Human rights and encryption refers to the ways in which digital encryption affects human rights. Encryption can be used as both a detriment and a boon to human rights; for example, encryption can be used to enforce digital rights management for video games. This kind of video game licensing can render software unusable long term and represents the erosion of consumer rights. At the same time, encryption is fundamental part of internet security. Asymmetrical encryption is used extensively online for authentication, providing users confidence their internet traffic is not being misdirected. Encryption is also used to obfuscate information as it travels from end-to-end over the internet, preventing eavesdropping and tampering. Encryption can also provide anonymity, which is an important consideration for freedom of expression. Despite its drawbacks, encryption is essential for a free, open, and trustworthy internet. == Background == === Human rights === Human rights are moral principles or norms for human behaviour that are regularly protected as legal rights in national and international law. They are commonly understood as inalienable, fundamental rights "to which a person is inherently entitled simply because they are a human being". Those rights are "inherent in all human beings" regardless of their nationality, location, language, religion, ethnic origin, or any other status. They are applicable everywhere and at every time and are universal and egalitarian. === Cryptography === Cryptography is a long-standing subfield of both mathematics and computer science. It can generally be defined as "the protection of information and computation using mathematical techniques." Encryption and cryptography are closely interlinked, although "cryptography" has a broader meaning. For example, a digital signature is "cryptography", but not technically "encryption". == Overview == Under international human rights law, freedom of expression is recognized as a human right under Article 19 of the Universal Declaration of Human Rights (UDHR) and the International Covenant on Civil and Political Rights (ICCPR). In Article 19 of the UDHR states that "everyone shall have the right to hold opinions without interference" and "everyone shall have the right to freedom of expression; this right shall include freedom to seek, receive and impart information and ideas of all kinds, regardless of frontiers, either orally, in writing or in print, in the form of art, or through any other media of his choice". Since the 1970s, the availability of digital computing and the invention of public-key cryptography have made encryption more widely available. (Previously, encryption techniques were the domain of nation-state actors.) Cryptographic techniques are also used to protect the anonymity of communicating actors and privacy more generally. The availability and use of encryption continue to lead to complex, important, and highly contentious legal policy debates. Some government agencies have made statements or proposals to lessen such usage and deployment due to hurdles it presents for government access. The rise of commercial end-to-end encryption services have pushed towards more debates around the use of encryption and the legal status of cryptography in general. Encryption, as defined above, is a set of cryptographic techniques to protect information. The normative value of encryption, however, is not fixed but varies with the type and purpose of the cryptographic methods used. Traditionally, encryption (cipher) techniques were used to ensure the confidentiality of communications and prevent access to information and communications by others and intended recipients. Cryptography can also ensure the authenticity of communicating parties and the integrity of communications contents, providing a key ingredient for enabling trust in the digital environment. There is a growing awareness within human rights organizations that encryption plays an important role in realizing a free, open, and trustworthy Internet. UN Special Rapporteur on the promotion and protection of the right to freedom of opinion and expression David Kaye observed, during the Human Rights Council in June 2015, that encryption and anonymity deserve a protected status under the rights to privacy and freedom of expression: "Encryption and anonymity, today's leading vehicles for online security, provide individuals with a means to protect their privacy, empowering them to browse, read, develop and share opinions and information without interference and enabling journalists, civil society organizations, members of ethnic or religious groups, those persecuted because of their sexual orientation or gender identity, activists, scholars, artists and others to exercise the rights to freedom of opinion and expression." == Encryption in media and communication == In the context of media and communication, two types of encryption in media and communication can be distinguished: It could be used as a result of the choice of a service provider or deployed by Internet users. Client-side encryption tools and technologies are relevant for marginalized communities, journalists and other online media actors practicing journalism as a way of protecting their rights. It could prevent unauthorized third party access, but the service provider implementing it would still have access to the relevant user data. End-to-end encryption is an encryption technique that refers to encryption that also prevents service providers themselves from having access to the user's communications. The implementation of these forms of encryption has sparked the most debate since the start of the 21st century. === Service providers deployed techniques to prevent unauthorized third-party access. === Among the most widely deployed cryptographic techniques is the securitization of communications channel between internet users and specific service providers from man-in-the-middle attacks, access by unauthorized third parties. Given the breadth of nuances involved, these cryptographic techniques must be run jointly by both the service user and the service provider in order to work properly. They require service providers, including online news publisher(s) or social network(s), to actively implement them into service design. Users cannot deploy these techniques unilaterally; their deployment is contingent on active participation by the service provider. The TLS protocol, which becomes visible to the normal internet user through the HTTPS header, is widely used for securing online commerce, e-government services and health applications as well as devices that make up networked infrastructures, e.g., routers, cameras. However, although the standard has been around since 1990, the wider spread and evolution of the technology has been slow. As with other cryptographic methods and protocols, the practical challenges related to proper, secure and (wider) deployment are significant and have to be considered. Many service providers still do not implement TLS or do not implement it well. In the context of wireless communications, the use of cryptographic techniques that protect communications from third parties are also important. Different standards have been developed to protect wireless communications: 2G, 3G and 4G standards for communication between mobile phones, base stations and base stations controllers; standards to protect communications between mobile devices and wireless routers ('WLAN'); and standards for local computer networks. One common weakness in these designs is that the transmission points of the wireless communication can access all communications e.g., the telecommunications provider. This vulnerability is exacerbated when wireless protocols only authenticate user devices, but not the wireless access point. Whether the data is stored on a device, or on a local server as in the cloud, there is also a distinction between 'at rest'. Given the vulnerability of cellphones to theft for instance, particular attention may be given to limiting service provided access. This does not exclude the situation that the service provider discloses this information to third parties like other commercial entities or governments. The user needs to trust the service provider to act in their interests. The possibility that a service provider is legally compelled to hand over user information or to interfere with particular communications with particular users, remains. === Privacy-enhancing Technologies === There are services that specifically market themselves with claims not to have access to the content of their users' communication. Service Providers can also take measures that restrict their ability to access information and communication, further increasing the protection of users against access to their information and communications. The integrity of these Privacy Enhancing Technologies (PETs), depends on delicate design decisions as well as the
FMLLR
In signal processing, Feature space Maximum Likelihood Linear Regression (fMLLR) is a global feature transform that are typically applied in a speaker adaptive way, where fMLLR transforms acoustic features to speaker adapted features by a multiplication operation with a transformation matrix. In some literature, fMLLR is also known as the Constrained Maximum Likelihood Linear Regression (cMLLR). == Overview == fMLLR transformations are trained in a maximum likelihood sense on adaptation data. These transformations may be estimated in many ways, but only maximum likelihood (ML) estimation is considered in fMLLR. The fMLLR transformation is trained on a particular set of adaptation data, such that it maximizes the likelihood of that adaptation data given a current model-set. This technique is a widely used approach for speaker adaptation in HMM-based speech recognition. Later research also shows that fMLLR is an excellent acoustic feature for DNN/HMM hybrid speech recognition models. The advantage of fMLLR includes the following: the adaptation process can be performed within a pre-processing phase, and is independent of the ASR training and decoding process. this type of adapted feature can be applied to deep neural networks (DNN) to replace traditionally used mel-spectrogram in end-to-end speech recognition models. fMLLR's speaker adaptation process leads to a significant performance boost for ASR models, hence outperforming other transform or features like MFCCs (Mel-Frequency Cepstral Coefficients) and FBANKs (Filter bank) coefficients. fMLLR features can be efficiently realized with speech toolkits like Kaldi. Major problem and disadvantage of fMLLR: when the amount of adaptation data is limited, the transformation matrices tends to easily overfit the given data. == Computing fMLLR transform == Feature transform of fMLLR can be easily computed with the open source speech tool Kaldi, the Kaldi script uses the standard estimation scheme described in Appendix B of the original paper, in particular the section Appendix B.1 "Direct method over rows". In the Kaldi formulation, fMLLR is an affine feature transform of the form x {\displaystyle x} → A {\displaystyle A} x {\displaystyle x} + b {\displaystyle +b} , which can be written in the form x {\displaystyle x} →W x ^ {\displaystyle {\hat {x}}} , where x ^ {\displaystyle {\hat {x}}} = [ x 1 ] {\displaystyle {\begin{bmatrix}x\\1\end{bmatrix}}} is the acoustic feature x {\displaystyle x} with a 1 appended. Note that this differs from some of the literature where the 1 comes first as x ^ {\displaystyle {\hat {x}}} = [ 1 x ] {\displaystyle {\begin{bmatrix}1\\x\end{bmatrix}}} . The sufficient statistics stored are: K = ∑ t , j , m γ j , m ( t ) Σ j m − 1 μ j m x ( t ) + {\displaystyle K=\sum _{t,j,m}\gamma _{j,m}(t)\textstyle \Sigma _{jm}^{-1}\mu _{jm}x(t)^{+}\displaystyle } where Σ j m − 1 {\displaystyle \textstyle \Sigma _{jm}^{-1}\displaystyle } is the inverse co-variance matrix. And for 0 ≤ i ≤ D {\displaystyle 0\leq i\leq D} where D {\displaystyle D} is the feature dimension: G ( i ) = ∑ t , j , m γ j , m ( t ) ( 1 σ j , m 2 ( i ) ) x ( t ) + x ( t ) + T {\displaystyle G^{(i)}=\sum _{t,j,m}\gamma _{j,m}(t)\left({\frac {1}{\sigma _{j,m}^{2}(i)}}\right)x(t)^{+}x(t)^{+T}\displaystyle } For a thorough review that explains fMLLR and the commonly used estimation techniques, see the original paper "Maximum likelihood linear transformations for HMM-based speech recognition ". Note that the Kaldi script that performs the feature transforms of fMLLR differs with by using a column of the inverse in place of the cofactor row. In other words, the factor of the determinant is ignored, as it does not affect the transform result and can causes potential danger of numerical underflow or overflow. == Comparing with other features or transforms == Experiment result shows that by using the fMLLR feature in speech recognition, constant improvement is gained over other acoustic features on various commonly used benchmark datasets (TIMIT, LibriSpeech, etc). In particular, fMLLR features outperform MFCCs and FBANKs coefficients, which is mainly due to the speaker adaptation process that fMLLR performs. In, phoneme error rate (PER, %) is reported for the test set of TIMIT with various neural architectures: As expected, fMLLR features outperform MFCCs and FBANKs coefficients despite the use of different model architecture. Where MLP (multi-layer perceptron) serves as a simple baseline, on the other hand RNN, LSTM, and GRU are all well known recurrent models. The Li-GRU architecture is based on a single gate and thus saves 33% of the computations over a standard GRU model, Li-GRU thus effectively address the gradient vanishing problem of recurrent models. As a result, the best performance is obtained with the Li-GRU model on fMLLR features. == Extract fMLLR features with Kaldi == fMLLR can be extracted as reported in the s5 recipe of Kaldi. Kaldi scripts can certainly extract fMLLR features on different dataset, below are the basic example steps to extract fMLLR features from the open source speech corpora Librispeech. Note that the instructions below are for the subsets train-clean-100,train-clean-360,dev-clean, and test-clean, but they can be easily extended to support the other sets dev-other, test-other, and train-other-500. These instruction are based on the codes provided in this GitHub repository, which contains Kaldi recipes on the LibriSpeech corpora to execute the fMLLR feature extraction process, replace the files under $KALDI_ROOT/egs/librispeech/s5/ with the files in the repository. Install Kaldi. Install Kaldiio. If running on a single machine, change the following lines in $KALDI_ROOT/egs/librispeech/s5/cmd.sh to replace queue.pl to run.pl: Change the data path in run.sh to your LibriSpeech data path, the directory LibriSpeech/ should be under that path. For example: Install flac with: sudo apt-get install flac Run the Kaldi recipe run.sh for LibriSpeech at least until Stage 13 (included), for simplicity you can use the modified run.sh. Copy exp/tri4b/trans. files into exp/tri4b/decode_tgsmall_train_clean_/ with the following command: Compute the fMLLR features by running the following script, the script can also be downloaded here: Compute alignments using: Apply CMVN and dump the fMLLR features to new .ark files, the script can also be downloaded here: Use the Python script to convert Kaldi generated .ark features to .npy for your own dataloader, an example Python script is provided:
Information explosion
Information explosion is the rapid increase in the amount of published information or data and the effects of this abundance. As the amount of available data grows, the problem of managing the information becomes more difficult, which can lead to information overload. The Online Oxford English Dictionary indicates use of the phrase in a March 1964 New Statesman article. The New York Times first used the phrase in its editorial content in an article by Walter Sullivan on June 7, 1964, in which he described the phrase as "much discussed". The earliest known use of the phrase was in a speech about television by NBC president Pat Weaver at the Institute of Practitioners of Advertising in London on September 27, 1955. The speech was rebroadcast on radio station WSUI in Iowa City and excerpted in the Daily Iowan newspaper two months later. Many sectors are seeing this rapid increase in the amount of information available such as healthcare, supermarkets, and governments. Another sector that is being affected by this phenomenon is journalism. Such a profession, which in the past was responsible for the dissemination of information, may be suppressed by the overabundance of information today. Techniques to gather knowledge from an overabundance of electronic information (e.g., data fusion may help in data mining) have existed since the 1970s. Another common technique to deal with such amount of information is qualitative research. Such approaches aim to organize the information, synthesizing, categorizing and systematizing in order to be more usable and easier to search. == Growth patterns == The world's technological capacity to store information grew from, optimally compressed, 2.6 exabytes in 1986 to 15.7 in 1993, over 54.5 in 2000, and to 295 exabytes in 2007. The world's technological capacity to receive information through one-way broadcast networks was 432 exabytes of (optimally compressed) information in 1986, 715 (optimally compressed) exabytes in 1993, 1,200 (optimally compressed) exabytes in 2000, and 1,900 in 2007. The world's effective capacity to exchange information through two-way telecommunications networks was 0.281 exabytes of (optimally compressed) information in 1986, 0.471 in 1993, 2.2 in 2000, and 65 (optimally compressed) exabytes in 2007. A new metric that is being used in an attempt to characterize the growth in person-specific information, is the disk storage per person (DSP), which is measured in megabytes/person (where megabytes is 106 bytes and is abbreviated MB). Global DSP (GDSP) is the total rigid disk drive space (in MB) of new units sold in a year divided by the world population in that year. The GDSP metric is a crude measure of how much disk storage could possibly be used to collect person-specific data on the world population. In 1983, one million fixed drives with an estimated total of 90 terabytes were sold worldwide; 30MB drives had the largest market segment. In 1996, 105 million drives, totaling 160,623 terabytes were sold with 1 and 2 gigabyte drives leading the industry. By the year 2000, with 20GB drive leading the industry, rigid drives sold for the year are projected to total 2,829,288 terabytes Rigid disk drive sales to top $34 billion in 1997. According to Latanya Sweeney, there are three trends in data gathering today: Type 1. Expansion of the number of fields being collected, known as the “collect more” trend. Type 2. Replace an existing aggregate data collection with a person-specific one, known as the “collect specifically” trend. Type 3. Gather information by starting a new person-specific data collection, known as the “collect it if you can” trend. == Related terms == Since "information" in electronic media is often used synonymously with "data", the term information explosion is closely related to the concept of data flood (also dubbed data deluge). Sometimes the term information flood is used as well. All of those basically boil down to the ever-increasing amount of electronic data exchanged per time unit. A term that covers the potential negative effects of information explosion is information inflation. The awareness about non-manageable amounts of data grew along with the advent of ever more powerful data processing since the mid-1960s. == Challenges == Even though the abundance of information can be beneficial in several levels, some problems may be of concern such as privacy, legal and ethical guidelines, filtering and data accuracy. Filtering refers to finding useful information in the middle of so much data, which relates to the job of data scientists. A typical example of a necessity of data filtering (data mining) is in healthcare since in the next years is due to have EHRs (Electronic Health Records) of patients available. With so much information available, the doctors will need to be able to identify patterns and select important data for the diagnosis of the patient. On the other hand, according to some experts, having so much public data available makes it difficult to provide data that is actually anonymous. Another point to take into account is the legal and ethical guidelines, which relates to who will be the owner of the data and how frequently he/she is obliged to the release this and for how long. With so many sources of data, another problem will be accuracy of such. An untrusted source may be challenged by others, by ordering a new set of data, causing a repetition in the information. According to Edward Huth, another concern is the accessibility and cost of such information. The accessibility rate could be improved by either reducing the costs or increasing the utility of the information. The reduction of costs according to the author, could be done by associations, which should assess which information was relevant and gather it in a more organized fashion. == Web servers == As of August 2005, there were over 70 million web servers. As of September 2007 there were over 135 million web servers. == Blogs == According to Technorati, the number of blogs doubles about every 6 months with a total of 35.3 million blogs as of April 2006. This is an example of the early stages of logistic growth, where growth is approximately exponential, since blogs are a recent innovation. As the number of blogs approaches the number of possible producers (humans), saturation occurs, growth declines, and the number of blogs eventually stabilizes.
Information history
Information history may refer to the history of each of the categories listed below (or to combinations of them). It should be recognized that the understanding of, for example, libraries as information systems only goes back to about 1950. The application of the term information for earlier systems or societies is a retronym. == Academic discipline == Information history is an emerging discipline related to, but broader than, library history. An important introduction and review was made by Alistair Black (2006). A prolific scholar in this field is also Toni Weller, for example, Weller (2007, 2008, 2010a and 2010b). As part of her work Toni Weller has argued that there are important links between the modern information age and its historical precedents. A description from Russia is Volodin (2000). Alistair Black (2006, p. 445) wrote: "This chapter explores issues of discipline definition and legitimacy by segmenting information history into its various components: The history of print and written culture, including relatively long-established areas such as the histories of libraries and librarianship, book history, publishing history, and the history of reading. The history of more recent information disciplines and practice, that is to say, the history of information management, information systems, and information science. The history of contiguous areas, such as the history of the information society and information infrastructure, necessarily enveloping communication history (including telecommunications history) and the history of information policy. The history of information as social history, with emphasis on the importance of informal information networks." "Bodies influential in the field include the American Library Association’s Round Table on Library History, the Library History Section of the International Federation of Library Associations and Institutions (IFLA), and, in the U.K., the Library and Information History Group of the Chartered Institute of Library and Information Professionals (CILIP). Each of these bodies has been busy in recent years, running conferences and seminars, and initiating scholarly projects. Active library history groups function in many other countries, including Germany (The Wolfenbuttel Round Table on Library History, the History of the Book and the History of Media, located at the Herzog August Bibliothek), Denmark (The Danish Society for Library History, located at the Royal School of Library and Information Science), Finland (The Library History Research Group, University of Tamepere), and Norway (The Norwegian Society for Book and Library History). Sweden has no official group dedicated to the subject, but interest is generated by the existence of a museum of librarianship in Bods, established by the Library Museum Society and directed by Magnus Torstensson. Activity in Argentina, where, as in Europe and the U.S., a "new library history" has developed, is described by Parada (2004)." (Black (2006, p. 447). === Journals === Information & Culture (previously Libraries & the Cultural Record, Libraries & Culture) Library & Information History (until 2008: Library History; until 1967: Library Association. Library History Group. Newsletter) == Information technology (IT) == The term IT is ambiguous although mostly synonym with computer technology. Haigh (2011, pp. 432-433) wrote "In fact, the great majority of references to information technology have always been concerned with computers, although the exact meaning has shifted over time (Kline, 2006). The phrase received its first prominent usage in a Harvard Business Review article (Haigh, 2001b; Leavitt & Whisler, 1958) intended to promote a technocratic vision for the future of business management. Its initial definition was at the conjunction of computers, operations research methods, and simulation techniques. Having failed initially to gain much traction (unlike related terms of a similar vintage such as information systems, information processing, and information science) it was revived in policy and economic circles in the 1970s with a new meaning. Information technology now described the expected convergence of the computing, media, and telecommunications industries (and their technologies), understood within the broader context of a wave of enthusiasm for the computer revolution, post-industrial society, information society (Webster, 1995), and other fashionable expressions of the belief that new electronic technologies were bringing a profound rupture with the past. As it spread broadly during the 1980s, IT increasingly lost its association with communications (and, alas, any vestigial connection to the idea of anybody actually being informed of anything) to become a new and more pretentious way of saying "computer". The final step in this process is the recent surge in references to "information and communication technologies" or ICTs, a coinage that makes sense only if one assumes that a technology can inform without communicating". Some people use the term information technology about technologies used before the development of the computer. This is however to use the term as a retronym. =
Long division
In arithmetic, long division is a standard division algorithm suitable for dividing multi-digit numbers that is simple enough to perform by hand. It breaks down a division problem into a series of easier steps. As in all division problems, one number, called the dividend, is divided by another, called the divisor, producing a result called the quotient. It enables computations involving arbitrarily large numbers to be performed by following a series of simple steps. The abbreviated form of long division is called short division, which is almost always used instead of long division when the divisor has only one digit. == History == Related algorithms have existed since the 12th century. Al-Samawal al-Maghribi (1125–1174) performed calculations with decimal numbers that essentially require long division, leading to infinite decimal results, but without formalizing the algorithm. Caldrini (1491) is the earliest printed example of long division, known as the Danda method in medieval Italy, and it became more practical with the introduction of decimal notation for fractions by Pitiscus (1608). The specific algorithm in modern use was introduced by Henry Briggs c. 1600. == Education == Inexpensive calculators and computers have become the most common tools for performing division in educational and professional contexts worldwide, reducing reliance on traditional paper-and-pencil techniques. Internally, these devices implement various division algorithms, many of which rely on iterative approximations and multiplication to improve computational efficiency. Educational approaches to teaching division vary across countries and regions, reflecting differing curricular priorities. In North America, long division has been de-emphasized or, in some cases, removed from portions of the curriculum as part of reform mathematics, which emphasizes conceptual understanding and the use of technology. In contrast, many education systems in Europe and Asia continue to emphasize mastery of standard algorithms, including long division, as a foundational arithmetic skill. For example, curricula in countries such as Japan and Germany typically introduce and reinforce long division during primary education, often alongside mental arithmetic strategies and problem-solving techniques. International assessments such as the Trends in International Mathematics and Science Study (TIMSS) highlight these differences, showing variation in how procedural fluency and conceptual understanding are balanced across educational systems. These differing approaches reflect broader educational philosophies regarding the balance between procedural fluency, conceptual understanding, and the role of technology in mathematics education. == Method == In English-speaking countries, long division does not use the division slash ⟨∕⟩ or division sign ⟨÷⟩ symbols but instead constructs a tableau. The divisor is separated from the dividend by a right parenthesis ⟨)⟩ or vertical bar ⟨|⟩; the dividend is separated from the quotient by a vinculum (i.e., an overbar). The combination of these two symbols is sometimes known as a long division symbol, division bracket, or even a bus stop. It developed in the 18th century from an earlier single-line notation separating the dividend from the quotient by a left parenthesis. The process is begun by dividing the left-most digit of the dividend by the divisor. The quotient (rounded down to an integer) becomes the first digit of the result, and the remainder is calculated (this step is notated as a subtraction). This remainder carries forward when the process is repeated on the following digit of the dividend (notated as 'bringing down' the next digit to the remainder). When all digits have been processed and no remainder is left, the process is complete. An example is shown below, representing the division of 500 by 4 (with a result of 125). 125 (Explanations) 4)500 4 ( 4 × 1 = 4) 10 ( 5 - 4 = 1) 8 ( 4 × 2 = 8) 20 (10 - 8 = 2) 20 ( 4 × 5 = 20) 0 (20 - 20 = 0) A more detailed breakdown of the steps goes as follows: Find the shortest sequence of digits starting from the left end of the dividend, 500, that the divisor 4 goes into at least once. In this case, this is simply the first digit, 5. The largest number that the divisor 4 can be multiplied by without exceeding 5 is 1, so the digit 1 is put above the 5 to start constructing the quotient. Next, the 1 is multiplied by the divisor 4, to obtain the largest whole number that is a multiple of the divisor 4 without exceeding the 5 (4 in this case). This 4 is then placed under and subtracted from the 5 to get the remainder, 1, which is placed under the 4 under the 5. Afterwards, the first as-yet unused digit in the dividend, in this case the first digit 0 after the 5, is copied directly underneath itself and next to the remainder 1, to form the number 10. At this point the process is repeated enough times to reach a stopping point: The largest number by which the divisor 4 can be multiplied without exceeding 10 is 2, so 2 is written above as the second leftmost quotient digit. This 2 is then multiplied by the divisor 4 to get 8, which is the largest multiple of 4 that does not exceed 10; so 8 is written below 10, and the subtraction 10 minus 8 is performed to get the remainder 2, which is placed below the 8. The next digit of the dividend (the last 0 in 500) is copied directly below itself and next to the remainder 2 to form 20. Then the largest number by which the divisor 4 can be multiplied without exceeding 20, which is 5, is placed above as the third leftmost quotient digit. This 5 is multiplied by the divisor 4 to get 20, which is written below and subtracted from the existing 20 to yield the remainder 0, which is then written below the second 20. At this point, since there are no more digits to bring down from the dividend and the last subtraction result was 0, we can be assured that the process finished. If the last remainder when we ran out of dividend digits had been something other than 0, there would have been two possible courses of action: We could just stop there and say that the dividend divided by the divisor is the quotient written at the top with the remainder written at the bottom, and write the answer as the quotient followed by a fraction that is the remainder divided by the divisor. We could extend the dividend by writing it as, say, 500.000... and continue the process (using a decimal point in the quotient directly above the decimal point in the dividend), in order to get a decimal answer, as in the following example. 31.75 4)127.00 12 (12 ÷ 4 = 3) 07 (0 remainder, bring down next figure) 4 (7 ÷ 4 = 1 r 3) 3.0 (bring down 0 and the decimal point) 2.8 (7 × 4 = 28, 30 ÷ 4 = 7 r 2) 20 (an additional zero is brought down) 20 (5 × 4 = 20) 0 In this example, the decimal part of the result is calculated by continuing the process beyond the units digit, "bringing down" zeros as being the decimal part of the dividend. This example also illustrates that, at the beginning of the process, a step that produces a zero can be omitted. Since the first digit 1 is less than the divisor 4, the first step is instead performed on the first two digits 12. Similarly, if the divisor were 13, one would perform the first step on 127 rather than 12 or 1. === Basic procedure for long division of n ÷ m === Find the location of all decimal points in the dividend n and divisor m. If necessary, simplify the long division problem by moving the decimals of the divisor and dividend by the same number of decimal places, to the right (or to the left), so that the decimal of the divisor is to the right of the last digit. When doing long division, keep the numbers lined up straight from top to bottom under the tableau. After each step, be sure the remainder for that step is less than the divisor. If it is not, there are three possible problems: the multiplication is wrong, the subtraction is wrong, or a greater quotient is needed. In the end, the remainder, r, is added to the growing quotient as a fraction, r⁄m. === Invariant property and correctness === The basic presentation of the steps of the process (above) focuses on what steps are to be performed, rather than the properties of those steps that ensure the result will be correct (specifically, that q × m + r = n, where q is the final quotient and r the final remainder). A slight variation of presentation requires more writing, and requires that we change, rather than just update, digits of the quotient, but can shed more light on why these steps actually produce the right answer by allowing evaluation of q × m + r at intermediate points in the process. This illustrates the key property used in the derivation of the algorithm (below). Specifically, we amend the above basic procedure so that we fill the space after the digits of the quotient under construction with 0's, to at least the 1's place, and include those 0's in the numbers we write below the division bra
Google Gadgets
Google Gadgets are dynamic web content that can be embedded on a web page. They can be added to and interact strongly with Google's iGoogle personalized home page (discontinued in November 2013, although iGoogle Gadgets still work on other websites) and the Google Desktop (discontinued in September 2011) application, as well as Google Wave (also no longer supported by Google) and Google Sites. Webmasters can add and customize a gadget to their own business or personal web site, a process called "syndication". Gadgets are developed by Google and third-party developers using the Google Gadgets API, using basic web technologies such as XML and JavaScript. == Multi-user persistent - Wave Gadgets == With the advent of Google Wave (now Apache Wave), gadgets became able to have persistent storage and multi-user capabilities and better state management. Gadgets using Google Wave in this way were simply known as 'Wave Gadgets'. For instance, a game written using a Google Gadget could use Google Wave technology to record a list of users and high scores without having to worry about how to permanently store the scores on a hosted server. The use of Google Wave would give the gadget multi-user and permanent storage capabilities. For example, scores could be stored in a Google Wave hosted permanently by Google at no cost to the user. As of early 2013, Google Gadgets were deprecated in Google Spreadsheets. Shortly after, they were removed from all spreadsheets. == Technology == Google Gadgets are written in XML and can have HTML and JavaScript components, and were able to use Google Wave. Here is an example of a Hello World program written using Google Gadget technology. Google Gadgets API is a Google API which allows developers to create Google Gadgets easily.
Snap rounding
Snap rounding is a method of approximating line segment locations by creating a grid and placing each point in the centre of a cell (pixel) of the grid. The method preserves certain topological properties of the arrangement of line segments. Drawbacks include the potential interpolation of additional vertices in line segments (lines become polylines), the arbitrary closeness of a point to a non-incident edge, and arbitrary numbers of intersections between input line-segments. The 3 dimensional case is worse, with a polyhedral subdivision of complexity n becoming complexity O(n4). There are more refined algorithms to cope with some of these issues, for example iterated snap rounding guarantees a "large" separation between points and non-incident edges. == Algorithm == ... (please edit). See, and https://www.cgal.org/ () == Properties == Canonicity: Efficiency; A number of efficient implementations exist. Conversely there are undesirable properties: Non-idempotence: Repeated applications can cause arbitrary drift of points. Exception on "Stable snap rounding" algorithms, see https://doi.org/10.1016/j.comgeo.2012.02.011