; can retry each file up to three times if the operation is interrupted; uses up to four parallel transfer threads, and does not apply bandwidth throttling. Running the above command again copies any new or changed files at the remote to the local folder but, like default rsync behaviour, will not delete from the local directory, files which have been removed from the remote. To additionally delete files from the local folder which have been removed from the remote - more like the behaviour of rsync with a --delete flag:- And to delete files from the source after they have been transferred to the local directory - more like the behaviour of rsync with a --remove-source-file flag:- To mount the remote directory at a mountpoint in the pre-existing, empty stuff directory in the home directory (the ampersand at the end makes the mount command run as a background process):- Default rclone syntax can be modified. Alternative transfer, filter, conflict and backend specific flags are available. Performance choices include number of concurrent transfer threads; chunk size; bandwidth limit profiling, and cache aggression. == Academic evaluation == In 2018, University of Kentucky researchers published a conference paper comparing use of rclone and other command line, cloud data transfer agents for big data. The paper was published as a result of funding by the National Science Foundation. Later that year, University of Utah's Center for High Performance Computing examined the impact of rclone options on data transfer rates. == Rclone use at HPC research sites == Examples are University of Maryland, Iowa State University, Trinity College Dublin, NYU, BYU, Indiana University, CSC Finland, Utrecht University, University of Nebraska, University of Utah, North Carolina State University, Stony Brook, Tulane University, Washington State University, Georgia Tech, National Institutes of Health, Wharton, Yale, Harvard, Minnesota, Michigan State, Case Western Reserve University, University of South Dakota, Northern Arizona University, University of Pennsylvania, Stanford, University of Southern California, UC Santa Barbara, UC Irvine, UC Berkeley, and SURFnet. == Rclone and cybercrime == May 2020 reports stated rclone had been used by hackers to exploit Diebold Nixdorf ATMs with ProLock ransomware. The FBI issued a Flash Alert MI-000125-MW on May 4, 2020, in relation to the compromise. They issued a further, related alert 20200901–001 in September 2020. Attackers had exfiltrated / encrypted data from organisations involved in healthcare, construction, finance, and legal services. Multiple US government agencies, and industrial entities were affected. Researchers established the hackers spent about a month exploring the breached networks, using rclone to archive stolen data to cloud storage, before encrypting the target system. Reported targets included LaSalle County, and the city of Novi Sad. The FBI warned January 2021, in Private Industry Notification 20210106–001, of extortion activity using Egregor ransomware and rclone. Organisations worldwide had been threatened with public release of exfiltrated data. In some cases rclone had been disguised under the name svchost. Bookseller Barnes & Noble, US retailer Kmart, games developer Ubisoft and the Vancouver metro system have been reported as victims. An April 2021, cybersecurity investigation into SonicWall VPN zero-day vulnerability SNWLID-2021-0001 by FireEye's Mandiant team established attackers UNC2447 used rclone for reconnaissance and exfiltration of victims' files. Cybersecurity and Infrastructure Security Agency Analysis Report AR21-126A confirmed this use of rclone in FiveHands ransomware attacks. A June 2021, Microsoft Security Intelligence Twitter post identified use of rclone in BazaCall cyber attacks. The attackers sent emails e
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Gemini Enterprise Agent Platform

Gemini Enterprise Agent Platform (formerly known as Vertex AI) is a managed machine learning (ML) and artificial intelligence (AI) platform developed by Google Cloud. It provides a unified environment for building, training, deploying, and scaling ML models and generative AI applications. The platform integrates tools for the full ML lifecycle, including data preparation, model training, evaluation, deployment, and monitoring, under a single API and user interface. Vertex AI was announced at Google I/O and released as a generally available product on May 18, 2021. At launch, Google described Vertex AI as unifying its AutoML offerings with its prior Cloud AI Platform capabilities, and as adding operational features intended to help teams move models from experimentation into production use. On April 22, 2026, Google announced Gemini Enterprise Agent Platform as the replacement evolution of Vertex AI. == History == Google Cloud announced the general availability of Vertex AI on May 18, 2021, at the Google I/O developer conference. The platform was designed to consolidate Google Cloud's previously separate ML offerings, including AutoML and the legacy AI Platform, into a single system. At launch, Google claimed that Vertex AI required roughly 80% fewer lines of code to train a model compared to competing platforms. In June 2023, Google made generative AI support in Vertex AI generally available, giving developers access to foundation models including PaLM 2, Imagen, and Codey through the platform's Model Garden and the newly launched Generative AI Studio. At the time of this launch, Model Garden included over 60 models from Google and its partners. In August 2023, at the Google Cloud Next conference, Google announced further updates to Vertex AI, including the addition of third-party models such as Claude 2 from Anthropic and Llama 2 from Meta to the Model Garden, as well as new tools called Vertex AI Extensions for connecting models to APIs for real-time data retrieval. At the same event, Vertex AI Search and Conversation were made generally available, providing enterprise search and chatbot capabilities powered by foundation models. In April 2024, at Google Cloud Next, the company introduced Vertex AI Agent Builder, a no-code tool for creating AI-powered conversational agents built on top of Gemini large language models. This brought together the existing Vertex AI Search and Conversation products with new developer tools for building generative AI experiences. == Features == === Model training === Vertex AI supports both AutoML, which enables code-free model training on tabular, image, text, or video data, and custom training, which gives users full control over the ML framework, training code, and hyperparameter tuning. The platform provides serverless training as well as dedicated training clusters with GPU and TPU accelerators. Vertex AI Vizier handles automatic hyperparameter tuning, and Vertex AI Experiments allows comparison and tracking of training runs. === Model Garden === The Vertex AI Model Garden is a curated catalog of over 200 enterprise-ready models, including Google's own foundation models (such as Gemini, Imagen, and Veo), third-party models (such as Anthropic's Claude and Mistral AI models), and popular open-source models (such as Llama and Gemma). Models are accessible as fully managed model-as-a-service APIs. === Pipelines (workflow orchestration) === Vertex AI Pipelines provides managed orchestration of ML workflows and supports pipelines built with the Kubeflow Pipelines SDK, among other options described in Google Cloud documentation. === Vertex AI Studio === Vertex AI Studio provides tools for prompt design, testing, and model management, allowing developers to prototype and build generative AI applications using natural language, code, images, or video. === Agent Builder and Agent Engine === Vertex AI Agent Builder is a suite of products for building, deploying, and governing AI agents in production environments. It supports development with the open-source Agent Development Kit (ADK) and other frameworks. Vertex AI Agent Engine provides the underlying infrastructure for deploying and scaling agents, with support for enterprise security features including HIPAA compliance, customer-managed encryption keys (CMEK), and VPC Service Controls. === Generative AI tooling and model access === Google markets Vertex AI as providing access to Google foundation models (including the Gemini family) and developer tools such as Vertex AI Studio, along with a model catalog that includes Google and selected open source models (marketed as "Model Garden"). Google has also offered products within Vertex AI aimed at building generative search and conversational applications, including offerings named "Vertex AI Search" and "Vertex AI Conversation" as reported in 2023 coverage of platform updates. === MLOps tools === The platform includes a range of MLOps capabilities: Vertex AI Pipelines for orchestrating and automating ML workflows as reusable pipelines. Vertex AI Feature Store for serving, sharing, and reusing ML features across projects. Vertex AI Model Registry for storing, versioning, and managing trained models. Vertex AI Model Monitoring for detecting training-serving skew and inference drift in deployed models. Vertex Explainable AI for interpreting model predictions. Vertex AI Workbench for managed JupyterLab notebook environments integrated with Google Cloud Storage and BigQuery. == Industry recognition == Google was named a Leader for the fifth consecutive year in the 2024 Gartner Magic Quadrant for Cloud AI Developer Services, a recognition that encompasses Vertex AI and its related offerings. Google was also recognized as a Leader in the 2024 Gartner Magic Quadrant for Data Science and Machine Learning Platforms and was named a Leader in the Forrester Wave for AI/ML Platforms, Q3 2024. In October 2025, Google was also named a Leader in the 2025 IDC (International Data Corporation) MarketScape for Worldwide GenAI Life-Cycle Foundation Model Software. == Pricing == Vertex AI uses a pay-as-you-go pricing model, with costs determined by the specific services consumed, including model training, prediction serving, and data storage. For generative AI tasks, pricing is based on a per-token model, with rates varying depending on the specific model used and whether tokens are input or output. Google offers a free tier for new users, which includes limited custom training hours and online prediction usage, along with an introductory US$300 in Google Cloud credits valid for 90 days. == Adoption == In the year following its 2021 launch, Google reported that usage of Vertex AI and BigQuery had driven 2.5 times more machine learning predictions compared to the prior year, and that active customers of Vertex AI Workbench had grown 25-fold over a six-month period. Early enterprise adopters included Ford, Wayfair, and Seagate, among others. Wayfair reported that it was able to run large model training jobs 5 to 10 times faster using the platform.
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Rclone

Rclone is an open source, multi threaded, command line computer program to manage or migrate content on cloud and other high latency storage. Its capabilities include sync, transfer, crypt, cache, union, compress and mount. The rclone website lists supported backends including S3 and Google Drive. Descriptions of rclone often carry the strapline "Rclone syncs your files to cloud storage". Those prior to 2020 include the alternative "Rsync for Cloud Storage". Rclone is well known for its rclone sync and rclone mount commands. It provides further management functions analogous to those ordinarily used for files on local disks, but which tolerate some intermittent and unreliable service. Rclone is commonly used with media servers such as Plex, Emby or Jellyfin to stream content direct from consumer file storage services. Official Ubuntu, Debian, Fedora, Gentoo, Arch, Brew, Chocolatey, and other package managers include rclone. == History == Nick Craig-Wood was inspired by rsync. Concerns about the noise and power costs arising from home computer servers prompted him to embrace cloud storage and he began developing rclone as open source software in 2012 under the name swiftsync. Rclone was promoted to stable version 1.00 in July 2014. In May 2017, Amazon Drive barred new users of rclone and other upload utilities, citing security concerns. Amazon Drive had been advertised as offering unlimited storage for £55 per year. Amazon's AWS S3 service continues to support new rclone users. The original rclone logo was updated in September 2018. In March 2020, Nick Craig-Wood resigned from Memset Ltd, a cloud hosting company he founded, to focus on open source software. Amazon's AWS April 2020 public sector blog explained how the Fred Hutch Cancer Research Center were using rclone in their Motuz tool to migrate very large biomedical research datasets in and out of AWS S3 object stores. In November 2020, rclone was updated to correct a weakness in the way it generated passwords. Passwords for encrypted remotes can be generated randomly by rclone or supplied by the user. In all versions of rclone from 1.49.0 to 1.53.2 the seed value for generated passwords was based on the number of seconds elapsed in the day, and therefore not truly random. CVE-2020-28924 recommended users upgrade to the latest version of rclone and check the passwords protecting their encrypted remotes. Release 1.55 of rclone in March 2021 included features sponsored by CERN and their CS3MESH4EOSC project. The work was EU funded to promote vendor-neutral application programming interfaces and protocols for synchronisation and sharing of academic data on cloud storage. == Backends and commands == Rclone supports the following services as backends. There are others, built on standard protocols such as WebDAV or S3, that work. WebDAV backends do not support rclone functionality dependent on server side checksum or modtime. Remotes are usually defined interactively from these backends, local disk, or memory (as S3), with rclone config. Rclone can further wrap those remotes with one or more of alias, chunk, compress, crypt or union, remotes. Once defined, the remotes are referenced by other rclone commands interchangeably with the local drive. Remote names are followed by a colon to distinguish them from local drives. For example, a remote example_remote containing a folder, or pseudofolder, myfolder is referred to within a command as a path example_remote:/myfolder. Rclone commands directly apply to remotes, or mount them for file access or streaming. With appropriate cache options the mount can be addressed as if a conventional, block level disk. Commands are provided to serve remotes over SFTP, HTTP, WebDAV, FTP and DLNA. Commands can have sub-commands and flags. Filters determine which files on a remote that rclone commands are applied to. rclone rc passes commands or new parameters to existing rclone sessions and has an experimental web browser interface. === Crypt remotes === Rclone's crypt implements encryption of files at rest in cloud storage. It layers an encrypted remote over a pre-existing, cloud or other remote. Crypt is commonly used to encrypt / decrypt media, for streaming, on consumer storage services such as Google Drive. Rclone's configuration file contains the crypt password. The password can be lightly obfuscated, or the whole rclone.conf file can be encrypted. Crypt can either encrypt file content and name, or additionally full paths. In the latter case there is a potential clash with encryption for cloud backends, such as Microsoft OneDrive, having limited path lengths. Crypt remotes do not encrypt object modification time or size. The encryption mechanism for content, name and path is available, for scrutiny, on the rclone website. Key derivation is with scrypt. === Example syntax (Linux) === These examples describe paths and file names but object keys behave similarly. To recursively copy files from directory remote_stuff, at the remote xmpl, to directory stuff in the home folder:- -v enables logging and -P, progress information. By default rclone checks the file integrity (hash) after copy; can retry each file up to three times if the operation is interrupted; uses up to four parallel transfer threads, and does not apply bandwidth throttling. Running the above command again copies any new or changed files at the remote to the local folder but, like default rsync behaviour, will not delete from the local directory, files which have been removed from the remote. To additionally delete files from the local folder which have been removed from the remote - more like the behaviour of rsync with a --delete flag:- And to delete files from the source after they have been transferred to the local directory - more like the behaviour of rsync with a --remove-source-file flag:- To mount the remote directory at a mountpoint in the pre-existing, empty stuff directory in the home directory (the ampersand at the end makes the mount command run as a background process):- Default rclone syntax can be modified. Alternative transfer, filter, conflict and backend specific flags are available. Performance choices include number of concurrent transfer threads; chunk size; bandwidth limit profiling, and cache aggression. == Academic evaluation == In 2018, University of Kentucky researchers published a conference paper comparing use of rclone and other command line, cloud data transfer agents for big data. The paper was published as a result of funding by the National Science Foundation. Later that year, University of Utah's Center for High Performance Computing examined the impact of rclone options on data transfer rates. == Rclone use at HPC research sites == Examples are University of Maryland, Iowa State University, Trinity College Dublin, NYU, BYU, Indiana University, CSC Finland, Utrecht University, University of Nebraska, University of Utah, North Carolina State University, Stony Brook, Tulane University, Washington State University, Georgia Tech, National Institutes of Health, Wharton, Yale, Harvard, Minnesota, Michigan State, Case Western Reserve University, University of South Dakota, Northern Arizona University, University of Pennsylvania, Stanford, University of Southern California, UC Santa Barbara, UC Irvine, UC Berkeley, and SURFnet. == Rclone and cybercrime == May 2020 reports stated rclone had been used by hackers to exploit Diebold Nixdorf ATMs with ProLock ransomware. The FBI issued a Flash Alert MI-000125-MW on May 4, 2020, in relation to the compromise. They issued a further, related alert 20200901–001 in September 2020. Attackers had exfiltrated / encrypted data from organisations involved in healthcare, construction, finance, and legal services. Multiple US government agencies, and industrial entities were affected. Researchers established the hackers spent about a month exploring the breached networks, using rclone to archive stolen data to cloud storage, before encrypting the target system. Reported targets included LaSalle County, and the city of Novi Sad. The FBI warned January 2021, in Private Industry Notification 20210106–001, of extortion activity using Egregor ransomware and rclone. Organisations worldwide had been threatened with public release of exfiltrated data. In some cases rclone had been disguised under the name svchost. Bookseller Barnes & Noble, US retailer Kmart, games developer Ubisoft and the Vancouver metro system have been reported as victims. An April 2021, cybersecurity investigation into SonicWall VPN zero-day vulnerability SNWLID-2021-0001 by FireEye's Mandiant team established attackers UNC2447 used rclone for reconnaissance and exfiltration of victims' files. Cybersecurity and Infrastructure Security Agency Analysis Report AR21-126A confirmed this use of rclone in FiveHands ransomware attacks. A June 2021, Microsoft Security Intelligence Twitter post identified use of rclone in BazaCall cyber attacks. The attackers sent emails e
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Automatic acquisition of sense-tagged corpora

The knowledge acquisition bottleneck is perhaps the major impediment to solving the word-sense disambiguation (WSD) problem. Unsupervised learning methods rely on knowledge about word senses, which is barely formulated in dictionaries and lexical databases. Supervised learning methods depend heavily on the existence of manually annotated examples for every word sense, a requisite that can so far be met only for a handful of words for testing purposes, as it is done in the Senseval exercises. == Existing methods == Therefore, one of the most promising trends in WSD research is using the largest corpus ever accessible, the World Wide Web, to acquire lexical information automatically. WSD has been traditionally understood as an intermediate language engineering technology which could improve applications such as information retrieval (IR). In this case, however, the reverse is also true: Web search engines implement simple and robust IR techniques that can be successfully used when mining the Web for information to be employed in WSD. The most direct way of using the Web (and other corpora) to enhance WSD performance is the automatic acquisition of sense-tagged corpora, the fundamental resource to feed supervised WSD algorithms. Although this is far from being commonplace in the WSD literature, a number of different and effective strategies to achieve this goal have already been proposed. Some of these strategies are: acquisition by direct Web searching (searches for monosemous synonyms, hypernyms, hyponyms, parsed gloss' words, etc.), Yarowsky algorithm (bootstrapping), acquisition via Web directories, and acquisition via cross-language meaning evidences. == Summary == === Optimistic results === The automatic extraction of examples to train supervised learning algorithms reviewed has been, by far, the best explored approach to mine the web for word-sense disambiguation. Some results are certainly encouraging: In some experiments, the quality of the Web data for WSD equals that of human-tagged examples. This is the case of the monosemous relatives plus bootstrapping with Semcor seeds technique and the examples taken from the ODP Web directories. In the first case, however, Semcor-size example seeds are necessary (and only available for English), and it has only been tested with a very limited set of nouns; in the second case, the coverage is quite limited, and it is not yet clear whether it can be grown without compromising the quality of the examples retrieved. It has been shown that a mainstream supervised learning technique trained exclusively with web data can obtain better results than all unsupervised WSD systems which participated at Senseval-2. Web examples made a significant contribution to the best Senseval-2 English all-words system. === Difficulties === There are, however, several open research issues related to the use of Web examples in WSD: High precision in the retrieved examples (i.e., correct sense assignments for the examples) does not necessarily lead to good supervised WSD results (i.e., the examples are possibly not useful for training). The most complete evaluation of Web examples for supervised WSD indicates that learning with Web data improves over unsupervised techniques, but the results are nevertheless far from those obtained with hand-tagged data, and do not even beat the most-frequent-sense baseline. Results are not always reproducible; the same or similar techniques may lead to different results in different experiments. Compare, for instance, Mihalcea (2002) with Agirre and Martínez (2004), or Agirre and Martínez (2000) with Mihalcea and Moldovan (1999). Results with Web data seem to be very sensitive to small differences in the learning algorithm, to when the corpus was extracted (search engines change continuously), and on small heuristic issues (e.g., differences in filters to discard part of the retrieved examples). Results are strongly dependent on bias (i.e., on the relative frequencies of examples per word sense). It is unclear whether this is simply a problem of Web data, or an intrinsic problem of supervised learning techniques, or just a problem of how WSD systems are evaluated (indeed, testing with rather small Senseval data may overemphasize sense distributions compared to sense distributions obtained from the full Web as corpus). In any case, Web data has an intrinsic bias, because queries to search engines directly constrain the context of the examples retrieved. There are approaches that alleviate this problem, such as using several different seeds/queries per sense or assigning senses to Web directories and then scanning directories for examples; but this problem is nevertheless far from being solved. Once a Web corpus of examples is built, it is not entirely clear whether its distribution is safe from a legal perspective. === Future === Besides automatic acquisition of examples from the Web, there are some other WSD experiments that have profited from the Web: The Web as a social network has been successfully used for cooperative annotation of a corpus (OMWE, Open Mind Word Expert project), which has already been used in three Senseval-3 tasks (English, Romanian and Multilingual). The Web has been used to enrich WordNet senses with domain information: topic signatures and Web directories, which have in turn been successfully used for WSD. Also, some research benefited from the semantic information that the Wikipedia maintains on its disambiguation pages. It is clear, however, that most research opportunities remain largely unexplored. For instance, little is known about how to use lexical information extracted from the Web in knowledge-based WSD systems; and it is also hard to find systems that use Web-mined parallel corpora for WSD, even though there are already efficient algorithms that use parallel corpora in WSD.
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Friendica

Friendica (formerly Friendika, originally Mistpark) is a free and open-source software distributed social network. It forms one part of the Fediverse, an interconnected and decentralized network of independently operated servers. == Features == Friendica users can connect with others via their own Friendica server, but may also fully integrate contacts from other platforms including Diaspora, Pump.io, GNU social, email, Discourse and more recently ActivityPub (including Mastodon, Pleroma and Pixelfed) and Bluesky into their 'newsfeed'. In addition to these two way connections, users can also use Friendica as a publishing platform to post content to WordPress, Tumblr, Insanejournal and Libertree. Posting to Google+ was also supported until that service was shut down. In addition, RSS feeds can be ingested. Because users are distributed across many servers, their "addresses" consist of a username, the "@" symbol, and the domain name of the Friendica instance in the same manner email addresses are formed. Twitter support was available but was deprecated due to API changes under Elon Musk's leadership rendering it unusable. Most of the functionality from major microblogging and social networking platforms are available in Friendica; for example, tagging users and groups via "@ mentions"; direct messages; hashtags; photo albums; "likes"; "dislikes"; comments; and re-shares of publicly visible posts. Published items can be edited and updated across the network. Comprehensive settings for privacy and the public visibility of posts allow users to regulate who can read which contributions, or see specific information about the user. Users can also create multiple profiles, allowing different groups of people (such as friends, or work mates) to see a different profile entirely when viewing the same page. User accounts can be downloaded or deleted, and can be imported to a different Friendica server if so required. Public forums can be created under different accounts, which can be switched between if the accounts are registered with the same email address. == Development == There is no corporation behind Friendica. The developers work on a voluntary basis and the project is run informally; the platform itself is used for the communication between the developers. There are different forums within Friendica, such as "Friendica Developers" and "Friendica Support". The source code of Friendica is hosted on GitHub. == Installation == The developers aim to make installation of the software as simple as possible for technical laymen. They argue that decentralization on small servers is a key condition for the freedom of users and their self-determination. The difficulty level is similar to an installation of WordPress. However, the installing on shared hosting is sometimes difficult because of missing PHP5 modules. Some volunteers also run public servers so that newcomers can also avoid the installation of their own software. == List of clients == Friendica implements multiple client-server API variants simultaneously. Along with endpoints needed to use enhanced Friendica features, it also implements the API used by GNU social, Twitter and since version 2021.06 also the one used by Mastodon. As a result, most GNU social and Mastodon clients can be used for Friendica. Examples of Friendica compatible clients include: Raccoon for Friendica, Friendiqa, Fedilab, AndStatus, Twidere and DiCa for Android, friendly for Sailfish OS, friclicli (CLI client), choqok and Friendiqa for Linux and Friendica Mobile for Windows 10. == Reception == Friendica was cited in January 2012 by Infoshop News as an "alternative to Google+ and Facebook" to be used on the Occupy Nigeria movement. In January 2012 Free Software Foundation Europe's blog cited Friendica as a reasonable alternative to centralized and controlled social networks such as Facebook or Google+. Biblical Notes writer J. Randal Matheny described Friendica in January 2012 as "One social networking option flying under the radar until recently deserves consideration as an already stable platform with a wide range of options, applications, plug-ins, and possibilities for opening up the Internet." In February 2012, the German computer magazine c't wrote: "Friendica demonstrates how decentralized social networks can become widely accepted." Another German publication, the professional magazine t3n listed Friendica as a Facebook rival in an online article in March 2012 about Facebook alternatives. It compared Friendica with similar social networks like Diaspora and identi.ca. MSN Tech & Gadgets contributor Emma Boyes wrote about Friendica in May 2012: "why you'll love it: you can use it to access all the other social networks and get recommendations of new friends and groups to join. Friendica is open source and decentralised. There's no corporation behind it and there are extensive privacy settings. You can choose from a variety of user interfaces and it boasts some cool features—for instance, being able to key in a list of your interests and use the 'profile match' feature to recommend other users who share them with you. A word of warning, though, the site is not as user-friendly as the others on this list, so it may be this one is one for the geeks." == Later reviews == Acquisition of Twitter by Elon Musk had revitalized public interest in Fediverse technologies in April 2022. Friendica received favorable reviews, with a PCMag article describing it as "mostly comparable to Facebook", drawing a parallel to Google+ and highlighting using it "for planning events, and its multiple profile feature means you can show a different face to your friends, coworkers, and family". The September 2022 issue of Linux Magazine contains a detailed comparison and walk-through of registering to and using basic functions of Diaspora, Friendica and Mastodon. They describe Friendica as "intuitive" and highlight the "huge choice of account settings" and that "Friendica does not require any specific hardware, so you can use an old computer system as a server." == Vulnerabilities == In September 2020, a hotfix was released to patch a security vulnerability that could leak sensitive information from the server environment since versions released in April 2019 (develop branch) and June 2019 (stable).
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Scroll (web service)

Scroll was a subscription-based web service developed by Scroll Labs Inc., offering ad-free access to websites in exchange for a fee. Scroll was not an ad blocker; instead, it partnered directly with internet publishers who voluntarily removed ads from their sites for Scroll users in exchange for a portion of the subscription fee. In May 2021, Scroll was acquired by Twitter. In October 2021, Scroll sent out an email announcing its integration into Twitter Blue within 30 days. == Functionality == Scroll enabled users to browse websites that partnered with Scroll without encountering online advertising, in exchange for a subscription fee. Unlike ad blocker, which disable advertisements without compensating the publisher, Scroll sent a browser cookie indicating that the user was a subscriber. The Scroll software integrated into the website detected this cookie and served an ad-free version of the site. In exchange for disabling advertisements, partner websites received a portion of the subscription fee. As of January 2020, Scroll retained 30% of the subscription fee, with the remaining 70% distributed among publisher sites. Payments to sites were made individually by users based on their 'engagement and loyalty,' rather than from a single pool of all subscription revenue. Scroll did not grant subscribers access to partner sites behind a paywall; it only removed ads from the site if the user also paid the publication's subscription fee. == History == Scroll was founded in 2016 by former Chartbeat Chief Executive Tony Haile. Scroll raised US$3 million in its first round of funding in 2016, including investments from The New York Times, Uncork Capital, and Axel Springer SE. By October 2018, Scroll had raised US$10 million in funding. In 2018, Scroll signed its first partner websites, which included The Atlantic, Fusion Media Group, Business Insider, Slate, MSNBC, The Philadelphia Inquirer, and Talking Points Memo. In February 2019, Scroll acquired the social media curation app Nuzzel. The same month, Mozilla and Scroll announced a partnership to run a "test pilot" together, but did not go into details. Scroll entered beta testing in 2019 and launched to the general public on January 28, 2020. In March 2020, Mozilla started offering Scroll as part of its "Firefox Better Web" service bundle. In May 2021, Scroll was acquired by Twitter, with the future of Scroll cited as being uncertain. An email to customers announcing the change said, "Later this year, Scroll will become part of a wider Twitter subscription that will expand on and adapt our services and functionality".
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NumPy

NumPy (pronounced NUM-py) is a library for the Python programming language, adding support for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays. The predecessor of NumPy, Numeric, was originally created by Jim Hugunin with contributions from several other developers. In 2005, Travis Oliphant created NumPy by incorporating features of the competing Numarray into Numeric, with extensive modifications. NumPy is open-source software and has many contributors. NumPy is fiscally sponsored by NumFOCUS. == History == === matrix-sig === The Python programming language was not originally designed for numerical computing, but attracted the attention of the scientific and engineering community early on. In 1995 the special interest group (SIG) matrix-sig was founded with the aim of defining an array computing package; among its members was Python designer and maintainer Guido van Rossum, who extended Python's syntax (in particular the indexing syntax) to make array computing easier. === Numeric === An implementation of a matrix package was completed by Jim Fulton, then expanded to support multi-dimensional arrays by Jim Hugunin and called Numeric (also variously known as the "Numerical Python extensions" or "NumPy"), with influences from the APL family of languages, Basis, MATLAB, FORTRAN, S and S+, and others. Hugunin, a graduate student at the Massachusetts Institute of Technology (MIT), joined the Corporation for National Research Initiatives (CNRI) in 1997 to work on JPython, leaving Paul Dubois of Lawrence Livermore National Laboratory (LLNL) to take over as maintainer. Other early contributors include David Ascher, Konrad Hinsen and Travis Oliphant. === Numarray === A new package called Numarray was written as a more flexible replacement for Numeric. Like Numeric, it too is now deprecated. Numarray had faster operations for large arrays, but was slower than Numeric on small ones, so for a time both packages were used in parallel for different use cases. The last version of Numeric (v24.2) was released on 11 November 2005, while the last version of numarray (v1.5.2) was released on 24 August 2006. There was a desire to get Numeric into the Python standard library, but Guido van Rossum decided that the code was not maintainable in its state then. === NumPy === In early 2005, NumPy developer Travis Oliphant wanted to unify the community around a single array package and ported Numarray's features to Numeric, releasing the result as NumPy 1.0 in 2006. This new project was part of SciPy. To avoid installing the large SciPy package just to get an array object, this new package was separated and called NumPy. Support for Python 3 was added in 2011 with NumPy version 1.5.0. In 2011, PyPy started development on an implementation of the NumPy API for PyPy. As of 2023, it is not yet fully compatible with NumPy. == Features == NumPy targets the CPython reference implementation of Python, which is a non-optimizing bytecode interpreter. Mathematical algorithms written for this version of Python often run much slower than compiled equivalents due to the absence of compiler optimization. NumPy addresses the slowness problem partly by providing multidimensional arrays and functions and operators that operate efficiently on arrays; using these requires rewriting some code, mostly inner loops, using NumPy. Using NumPy in Python gives functionality comparable to MATLAB since they are both interpreted, and they both allow the user to write fast programs as long as most operations work on arrays or matrices instead of scalars. In comparison, MATLAB boasts a large number of additional toolboxes, notably Simulink, whereas NumPy is intrinsically integrated with Python, a more modern and complete programming language. Moreover, complementary Python packages are available; SciPy is a library that adds more MATLAB-like functionality and Matplotlib is a plotting package that provides MATLAB-like plotting functionality. Although MATLAB can perform sparse matrix operations, NumPy alone cannot perform such operations and requires the use of the scipy.sparse library. Internally, both MATLAB and NumPy rely on BLAS and LAPACK for efficient linear algebra computations. Python bindings of the widely used computer vision library OpenCV utilize NumPy arrays to store and operate on data. Since images with multiple channels are simply represented as three-dimensional arrays, indexing, slicing or masking with other arrays are very efficient ways to access specific pixels of an image. The NumPy array as universal data structure in OpenCV for images, extracted feature points, filter kernels and many more vastly simplifies the programming workflow and debugging. Importantly, many NumPy operations release the global interpreter lock, which allows for multithreaded processing. NumPy also provides a C API, which allows Python code to interoperate with external libraries written in low-level languages. === The ndarray data structure === The core functionality of NumPy is its "ndarray", for n-dimensional array, data structure. These arrays are strided views on memory. In contrast to Python's built-in list data structure, these arrays are homogeneously typed: all elements of a single array must be of the same type. Such arrays can also be views into memory buffers allocated by C/C++, Python, and Fortran extensions to the CPython interpreter without the need to copy data around, giving a degree of compatibility with existing numerical libraries. This functionality is exploited by the SciPy package, which wraps a number of such libraries (notably BLAS and LAPACK). NumPy has built-in support for memory-mapped ndarrays. === Limitations === Inserting or appending entries to an array is not as trivially possible as it is with Python's lists. The np.pad(...) routine to extend arrays actually creates new arrays of the desired shape and padding values, copies the given array into the new one and returns it. NumPy's np.concatenate([a1,a2]) operation does not actually link the two arrays but returns a new one, filled with the entries from both given arrays in sequence. Reshaping the dimensionality of an array with np.reshape(...) is only possible as long as the number of elements in the array does not change. These circumstances originate from the fact that NumPy's arrays must be views on contiguous memory buffers. Algorithms that are not expressible as a vectorized operation will typically run slowly because they must be implemented in "pure Python", while vectorization may increase memory complexity of some operations from constant to linear, because temporary arrays must be created that are as large as the inputs. Runtime compilation of numerical code has been implemented by several groups to avoid these problems; open source solutions that interoperate with NumPy include numexpr and Numba. Cython and Pythran are static-compiling alternatives to these. Many modern large-scale scientific computing applications have requirements that exceed the capabilities of the NumPy arrays. For example, NumPy arrays are usually loaded into a computer's memory, which might have insufficient capacity for the analysis of large datasets. Further, NumPy operations are executed on a single CPU. However, many linear algebra operations can be accelerated by executing them on clusters of CPUs or of specialized hardware, such as GPUs and TPUs, which many deep learning applications rely on. As a result, several alternative array implementations have arisen in the scientific python ecosystem over the recent years, such as Dask for distributed arrays and TensorFlow or JAX for computations on GPUs. Because of its popularity, these often implement a subset of NumPy's API or mimic it, so that users can change their array implementation with minimal changes to their code required. A library named CuPy, accelerated by Nvidia's CUDA framework, has also shown potential for faster computing, being a 'drop-in replacement' of NumPy. == Examples == NumPy is conventionally imported as np. === Basic operations === === Universal functions === === Linear algebra === === Multidimensional arrays === === Incorporation with OpenCV === === Nearest-neighbor search === Functional Python and vectorized NumPy version. === F2PY === Quickly wrap native code for faster scripts.
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Dhammin

Dhammin (Arabic: ضمّن) is a political platform that manages candidates' electoral campaigns for the National Assembly, Municipal Council or Cooperative Society councils of Kuwait. The platform was founded by Abdullah Al-Salloum and it is, according to news reports and interviews, the first within the field to apply distributed-systems' methodologies.
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Web container

A web container (also known as a servlet container; and compare "webcontainer") is the component of a web server that interacts with Jakarta Servlets. A web container is responsible for managing the lifecycle of servlets, mapping a URL to a particular servlet and ensuring that the URL requester has the correct access-rights. A web container handles requests to servlets, Jakarta Server Pages (JSP) files, and other types of files that include server-side code. The Web container creates servlet instances, loads and unloads servlets, creates and manages request and response objects, and performs other servlet-management tasks. A web container implements the web component contract of the Jakarta EE architecture. This architecture specifies a runtime environment for additional web components, including security, concurrency, lifecycle management, transaction, deployment, and other services. == List of Servlet containers == The following is a list of notable applications which implement the Jakarta Servlet specification from Eclipse Foundation, divided depending on whether they are directly sold or not. === Open source Web containers === Apache Tomcat (formerly Jakarta Tomcat) is an open source web container available under the Apache Software License. Apache Tomcat 6 and above are operable as general application container (prior versions were web containers only) Apache Geronimo is a full Java EE 6 implementation by Apache Software Foundation. Enhydra, from Lutris Technologies. GlassFish from Eclipse Foundation (an application server, but includes a web container). Jetty, from the Eclipse Foundation. Also supports SPDY and WebSocket protocols. Open Liberty, from IBM, is a fully compliant Jakarta EE server Virgo from Eclipse Foundation provides modular, OSGi based web containers implemented using embedded Tomcat and Jetty. Virgo is available under the Eclipse Public License. WildFly (formerly JBoss Application Server) is a full Java EE implementation by Red Hat, division JBoss. === Commercial Web containers === iPlanet Web Server, from Oracle. JBoss Enterprise Application Platform from Red Hat, division JBoss is subscription-based/open-source Jakarta EE-based application server. WebLogic Application Server, from Oracle Corporation (formerly developed by BEA Systems). Orion Application Server, from IronFlare. Resin Pro, from Caucho Technology. IBM WebSphere Application Server. SAP NetWeaver.
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Focus recovery based on the linear canonical transform

For digital image processing, the Focus recovery from a defocused image is an ill-posed problem since it loses the component of high frequency. Most of the methods for focus recovery are based on depth estimation theory. The Linear canonical transform (LCT) gives a scalable kernel to fit many well-known optical effects. Using LCTs to approximate an optical system for imaging and inverting this system, theoretically permits recovery of a defocused image. == Depth of field and perceptual focus == In photography, depth of field (DOF) means an effective focal length. It is usually used for stressing an object and deemphasizing the background (and/or the foreground). The important measure related to DOF is the lens aperture. Decreasing the diameter of aperture increases focus and lowers resolution and vice versa. == The Huygens–Fresnel principle and DOF == The Huygens–Fresnel principle describes diffraction of wave propagation between two fields. It belongs to Fourier optics rather than geometric optics. The disturbance of diffraction depends on two circumstance parameters, the size of aperture and the interfiled distance. Consider a source field and a destination field, field 1 and field 0, respectively. P1(x1,y1) is the position in the source field, P0(x0,y0) is the position in the destination field. The Huygens–Fresnel principle gives the diffraction formula for two fields U(x0,y0), U(x1,y1) as following: U ( x 0 , y 0 ) = 1 j λ ∫ ∫ U ( x 1 , y 1 ) e j k r 01 r 01 cos ⁡ θ d x 1 d y 1 {\displaystyle \mathbf {U} (x_{0},y_{0})={\frac {1}{j\lambda }}\int \!\int \mathbf {U} (x_{1},y_{1}){\frac {e^{jkr_{01}}}{r_{01}}}\cos \theta dx_{1}dy_{1}} where θ denotes the angle between r 01 {\displaystyle r_{01}} and z {\displaystyle z} . Replace cos θ by r 01 z {\displaystyle {\frac {r_{01}}{z}}} and r 01 {\displaystyle r_{01}} by [ ( x 0 − x 1 ) 2 + ( y 0 − y 1 ) 2 + z 2 ] 1 / 2 {\displaystyle [(x_{0}-x_{1})^{2}+(y_{0}-y_{1})^{2}+z^{2}]^{1/2}} we get U ( x 0 , y 0 ) = 1 j λ z ∫ ∫ U ( x 1 , y 1 ) exp ⁡ ( j k z [ 1 + ( x 0 − x 1 z ) 2 + ( y 0 − y 1 z ) 2 ] 1 / 2 ) 1 + ( x 0 − x 1 z ) 2 + ( y 0 − y 1 z ) 2 d x 1 d y 1 {\displaystyle \mathbf {U} (x_{0},y_{0})={\frac {1}{j\lambda z}}\int \!\int \mathbf {U} (x_{1},y_{1}){\frac {\exp(jkz[1+({\frac {x_{0}-x_{1}}{z}})^{2}+({\frac {y_{0}-y_{1}}{z}})^{2}]^{1/2})}{1+({\frac {x_{0}-x_{1}}{z}})^{2}+({\frac {y_{0}-y_{1}}{z}})^{2}}}dx_{1}dy_{1}} The further distance z or the smaller aperture (x1,y1) causes a greater diffraction. A larger DOF can lead to a more effective focused wave distribution. This seems to be a conflict. Here are the notations: Diffraction In a real imaging environment, the depths of objects comparing to the aperture are usually not enough to lead to serious diffraction. However, a long enough depth of the object can truly blurs the image. Effective Focus Small aperture, small blurring radius, few wave information. Loses details in comparing to a large aperture. In conclusion, diffraction explains a micro behavior whereas DOF shows a macro behavior. Both of them are related to aperture size. == Linear canonical transform == As the meaning of "canonical", the linear canonical transform (LCT) is a scalable transform that connects to many important kernels such as the Fresnel transform, Fraunhofer transform and the fractional Fourier transform. It can be easily controlled by its four parameters, a, b, c, d (3 degrees of freedom). The definition: L M ( f ( u ) ) = ∫ L M ( u , u ′ ) f ( u ′ ) d u ′ {\displaystyle L_{M}(f(u))=\int L_{M}(u,u')f(u')du'} where L M ( u , u ′ ) = { 1 b e − j π / 4 e [ j π ( d b u 2 ) − 2 1 b u u ′ + a b u ′ 2 ] , if b ≠ 0 d e j 2 c d u 2 δ ( u ′ − d u ) , if b = 0 {\displaystyle L_{M}(u,u')={\begin{cases}{\sqrt {\frac {1}{b}}}e^{-j\pi /4}e^{[j\pi ({\frac {d}{b}}u^{2})-2{\frac {1}{b}}uu'+{\frac {a}{b}}u'^{2}]},&{\mbox{if }}b\neq 0\\{\sqrt {d}}e^{{\frac {j}{2}}cdu^{2}}\delta (u'-du),&{\mbox{if }}b=0\end{cases}}} Consider a general imaging system with object distance z0, focal length of the thin lens f and an imaging distance z1. The effect of the propagation in freespace acts as nearly a chirp convolution, that is, the formula of diffraction. Besides, the effect of the propagation in thin lens acts as a chirp multiplication. The parameters are all simplified as paraxial approximations while meeting the freespace propagation. It does not consider aperture size. From the properties of the LCT, it is possible to obtain those 4 parameters for this optical system as: [ 1 − z 1 f λ z 0 − λ z 0 z 1 f + λ z 1 − 1 λ f 1 − z 0 f ] {\displaystyle {\begin{bmatrix}1-{\frac {z_{1}}{f}}\quad &\lambda z_{0}-{\frac {\lambda z_{0}z_{1}}{f}}+\lambda z_{1}\\-{\frac {1}{\lambda f}}\quad &1-{\frac {z_{0}}{f}}\end{bmatrix}}} Once the values of z1, z0 and f are known, the LCT can simulate any optical system.
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