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'|

RFinder

RFinder ("repeater finder") is a subscription-based website and mobile app. RFinder's main service is the World Wide Repeater Directory (WWRD), which is a directory of amateur radio repeaters. RFinder is the official repeater directory of several amateur radio associations. RFinder has listings for several amateur radio modes, including FM, D-STAR, DMR, and ATV. == World Wide Repeater Directory == Repeaters are listed in the directory along with its call sign, Maidenhead Locator System and GPS coordinates, transmit/receive offset ("split"), CTCSS and DCS squelch settings, and VoIP settings (IRLP and Echolink nodes). The directory has over 50,000 repeater listings in over 170 countries. === Website === The RFinder website has several search options including for routes. === Forums === RFinder user forums is for help and support for the app and hardware. === Mobile app === RFinder has mobile apps for Android and iOS. When using the mobile app, RFinder can display the distance to repeaters, based on the mobile device's current location. === ARRL Repeater Directory === The ARRL publishes the ARRL Repeater Directory which contains over 31,000 repeater listings for the US and Canada with listings provided by RFinder. == Subscription == RFinder requires a subscription. A one-year subscription is US$12.99. == Radio programming software == Some radio programming software applications can query RFinder and download repeater listing to program radios. Compatible software includes: CHIRP RT Systems == Radio associations == RFinder is the official repeater directory of the following associations: Amateur Radio Society Italy American Radio Relay League Cayman Amateur Radio Society Deutscher Amateur Radio Club Federacion Mexicana de Radio Experimentadores L’association Réseau des Émetteurs Français Lietuvos Radijo Mėgėjų Draugija Liga de Amadores Brasilieros de Radio Emissão Radio Amateurs of Canada Radio Society of Great Britain Rede dos Emissores Portugueses Unión de Radioaficionados Españoles

Data thinking

Data Thinking is a framework that integrates data science with the design process. It combines computational thinking, statistical thinking, and domain-specific knowledge to guide the development of data-driven solutions in product development. The framework is used to explore, design, develop, and validate solutions, with a focus on user experience and data analytics, including data collection and interpretation The framework aims to apply data literacy and inform decision-making through data-driven insights. == Major components == According to "Computational thinking in the era of data science": Data thinking involves understanding that solutions require both data-driven and domain-knowledge-driven rules. Data thinking evaluates whether data accurately represents real-life scenarios and improves data collection where necessary. The framework highlights the importance of preserving domain-specific meaning during data analysis. Data thinking incorporates statistical and logical analysis to identify patterns and irregularities. Data thinking involves testing solutions in real-life contexts and iteratively improving models based on new data. The process requires evaluating problems from multiple abstraction levels and understanding the potential for biases in generalizations. == Major phases == === Strategic context and risk analysis === Analyzing the broader digital strategy and assessing risks and opportunities is a common step before beginning a project. Techniques like coolhunting, trend analysis, and scenario planning can be used to assist with this. === Ideation and exploration === In this phase, focus areas are identified, and use cases are developed by integrating organizational goals, user needs, and data requirements. Design thinking methods, such as personas and customer journey mapping, are applied. === Prototyping === A proof of concept is created to test feasibility and refine solutions through iterative evaluation to optimize for effective performance. === Implementation and monitoring === Solutions are tested and monitored for performance and continual improvement. == Implementing Data Thinking == The following resources explain more about data thinking and its applications: "Data Thinking: Framework for data-based solutions" by StackFuel "What is Data Thinking? A modern approach to designing a data strategy" by Mantel Group "Data Science Thinking" by SpringerLink These sources provide detailed insights into the methodology, phases, and benefits of adopting Data Thinking in organizational processes.

Embedded analytics

Embedded analytics enables organisations to integrate analytics capabilities into their own, often software as a service, applications, portals, or websites. This differs from embedded software and web analytics (also commonly known as product analytics). This integration typically provides contextual insights, quickly, easily and conveniently accessible since these insights should be present on the web page right next to the other, operational, parts of the host application. Insights are provided through interactive data visualisations, such as charts, diagrams, filters, gauges, maps and tables often in combination as dashboards embedded within the system. This setup enables easier, in-depth data analysis without the need to switch and log in between multiple applications. Embedded analytics is also known as customer facing analytics. Embedded analytics is the integration of analytic capabilities into a host, typically browser-based, business-to-business, software as a service, application. These analytic capabilities would typically be relevant and contextual to the use-case of the host application. == History == The term "embedded analytics" was first used by Howard Dresner: consultant, author, former Gartner analyst and inventor of the term "business intelligence" said Howard Dresner while he was working for Hyperion Solutions, a company that Oracle bought in 2007. Oracle started then to use the term "embedded analytics" at their press release for Oracle Rapid Planning on 2009 . == Considerations with embedded analytics == When evaluating embedding analytics, consideration would normally be given to integration at various levels, these would likely include: security integration, data integration, application logic integration, business rules integration, and user experience integration. This is in contrast to traditional BI, which expects users to leave their workflow applications to look at data insights in a separate set of tools. This immediacy makes embedded analytics much more intuitive and likely to be valued by users. A December 2016 report from Nucleus Research found that using BI tools, which require toggling between applications, can take up as much as 1–2 hours of an employee's time each week, whereas embedded analytics eliminate the need to toggle between apps.

Social media as a news source

Social media as a news source is defined as the use of online social media platforms such as Instagram, TikTok, and Facebook rather than the use of traditional media platforms like the newspaper or live TV to obtain news. Television had just begun to turn a nation of people who once listened to media content into watchers of media content between the 1950s and the 1980s when the popularity of social media had also begun creating a nation of media content creators. Almost half of Americans use social media as a news source, according to the Pew Research Center. As social media's role in news consumption grows, questions have emerged about its impact on knowledge, the formation of echo chambers, and the effectiveness of fact-checking efforts in combating misinformation. Social media platforms allow user-generated content and sharing content within one's own virtual network. Using social media as a news source allows users to engage with news in a variety of ways including: Consuming and discovering news Sharing or reposting news Posting one's own photos, videos, or reports of news (i.e., engage in citizen or participatory journalism) Commenting on news posts Using social media as a news source has become an increasingly popular way for people of all age groups to obtain current and important information. Just like many other new forms of technology there are going to be pros and cons. There are ways that social media positively affects the world of news and journalism but it is important to acknowledge that there are also ways in which social media has a negative effect on the news. With this accessibility, people now have more ways to consume false news, biased news, and even disturbing content. In 2019, the Pew Research Center created a poll that reported Americans are wary about the ways that social media sites share news and certain content. This wariness of accuracy grew as awareness that social media sites could be exploited by bad actors who concoct false narratives and fake news. == Relationship to traditional news sources == Unlike traditional news platforms such as newspapers and news shows, social media platforms allow people without professional journalistic backgrounds to create news and cover events that news agencies might not cover. Social media users may read a set of news that differs slightly from what newspaper editors prioritize in the print press. A 2019 study found that Facebook and Twitter users are more likely to share politics, public affairs, and visual media news. Typically social media users circulate more towards posting about negative news. A study of tweets found that while optimistic-sounding and neutral-sounding tweets were equally likely to express certainty or uncertainty, the pessimistic tweets were nearly twice as likely to appear certain of an outcome than uncertain. These results could imply that posts of a more pessimistic nature that are also written with an air of certainty are more likely to be shared or otherwise permeate groups on Twitter. A similar bias towards negativity has developed on Facebook, where internal memos revealed that an algorithm built to promote "meaningful social interaction" actually incentivized publishers to promote negative and sensational news. Biases towards negativity need to be considered when the utility of new media is addressed, as the potential for human opinion to overemphasize any particular news story is greater despite general improvement. In order to compete in this rapidly changing technological environment, there has been an upheaval of traditional news sources onto online spaces. The production and circulation of newspaper prints have continued to globally decline in accordance with the increasing presence of news outlets on social media. Prominent platforms such as Twitter and Facebook have been key in engaging users through the integration of journalistic news into their newsfeeds. This feature has now become a foundational part of these apps' interfaces. Social media incentivizes both legacy news brands and individual professional journalists to share their reporting and interact with audiences on social platforms to boost engagement. However, most people who consume news on social media report that accessing news is not their main motivation for being on social media, but rather, they see and consume news incidentally. Nonetheless, informational interviews reveal that these consumers rely on being informed through social media. Some news consumers attest that a news brand's participation in social media does not improve their trust in the brand and that more in-depth reporting and more transparency about biases would improve trust instead. == Use as a news source == Globally, data from 2020 shows that over 70% of adult participants from Kenya, South Africa, Chile, Bulgaria, Greece, and Argentina utilized social media for news while those from France, the UK, the Netherlands, Germany, and Japan were reportedly less than 40 percent. According to the Pew Research Center, 20% of adults in the United States in 2018 said they get their news from social media "often," compared to 16% who said they often get news from print newspapers, 26% who often get it from the radio, 33% who often get it from news websites, and 49% who often get it from TV. The same survey found that social media was the most popular way for American adults age 18–29 to get news, the second-to-last most popular way for Americans age 20–49 to get news, and the least popular way for American adults age 50-64 and 65+ to get the news. In 2019, the Pew Research Center found that over half of Americans (54%) either got their news "sometimes" or "often" from social media, and Facebook was the most popular social media site where American adults got their news. However, at least 50% off all respondents reported that the following were either a "very big problem" or a "moderately big problem" for getting news on social media: One-sided news (83%) Inaccurate news (81%) Censorship of the news (69%) Uncivil discussions about the news (69%) Harassment of journalists (57%) News organizations or personalities being banned (53%) Violent or disturbing news images or videos (51%) In a later survey from the same year, the Pew Research Center reported that 18% of American adults reported that the most common way they get news about politics and the election was from social media. Additional source information shows that from politics and the United States presidential election in 2016, the popularity of fake news had grown to global attention. With this information, the study explains that more than 60 percent of adults receive their news from social media, the most popular being Facebook. With the increase of fake news, and the large amount of adult participation on these social media sites, it made it much harder for those who were searching for news to find a source that they could find credible. Another study found that adult participants found their own friends on Facebook to be a more reliable source of information online compared to a professional news organization. Although, when news was posted by a news organization online, they were then found more reliable compared to when they are shared by their online friends. Showing that adult participants found that the news that was only posted on Facebook and social media was much more credible to them than compared to other forms of information spreading. The study further states that these outcomes have the potential explanation that the topic of the news article played a part in the ways they were affected. This could have affected the way adult participants interacted with the different news sources, such as their online friends compared to a news organization, prominently because depending on the story, they want to have the correct information about the news from the most credible source. === By young people === Social media platforms are some of the most easily accessible forms of news and with the growing generations, the technology is only going to grow. With that, the use of social media in younger generations is also going to grow alongside it. Technology in the hands of young kids can be a concern moving into the future. Globally, there is evidence that through social media, youth have become more directly involved in protests, social campaigns and generally, in the sharing of news across multiple platforms. The number of people who use social media platforms such as Twitter, Facebook, Instagram, or Snapchat as ways to seek information has increased significantly in recent years especially for people who are part of the younger generation.TikTok is a rapidly expanding platform that young adults can use to find news content on social media. TikTok is one of the sites that young adults and teens utilize to get news about trending themes and controversial topics. The younger generation accepts without hesitation the information that thei

Tertiary review

In software engineering, a tertiary review is a systematic review of systematic reviews. It is also referred to as a tertiary study in the software engineering literature. However, Umbrella review is the term more commonly used in medicine. Kitchenham et al. suggest that methodologically there is no difference between a systematic review and a tertiary review. However, as the software engineering community has started performing tertiary reviews new concerns unique to tertiary reviews have surfaced. These include the challenge of quality assessment of systematic reviews, search validation and the additional risk of double counting. == Examples of Tertiary reviews in software engineering literature == Test quality Machine Learning Test-driven development

IEBus

IEBus (Inter Equipment Bus) is a communication bus specification "between equipments within a vehicle or a chassis" of Renesas Electronics. It defines OSI model layer 1 and layer 2 specification. IEBus is mainly used for car audio and car navigations, which established de facto standard in Japan, though SAE J1850 is major in United States. IEBus is also used in some vending machines, which major customer is Fuji Electric. Each button on the vending machine has an IEBus ID, i.e. has a controller. Detailed specification is disclosed to licensees only, but protocol analyzers are provided from some test equipment vendors. Its modulation method is PWM (Pulse-Width Modulation) with 6.00 MHz base clock originally, but most of automotive customers use 6.291 MHz, and physical layer is a pair of differential signalling harness. Its physical layer adopts half-duplex, asynchronous, and multi-master communication with carrier-sense multiple access with collision detection (CSMA/CD) for medium access control. It allows for up to fifty units on one bus over a maximum length of 150 meters. Two differential signalling lines are used with Bus+ / Bus− naming, sometimes labeled as Data(+) / Data(−). It is sometimes described as "IE-BUS", "IE-Bus," or "IE Bus," but these are incorrect. In formal, it is "IEBus." IEBus® and Inter Equipment Bus® are registered trademark symbols of Renesas Electronics Corporation, formerly NEC Electronics Corporation, (JPO: Reg. No.2552418 and 2552419, respectively). == History == In the middle of '80s, semiconductor unit of NEC Corporation, currently Renesas Electronics, started the study for increasing demands for automotive audio systems. IEBus is introduced as a solution for the distributed control system. In the late 1980s, several similar specifications, including the Domestic Digital Bus (D2B), the Japanese Home Bus (HBS), and the European Home System (EHS) are proposed by different companies or organizations. These were once discussed as IEC 61030, but it was withdrawn in 2006. IEBus is also a similar specification (refer to "Transfer signal format" section), but not listed in these criteria. As the result, IEBus becomes a de facto standard of car audio in Japan. Regarding the Domestic Digital Bus (D2B), it is re-defined as D2B Optical by Mercedes-Benz independently. As for Japanese Home Bus System (HBS), it is defined in 1988 as Home Bus System Standard Specification, ET-2101 by JEITA and REEA (Radio Engineering & Electronics Assiation) in Japan. It is being used by several Japanese air conditioner manufacturers (for example, M-Net from Mitsubishi and the P1/P2 or F1/F2 bus from Daikin). Fujitsu provided HBPC (Home Bus Protocol Controller) chip as MB86046B. But it is unclear whether Fujitsu (currently, Cypress) still manufactures this HBPC LSI as of 2018. Mitsumi Electric provides the MM1007 and MM1192 driver ICs for HBS. The HBS specification is also discussed in the Echonet Consortium. In 2014, a utility model patent for protocol converter from HBS to RS-485 is granted in China as "CN204006496U." Regarding the replacement of IEBus, a paper by Hyundai Autonet, currently Hyundai Mobis, describes as follows. "In communication methods for digital input capable amplifiers, Inter Equipment Bus (IEBus) was used in early times, but for now, Controller Area Network (CAN) is mainly used." == Protocol overview == A master talks to a slave. Each unit has a master and a slave address register. Only one device can talk on the bus at any given time. There is a pecking order for the types of communications which will take precedence over another. Each communication from master to slave must be replied to by the slave going back to the master with acknowledge bits each of those show ACK or NAK. If the master does not receive the ACK within a predefined time allowance for a mode, it drops the communication and returns to its standby (listen) mode. Detailed specification of OSI model layer 2 is disclosed to licensees only, but protocol analyzers are provided from some test equipment vendors. In 2012, one of Chinese manufacturer's patent is granted as "CN202841169U". An open-source software emulator called "IEBus Studio" exists on a repository of SourceForge, but the last update was on 2008-02-24. Another open-source analyzer software called "IEBusAnalyzer" is available on GitHub repository. Some hobbyist made some tools also. === Physical layer (OSI model layer 1) specification overview === From μPD6708 data sheet. and μPD78098B Subseries user's manual, hardware. Communication system Half-duplex asynchronous communication Multi-master system All the units connected to the IEBus can transfer data to the other units. Broadcast communication function (communication between one unit and multiple units) Normally, communication is individually carried out from one unit to another. By using the broadcast communication function, however, communication can be executed from one unit to plural units as follows: Group broadcast communication: Broadcast communication to group units Simultaneous broadcast communication: Broadcast communication to all units Effective transmission rate The effective transmission rate can be selected from the following three communication modes: Mixture of the plural of modes in the same bus line is not allowed. Correct communication between different base clock is not possible. Access control CSMA/CD (Carrier Sense Multiple Access with Collision Detection) The priority of occupying IEBus is as follows: «1» Broadcast communication takes precedence over individual communication. «2» The lower the master address, the higher the priority. Communication scale Number of units: 50 MAX. Cable length: 150 m MAX. (when a twisted pair cable is used) Load capacity: MAX. 8000 pF; between Bus+ and Bus−, (6.000000 MHz base clock) MAX. 7100 pF; between Bus+ and Bus−, (6.291456 MHz base clock) Terminating resistor: 120 Ω Logic level Logic 1: Low level. Voltage difference between Bus+ and Bus− is under 20mV Logic 0: High Level. Voltage difference between Bus+ and Bus− is over 120mV In-phase input voltage high: Bus+ ≤ (VDD-1.0) V, Bus− ≥ 1.0 V === Transfer signal format === From μPD6708 data sheet. and μPD78098B Subseries user's manual, hardware. This frame format is much similar to that of Domestic Digital Bus (D2B). All fields are MSB first. ==== Functions of Control bits ==== === Bit format === Each IEBus bit consists of four periods. Preparation period: The first or subsequent low-level (logic "1") period Synchronization period: Next high-level (logic "0") period Data period: Period indicating value of bit; ether low-level (logic "1") or high-level (logic "0") Stop period: The last low-level (logic "1") period Synchronization is done by each bit. Time lengths of the synchronization period and data period are almost the same. The time of the entire bits' and each bit's specification, related to the time of each period allocated to it, differ depending both on the type of the transmit bit and on whether the unit is the master or a slave unit. == Automotive manufacturers using IEBus == Each manufacturer has its own name, but it is not an alias of IEBus. Those are specifications of wire harness which comprise control cables based on IEBus, OSI model layer 3 and above communication protocol, audio cables, interconnection couplers, and so on. === Pioneer === Pioneer Corporation employed IEBus for its original branded car audio in early '90s. In its earlier stage, it was used just for control bus between the head unit in dashboard and the CD changer usually placed in trunk room. Nowadays, the specification includes connection between head units, navigation systems, rear speaker systems, and so on. IP-Bus: Wire harness specification. === Toyota === Pioneer Corporation pushed Toyota Motor Corporation to adopt IEBus as the genuine parts. In 1994, Toyota decided to employ IEBus for its genuine specification, but it is slightly different from that of Pioneer. It is named as AVC-LAN. AVC-LAN: Wire harness specification, based on mode 2. === Honda/Acura === Pioneer Corporation also pushed Honda Motor. Honda also decided to adopt IEBus as its genuine parts specification just after Toyota do so. GA-NET II: Wire harness specification. Honda Music Link: Honda genuine gadget to connect Apple Inc. products. A hobbyist made touch screen controller on Acura TSX for a Car PC installed in the trunk. === Sirius XM Satellite Radio === Sirius XM Satellite Radio is a satellite broadcasting radio operator in US. Its digital media receiver equipment utilizes IEBus. == Evaluation boards == === SAKURA board === GR-SAKUKRA board and GR-SAKURA-FULL board are Renesas official promotion boards of RX63N chip, which enables IEBus mode 0 and 1, but not mode 2, i.e. not available for Toyota AVC-LAN. They are an Arduino pin compatible low-price ones, suitable for hobbyists. Their color of printed circuit board is SAKURA in Japanese, which means cherry blossom. To e