AI Chat To Pdf

AI Chat To Pdf — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

  • Passenger drone

    Passenger drone

    A passenger drone is an autonomous aircraft that is designed to carry a small number of passengers to a destination. In 2021, Ehang, a technology company based in Guangzhou, China, developed the Ehang 184, the world's first passenger drone. == History == Unmanned aerial vehicles were first introduced in World War 1, when Britain first developed the Aerial Target, an aircraft controlled remotely through radio signals. A year later in the United States, testing of Kettering Bug, a 12-foot long biplane attached with a bomb and that launched via a “slingshot-like rail”, was also under progress. Both of their unreliable test results and their possibility of endangering friendly troops in deployment caused neither aircraft to be used during the war. Production of UAVs continued after World War I and into World War II and the Vietnam War, where they would be invaluable in assisting with training as well as reconnaissance. Late 20th century also saw the proposition and development of unique methods of travel, including personal jetpacks and even flying cars. While the previously mentioned are not drones, they serve as a precursor and foundation for the passenger drones of today. The first passenger drone was unveiled on January 6 of 2016 at the international Consumer Electronics Show (CES) in Las Vegas. Produced by Ehang, a Chinese company based in Guangzhou, the 184 was a one passenger drone equipped with four propellers that could fly for approximately 23 minutes at a top speed of 63 mph. Since then, many new companies have entered the market, but none yet have been accessible by the public. == Technological development == Since 2013, improvements in designs to wing structures have contributed to the economic feasibility of passenger drones. New structural advancements, such as the flapping-wing propulsion system based on the mechanisms of birds’ wings, are more available as they have proven their capabilities in laboratory testing. As of September 29th, 2015, most market-ready drones are delivery drones with a carrying capacity limited to small packages - with a typical max capacity of under 5 pounds. However, while the technology exists for drones with larger carrying capacities, specifically those capable of carrying multiple humans, the execution of this technology is not yet market accessible. This capacity limit must be addressed for passenger drones; given current designs strive to carry a maximum of 5 people. However, some estimates believe that passengers drones could become a reality, specifically for paid transportation and emergency purposes, as early as 2026. With implementation of this technology, there could be significant effects on ground traffic including reducing gridlock in heavily congested areas and conserving up to 15% of the fuel currently used in heavy traffic patterns. However, extensive growth of the passenger drone market also risks clouding the low-altitude airspace and causing new safety risks. However, this concern is being addressed by recent advancements in the Internet of Drones (IoD) which links drones together to ensure appropriate pathing and reduce mid-air collisions. While this brings additional security issues, including maintaining reliable communication channels in the case of technological failure, researchers hope that this will help reduce crashes that can result in damage to passengers, buildings, and people in and around the airspace. == Notable companies == Ehang is a Chinese company that has developed numerous drones including passenger plane Ehang 184. EHang 184 was their first model, developed as an eight dual rotor wing blade drone that can carry two passengers. The model was retired in 2020 and is replaced by the Ehang 216. Ehang also released a one passenger drone, Ehang 116. Ehang in 2021 unveiled the model VT-30. VT-30 is designed to have eight dual rotor wing blades to complement its fixed wing platform. Flyastro, a Texas-based drone company, developed the Astro ALTA, with two and four person passenger models. The company is known for being the first to develop a solar-powered airplane. The development team initially began with the model, Elroy. It was a two passenger drone with similar design to the ALTA. Once flight was achieved, the model Astro ALTA began development. Joby Aviation is a California based company that has developed a five passenger drone, with one seat for the pilot. The company expects to complete its FAA certification process 2022. Joby in 2020 acquired a 75 million dollar investment from service provider Uber Technologies Inc., leading to Uber Elevate and Expands partnership. Archer Aviation is a California-based company that has developed a two passenger model called Maker. It has fixed wings with twelve rotor wings. Archer is developing five person model. United Airlines has partnered with Archer for commercial sale of the model, Maker. Maker is expected to be released within Los Angeles and Miami by 2024. CityAirbus is a drone project developed by Airbus, a European multinational aerospace company, based in the Netherlands. CityAirbus has developed a four- person passenger drone with fixed wings that include rotor wing blades. Its expected certification for public flight is in 2025. Boeing, an American multinational aviation corporation is developing a passenger drone model called the Passenger Air Vehicle (PAV). The model is a fixed wing with eight rotor blade wings attached onto a platform underneath the base structure. This model can hold two passengers and still is in development. Volocopter is a German aircraft manufacturer that is developing a passenger drone called Volocity. The model consist of eighteen rotor wings above the cockpit on a circular ring. Japan Airlines, an investor of Volocopter plans to have public test in Japan as early as 2023. == Future use == === Potential benefits === Passenger drones can greatly reduce the time for travel. As passenger drones flight paths are not restricted by conventional roads, the travel distance is shortened. Current ventures such as Joby Aviation, after acquiring Uber Air, plan to take advantage of this technology in the form of air taxis. Other potential benefits include the use of passenger drones by emergency services such as search and rescue missions and the delivery of life saving goods. Companies like Ehang have already begun using passenger drones as emergency vehicles as a response to the potential river collapses during the flood season in China. === Concerns === Passenger and air traffic safety remains at the forefront of concerns. Regulations for air traffic centered around passenger drones are still underway and would continue to develop with increasing use cases for passenger drones. Remote security threats on commercial drones such as Man-In-The-Middle (MITM) attack have also exposed the vulnerabilities in current drone systems. Among American adults, 54 percent say that they would feel unsafe flying inside a passenger drone. Passenger drones can be very noisy; a single passenger drone such as Joby Aviation’s all-electric vertical take-off and landing (“eVTOL”) aircraft has an estimated noise production of 70 decibels (dB), a noise level equating to “loud traffic”.

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  • Corpus manager

    Corpus manager

    A corpus manager (corpus browser or corpus query system) is a tool for multilingual corpus analysis, which allows effective searching in corpora. A corpus manager usually represents a complex tool that allows one to perform searches for language forms or sequences. It may provide information about the context or allow the user to search by positional attributes, such as lemma, tag, etc. These are called concordances. Other features include the ability to search for collocations, frequency statistics as well as metadata information about the processed text. The narrower meaning of corpus manager refers only to the server side or the corpus query engine, whereas the client side is simply called the user interface. A corpus manager can be software installed on a personal computer or it might be provided as a web service. == List of corpus managers == BNCweb – a web-based interface for the British National Corpus CQPweb - a web-based interface for the study of a large variety of corpora including the Spoken BNC2014 BYU-BNC – a website that allows searches of the British National Corpora and others created at Brigham Young University Coma – a tool extension of the system EXMARaLDA for working with oral corpora on a computer NoSketch Engine – a free open-source corpus management system combining Manatee (back-end) and Bonito (web interface) KonText – an extended and modified web interface to NoSketch Engine (a Bonito replacement) Sketch Engine – text corpus management and analysis software with more than 500 corpora in 90+ languages Spoco WordSmith Tools – a software package primarily for linguists

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  • Intelligent character recognition

    Intelligent character recognition

    Intelligent character recognition (ICR) is a method of extracting handwritten text from images. It is a more sophisticated type of OCR technology that recognizes different handwriting styles and fonts to intelligently interpret data from physical documents. ICR is used to organize paper-based unstructured data by scanning documents, extracting information, and adapting extracted data for database storage. ICR algorithms collaborate with OCR to automate data entry from forms by removing the need for keystrokes. It has a high degree of accuracy and is a dependable method for processing various handwritten media quickly. == Capabilities == Most ICR software has a self-learning neural network-based algorithms, which automatically update the recognition database for new handwriting patterns. It extends the usefulness of scanning devices for the purpose of document processing, from printed character recognition (a function of OCR) to hand-written matter recognition. Because this process is involved in recognizing hand writing, accuracy levels may, in some circumstances, not be very good but can achieve 97%+ accuracy rates in reading handwriting in structured forms. Often to achieve these high recognition rates several read engines are used within the software and each is given elective voting rights to determine the true reading of characters. In numeric fields, engines which are designed to read numbers take preference, while in alpha fields, engines designed to read hand written letters have higher elective rights. When used in conjunction with a bespoke interface hub, hand-written data can be automatically populated into a back office system avoiding laborious manual keying and can be more accurate than traditional human data entry. === Automated forms processing === An important development of ICR was the invention of automated forms processing in 1993 by Joseph Corcoran who was awarded a patent on the invention. This involved a three-stage process of capturing the image of the form to be processed by ICR and preparing it to enable the ICR engine to give best results, then capturing the information using the ICR engine and finally processing the results to automatically validate the output from the ICR engine. This application of ICR increased the usefulness of the technology and made it applicable for use with real world forms in normal business applications. Modern software applications use ICR as a technology of recognizing text in forms filled in by hand (hand-printed). == Differences between ICR and OCR == === OCR === Optical character recognition (OCR) is commonly considered to apply to any recognition technique that reads machine printed text. An example of a traditional OCR use case would be to translate the characters from an image of a printed document, such as a book page, newspaper clipping, or legal contract, into a separate file that could be searched and updated with a word processor or document viewer. It's also quite helpful for automating the processing of forms. Information can be swiftly extracted from form fields and entered into another application, like a spreadsheet or database, by zonally applying the OCR engine to those fields. Yet, data is typically manually input rather than typed into form fields. Character identification becomes even more challenging while reading handwritten material. The diversity of more than 700,000 printed font variants is tiny compared to the near unlimited variations in hand-printed characters. The recognition program must take into account not just stylistic differences but also the kind of writing implement used, the standard of the paper, errors, hand stability, and smudges or running ink. === ICR === Intelligent character recognition (ICR) makes use of continuously improving algorithms to collect more information about the variances in hand-printed characters and more precisely identify them. ICR, which was created in the early 1990s to aid in the automation of forms processing, enables the conversion of manually entered data into text that is simple to read, search for, and change. When used to read characters that are obviously divided into distinct areas or zones, such as fixed fields seen on many structured forms, it works best. Both OCR and ICR can be configured to read a variety of languages; however, limiting the expected character set to a smaller number of languages will produce better recognition outcomes. ICR cannot read cursive handwriting since it must still be able to assess each character individually. While writing in cursive, it might be difficult to tell where one character ends and another one begins, and there are more differences across samples than when hand-printing text. A more recent method called intelligent word recognition (IWR) focuses on reading a word in context rather than recognizing individual characters. == Intelligent word recognition == Intelligent word recognition (IWR) can recognize and extract not only printed-handwritten information, cursive handwriting as well. ICR recognizes on the character-level, whereas IWR works with full words or phrases. Capable of capturing unstructured information from every day pages, IWR is said to be more evolved than hand print ICR. Not meant to replace conventional ICR and OCR systems, IWR is optimized for processing real-world documents that contain mostly free-form, hard-to-recognize data fields that are inherently unsuitable for ICR. This means that the highest and best use of IWR is to eliminate a high percentage of the manual entry of handwritten data and run-on hand print fields on documents that otherwise could be keyed only by humans.

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  • AI Resume Builders Reviews: What Actually Works in 2026

    AI Resume Builders Reviews: What Actually Works in 2026

    Shopping for the best AI resume builder? An AI resume builder is software that uses machine learning to help you get more done — it keeps getting smarter as the underlying models improve. Pricing, accuracy, and the size of the model behind the tool are the three factors that most affect daily usefulness. Whether you are a beginner or a pro, the right AI resume builder slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.

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  • Tom's Planner

    Tom's Planner

    Tom's Planner is a web-based tool and application service provider for project planning, management and collaboration. == History == Tom's Planner is based on Curaçao. In November 2009, it announced its public beta launch on TechCrunch and moved out of beta in August 2010. In 2013 Tom's Planner acquired its competitor Gantto. == Software == Tom's Planner is project management software that enables the creation of project schedules (Gantt charts) using a visual perspective. Tom's Planner uses the Freemium Business Model. Users can register for a free account or choose a paid version. Tom's Planner is available in five languages and is used by thousands of users on a daily basis in more than 100 countries worldwide. Customers range from fortune 500 companies to small mom-and-pop shops. == Reviews == Tom's Planner has been reviewed by PC World, TechCrunch, Lifehacker, and several other periodicals.

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  • Danqi Chen

    Danqi Chen

    Danqi Chen (Chinese: 陈丹琦; pinyin: Chén Dānqí, IPA: [ʈ͡ʂʰə̌n tan t͡ɕʰǐ]; born in Changsha, China) is a Chinese computer scientist and assistant professor at Princeton University specializing in the AI field of natural language processing (NLP). In 2019, she joined the Princeton NLP group, alongside Sanjeev Arora, Christiane Fellbaum, and Karthik Narasimhan. She was previously a visiting scientist at Facebook AI Research (FAIR). She earned her Ph.D. at Stanford University and her BS from Tsinghua University. Chen is the author of Neural Reading Comprehension and Beyond, a dissertation on using artificial intelligence to access knowledge in ordinary and structured documents. She is the author or co-author of a number of journal articles, including Reading Wikipedia to Answer Open-Domain Questions. Google's SyntaxNet is based on algorithms developed by Danqi Chen and Christopher Manning at Stanford. Her primary research interests are in text understanding and knowledge representation and reasoning. She won a gold medal at the 2008 International Informatics Olympiad. She is known among friends as CDQ. A well known algorithm in competitive programming, CDQ Divide and Conquer, is named after this acronym. She is married to Huacheng Yu, an assistant professor in theoretical computer science at Princeton University.

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  • AI Blog Writers Reviews: What Actually Works in 2026

    AI Blog Writers Reviews: What Actually Works in 2026

    In search of the best AI blog writer? An AI blog writer is software that uses machine learning to help you get more done — it turns a rough idea into a polished result in seconds. When choosing one, weigh output quality, pricing, export formats, and how well it fits the tools you already use. Whether you are a beginner or a pro, the right AI blog writer slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.

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  • Is an AI Writing Assistant Worth It in 2026?

    Is an AI Writing Assistant Worth It in 2026?

    In search of the best AI writing assistant? An AI writing assistant is software that uses machine learning to help you get more done — it turns a rough idea into a polished result in seconds. When choosing one, weigh output quality, pricing, export formats, and how well it fits the tools you already use. Whether you are a beginner or a pro, the right AI writing assistant slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.

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  • The Cancer Imaging Archive

    The Cancer Imaging Archive

    The Cancer Imaging Archive (TCIA) is an open-access database of medical images for cancer research. The site is funded by the National Cancer Institute's (NCI) Cancer Imaging Program, and the contract is operated by the University of Arkansas for Medical Sciences. Data within the archive is organized into collections which typically share a common cancer type and/or anatomical site. The majority of the data consists of CT, MRI, and nuclear medicine (e.g. PET) images stored in DICOM format, but many other types of supporting data are also provided or linked to, in order to enhance research utility. All data are de-identified in order to comply with the Health Insurance Portability and Accountability Act and National Institutes of Health data sharing policies. TCIA resources are intended to support: Development of computer aided diagnosis methods (quantitative imaging) Evaluation of unbiased science reproducibility by acceptable standard statistical methods Research on correlation of clinical diagnostic medical images with digital microscopic histological images Exploratory biomarker research for which imaging is a key element Collaboration between cross-disciplinary investigators where imaging is crucial to research on tumor heterogeneity, between patients and within the tumor; tissue temporal response tracking - objective measurements of tumor progression; imaging genomics and Big Data linkages and analysis (clinical, histo-pathology, genomics) TCIA is recognized as a recommended repository for the Scientific Data, PLOS One, and F1000Research journals. It is also listed in the Registry of Research Data Repositories. == History == Prior to the creation of TCIA, the NCI funded development of the National Biomedical Imaging Archive. NBIA is an open-source Web application which was designed to allow the storage and query of DICOM images. TCIA was subsequently initiated in December 2010 to expand data sharing activities by funding a service component which would help address the technical and policy challenges associated with medical imaging research. TCIA leverages open-source tools such as NBIA and Clinical Trials Processor in order to provide its services. == Organization of the archive == The site content is organized into five categories: About Us - Provides a general overview of the site the organizations responsible for operating it. Share Your Data - Provides an overview of how to apply to upload data to the archive. Access the Archive - Provides information about the available data, methods for accessing that data and system usage metrics. Research Activities - Provides information about major research initiatives being conducted using TCIA data as well as information about publication guidelines. Help - Provides information about how to get support using the archive as well as documentation and data usage policies. == Methods for accessing data == Most collections on the Cancer Imaging Archive can be accessed without an account, but a few are restricted to specific users and therefore require an account to access them. TCIA has several ways to browse, filter, and download data. They include: Downloading the entire contents of a collection in bulk Leveraging the NBIA application to filter or search within or across collections Utilizing the RESTful Application programming interface to filter or search within or across collections === Browsing, bulk downloading and access to supporting data === The home page includes a list of all available collections. Basic information about the data such as the cancer type, cancer location, modalities, and number of subjects are also provided. Clicking on a collection name presents a page which describes the data including its original research purpose, how the data were generated, and how it might be useful to other TCIA users. For example, doi:10.7937/K9/TCIA.2015.L4FRET6Z describes the NSCLC-Radiomics-Genomics Collection. In the lower section of the page there are links to search or download the images and any available supporting data in the Data Access tab. Additional tabs provide information about data versions and how to cite the data if used in publications. Many collections contain additional data types such as genomics, patient demographics, treatment details, and expert analyses of the images. This data is usually only found by browsing the collection pages as opposed to searching in NBIA or using the API. === Filtering or searching with NBIA === On each Collection page and also in the main menu of the site there are links to "Search TCIA". This will load the NBIA application which allows simple, advanced and free text searches. Search results follow the conventional DICOM hierarchy of patient -> study -> series. TCIA provides comprehensive documentation on the various features of the NBIA software. === RESTful API === A number of search and download commands are also available through the API. New iterations on the API are released as new versions, so that existing applications developed against older versions of the API continue to function. == Research activities == A list of known publications based on TCIA data is maintained as a convenience to researchers who might want to investigate how it has been used previously. In addition to peer-reviewed publications there are also several major research initiatives described in the Research Activities section of the site. === The CIP TCGA Radiology Initiative for Radiogenomics Research === A large number of collections contain subjects which were analyzed as part of the NIH/NHGRI database known as The Cancer Genome Atlas (TCGA). This offers researchers the ability to correlate clinical images using shared unique identifiers each study that has in TCGA extensive genomic analysis, digital pathology slides and bulk download of individual demographic data and clinical data. A multi-institutional network of investigators volunteering their time is using the data to develop methods to determine prognosis or predict the response to therapy. TCGA collections are designated by nomenclature shared by the TCGA Data Portal (e.g.: TCGA-BRCA, TCGA-GBM, etc). They are subject to a special publication policy which is unique from the other public data on TCIA. === Challenge competitions === TCIA also provides specific data sets used for "Challenge" competitions such as international digital image-focused professional societies like MICCAI, SPIE, or ISBI. A directory of previous and upcoming challenges is maintained on the site. === Digital object identifiers === To facilitate data sharing, many publications encourage authors to include data citations to the data that the authors used in creating the results described in their scholarly papers. In addition, new journals are now available for describing data collections outright (e.g., Nature Scientific Data). TCIA assigns digital object identifiers (DOIs) to all collections when they are submitted, and also has the ability to create persistent identifiers linked to subsets of data held within TCIA that authors may use for data citations in their scholarly papers.

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  • The Best Free AI Paragraph Rewriter for Beginners

    The Best Free AI Paragraph Rewriter for Beginners

    Shopping for the best AI paragraph rewriter? An AI paragraph rewriter is software that uses machine learning to help you get more done — it keeps getting smarter as the underlying models improve. Pricing, accuracy, and the size of the model behind the tool are the three factors that most affect daily usefulness. Whether you are a beginner or a pro, the right AI paragraph rewriter slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.

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  • Best AI Sales Assistants in 2026

    Best AI Sales Assistants in 2026

    Shopping for the best AI sales assistant? An AI sales assistant is software that uses machine learning to help you get more done — it keeps getting smarter as the underlying models improve. Pricing, accuracy, and the size of the model behind the tool are the three factors that most affect daily usefulness. Whether you are a beginner or a pro, the right AI sales assistant slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.

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  • Comparison of machine translation applications

    Comparison of machine translation applications

    Machine translation is an algorithm which attempts to translate text or speech from one natural language to another. == General information == Basic general information for popular machine translation applications. == Languages features comparison == The following table compares the number of languages which the following machine translation programs can translate between. (Moses and Moses for Mere Mortals allow you to train translation models for any language pair, though collections of translated texts (parallel corpus) need to be provided by the user. The Moses site provides links to training corpora.) This is not an all-encompassing list. Some applications have many more language pairs than those listed below. This is a general comparison of key languages only. A full and accurate list of language pairs supported by each product should be found on each of the product's websites. === Multi-pair translations === === Paired translations ===

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  • Transcription software

    Transcription software

    Transcription software assists in the conversion of human speech into a text transcript. Audio or video files can be transcribed manually or automatically. Transcriptionists can replay a recording several times in a transcription editor and type what they hear. By using transcription hot keys, the manual transcription can be accelerated, the sound filtered, equalized or have the tempo adjusted when the clarity is not great. With speech recognition technology, transcriptionists can automatically convert recordings to text transcripts by opening recordings in a PC and uploading them to a cloud for automatic transcription, or transcribe recordings in real-time by using digital dictation. Depending on quality of recordings, machine generated transcripts may still need to be manually verified. The accuracy rate of the automatic transcription depends on several factors such as background noises, speakers' distance to the microphone, and accents. Transcription software, as with transcription services, is often used for business, legal, or medical purposes. Compared with audio content, a text transcript is searchable, takes up less computer memory, and can be used as an alternate method of communication, such as for subtitles and closed captions. Some clinical environments also use digital tools to support transcription workflows, including ambient documentation systems that employ Speech recognition to capture portions of clinical encounters and generate draft notes for later review. These tools are typically used alongside conventional transcription methods. The definition of transcription "software", as compared with transcription "service", is that the former is sufficiently automated that a user can run the entire system without engaging outside personnel. New software-as-a-service and cloud computing models use artificial intelligence, machine learning and natural language processing to convert speech to text and continuously learn new phrases and accents. AI transcription can, however, lead to hallucinations and other errors. == Development == Research at Google released a free android app Google Live Transcribe, it runs on Google Cloud. Google Chrome developed and has an available built in English Live Caption. Google Docs, Google Translate, Google Assistant, GBoard Google Text to Speech engine support transcription tool too. OpenAI launched Whisper, an open-source speech recognition deep learning model in September 2022. In 2024, an AI-powered transcription platform, Transkriptor, was launched, enabling the automatic conversion of audio and video recordings into text using speech recognition technology, with support for transcription in 100 languages and processing of content uploaded via a web interface as well as mobile and browser extensions. It is part of the Tor.app suite of AI-based language processing tools.

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  • Cobham's theorem

    Cobham's theorem

    Cobham's theorem is a theorem in combinatorics on words that has important connections with number theory, notably transcendental numbers, and automata theory. Informally, the theorem gives the condition for the members of a set S of natural numbers written in bases b1 and base b2 to be recognised by finite automata. Specifically, consider bases b1 and b2 such that they are not powers of the same integer. Cobham's theorem states that S written in bases b1 and b2 is recognised by finite automata if and only if S differs by a finite set from a finite union of arithmetic progressions. The theorem was proved by Alan Cobham in 1969 and has since given rise to many extensions and generalisations. == Definitions == Let n > 0 {\displaystyle n>0} be an integer. The representation of a natural number n {\textstyle n} in base b {\textstyle b} is the sequence of digits n 0 n 1 ⋯ n h {\displaystyle n_{0}n_{1}\cdots n_{h}} such that n = n 0 + n 1 b + ⋯ + n h b h {\displaystyle n=n_{0}+n_{1}b+\cdots +n_{h}b^{h}} where 0 ≤ n 0 , n 1 , … , n h < b {\displaystyle 0\leq n_{0},n_{1},\ldots ,n_{h} 0 {\displaystyle n_{h}>0} . The word n 0 n 1 ⋯ n h {\displaystyle n_{0}n_{1}\cdots n_{h}} is often denoted ⟨ n ⟩ b {\displaystyle \langle n\rangle _{b}} , or more simply, n b {\displaystyle n_{b}} . A set of natural numbers S is recognisable in base b {\textstyle b} or more simply b {\textstyle b} -recognisable or b {\textstyle b} -automatic if the set { n b ∣ n ∈ S } {\displaystyle \{n_{b}\mid n\in S\}} of the representations of its elements in base b {\displaystyle b} is a language recognisable by a finite automaton on the alphabet { 0 , 1 , … , b − 1 } {\displaystyle \{0,1,\ldots ,b-1\}} . Two positive integers k {\displaystyle k} and ℓ {\displaystyle \ell } are multiplicatively independent if there are no non-negative integers p {\displaystyle p} and q {\displaystyle q} such that k p = ℓ q {\displaystyle k^{p}=\ell ^{q}} . For example, 2 and 3 are multiplicatively independent, but 8 and 16 are not since 8 4 = 16 3 {\displaystyle 8^{4}=16^{3}} . Two integers are multiplicatively dependent if and only if they are powers of a same third integer. == Problem statements == === Original problem statement === More equivalent statements of the theorem have been given. The original version by Cobham is the following: Another way to state the theorem is by using automatic sequences. Cobham himself calls them "uniform tag sequences." The following form is found in Allouche and Shallit's book:We can show that the characteristic sequence of a set of natural numbers S recognisable by finite automata in base k is a k-automatic sequence and that conversely, for all k-automatic sequences u {\displaystyle u} and all integers 0 ≤ i < k {\displaystyle 0\leq i 1 {\displaystyle \alpha >1} is the dominant eigenvalue of the matrix of morphism f {\displaystyle f} , namely, the matrix M ( f ) = ( m x , y ) x ∈ B , y ∈ A {\displaystyle M(f)=(m_{x,y})_{x\in B,y\in A}} , where m x , y {\displaystyle m_{x,y}} is the number of occurrences of the letter x {\displaystyle x} in the word f ( y ) {\displaystyle f(y)} . A set S of natural numbers is α {\displaystyle \alpha } -recognisable if its characteristic sequence s {\displaystyle s} is α {\displaystyle \alpha } -substitutive. A last definition: a Perron number is an algebraic number z > 1 {\displaystyle z>1} such that all its conjugates belong to the disc { z ′ ∈ C , | z ′ | < z } {\displaystyle \{z'\in \mathbb {C} ,|z'| Read more →

  • Marius Lindauer

    Marius Lindauer

    Marius Lindauer (born December 25, 1985, in Berlin, Germany) is a German computer scientist and professor of machine learning at the institute of artificial intelligence of the Leibniz University Hannover. He is known for his research on Automated Machine Learning and other meta-algorithmic approaches. == Life == Marius Lindauer studied computer science at the University of Potsdam from 2005 to 2010. Under the supervision of Torsten Schaub and Holger Hoos, he received his Dr. rer. nat. at the University of Potsdam in 2015. In 2014, he joined the Machine Learning research lab led by Frank Hutter as the first postdoctoral researcher and helped to build up the group. He then joined the Leibniz University Hannover as a professor in 2019 to lead the Machine learning research lab. He founded the Institute of Artificial Intelligence at the Leibniz University Hannover in 2022. Additionally, he is the co-head of the automl.org research group, automl.space community effort, and co-founder of the COSEAL research network, where he currently serves as an advisory board member. He is also a supporting member of CLAIRE, and a member of ELLIS. His research is published in renowned journals and conferences. == Achievements == During his Ph.D., Marius won several international competitions in the fields of solving hard combinatorial optimization problems, including 1st place in the NP-track of the answer set programming competition 2011 with claspfolio, the Hard Combinatorial SAT+UNSAT of the SAT challenge 2012 with clasp-crafted and two tracks of the configurable SAT solver challenge 2013 with clasp-cssc. During his PostDoc and later on, he was involved in winning tracks of the first and second AutoML challenge with auto-sklearn and the black-box optimization challenge for machine learning at NeurIPS'20. == Research Directions == Marius has delved into many research topics, all of which are unified under the umbrella of automating parts of the Machine Learning pipeline. His research touches many different aspects: Hyperparameter Optimization Multi-Fidelity Optimization Automated Reinforcement Learning Interactive AutoML Green AutoML Explainable AutoML

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