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Modular arithmetic

In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones Arithmeticae, published in 1801. A familiar use of modular arithmetic is in the 12-hour clock, in which the day is divided into two 12-hour periods. If the time is 7:00 now 8 hours it will be 3:00. Usual addition would suggest that the time should be 7 + 8 = 15, but this is not the answer because clock time "wraps around" every 12 hours; because the hour number starts over after it reaches 12, this is arithmetic modulo 12. In terms of the definition below, 15 is congruent to 3 modulo 12, so the time called "15:00" has the equivalent clock form "3:00". Modular arithmetic can be handled mathematically by introducing a congruence relation on the integers, compatible with the operations on integers: addition and multiplication. For a positive integer n, two numbers a and b are said to be congruent modulo n, if their difference a − b is an integer multiple of n.

This congruence relation is considered when a and b are integers, is denoted: a ≡ b. The parentheses mean. Sometimes, = is used instead of ≡; the number n is called the modulus of the congruence. The congruence relation may be rewritten as a = k n + b, explicitly showing its relationship with Euclidean division. However, b need not be the remainder of the division of a by n. More what the statement a ≡ b mod n asserts is that a and b have the same remainder when divided by n; that is, a = p n + r, b = q n + r, where 0 ≤ r < n is the common remainder. Subtracting these two expressions, we recover the previous relation: a − b = k n, by setting k = p − q. For example, 38 ≡ 14 because 38 − 14 = 24, a multiple of 12, or, because both 38 and 14 have the same remainder 2 when divided by 12; the same rule holds for negative values: − 8 ≡ 7 2 ≡ − 3 − 3 ≡ − 8. Because it is common to consider several congruence relations for different moduli at the same time, the modulus is incorporated in the notation; the congruence relation for a given modulus is considered to be a binary relation.

The congruence relation satisfies all the conditions of an equivalence relation: Reflexivity: a ≡ a Symmetry: a ≡ b if b ≡ a for all a, b, n. Transitivity: If a ≡ b and b ≡ c a ≡ c If a1 ≡ b1 and a2 ≡ b2, or if a ≡ b, then: a + k ≡ b + k for any integer k k a ≡ k b for any integer k a1 + a2 ≡ b1 + b2 a1 – a2 ≡ b1 – b2 a1 a2 ≡ b1 b2 ak ≡ bk for any non-negative integer k p ≡ p, for any polynomial p with integer coefficients If a ≡ b it is false, in general, that ka ≡ kb. However, one has: If c ≡ d, where φ is Euler's totient function ac ≡ ad provided a is coprime with nFor cancellation of common terms, we have the following rules: If a + k ≡ b + k for any integer k a ≡ b If k a ≡ k b and k is coprime with n a ≡ b The modular multiplicative inverse is defined by the following rules: Existence: there exists an integer denoted a–1 such that aa–1 ≡ 1 if and only if a is coprime with n; this integer a–1 is called a modular multiplicative inverse of a modulo n. If a ≡ b and a–1 exists a–1 ≡ b–1 If a x ≡ b and a is coprime to n, the solution to this linear congruence is given by x ≡ a–1b The multiplicative inverse x ≡ a–1 may be efficiently computed by solving Bézout's equation a x + n y = 1 for x, y using the Extended Euclidean algorithm.

In particular, if p is a prime number a is coprime with p for every a such that 0 < a < p.

Logie Award for Most Outstanding News Coverage or Public Affairs Report

The Silver Logie for Most Outstanding News Coverage or Public Affairs Report is an award presented annually at the Australian TV Week Logie Awards. The award is given to recognise outstanding public affairs reporting; the first award for news coverage was awarded at the 12th Annual TV Week Logie Awards ceremony, held in 1970 as Best News Reporting. In 1971, two awards were presented for Most Outstanding News Coverage and Most Outstanding Coverage Of Political Affairswith the latter changed to Outstanding Contribution To TV Journalism the following year. From 1973 they were Best Best Public Affairs Program. Over the years, these award categories have changed to recognise news reports, news or public affairs programs, special reports or public affairs reports. At the 60th Annual TV Week Logie Awards in 2018, the industry voted awards for news and public affairs Most Outstanding News Coverage and Most Outstanding Public Affairs Report were combined to create the award for Most Outstanding News Coverage or Public Affairs Report.

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Mbox

Mbox is a generic term for a family of related file formats used for holding collections of email messages, first implemented for Fifth Edition Unix. All messages in an mbox mailbox are stored as plain text in a single file; each message starts with the four characters "From" followed by a space and the sender's email address. RFC 4155 defines. Unlike the Internet protocols used for the exchange of email, the format used for the storage of email has never been formally defined through the RFC standardization mechanism and has been left to the developer of an email client. However, the POSIX standard defined a loose frame in conjunction with the mailx program. In 2005 the application/mbox media type was standardized as RFC 4155, hints that mbox stores mailbox messages in their original Internet Message format, except for the used newline character, seven-bit clean data storage, the requirement that each newly added message is terminated with a empty line within the mbox database. A format similar to mbox is the MH Message Handling System.

Other systems, such as Microsoft Exchange Server and the Cyrus IMAP server store mailboxes in centralised databases managed by the mail system and not directly accessible by individual users. The maildir mailbox format is cited as an alternative to the mbox format for network email storage systems; the mbox format uses a single blank line followed by the string'From' to delimit messages. Over the decades that followed, four popular but incompatible variants arose: mboxo, mboxrd and mboxcl2; the naming scheme was developed by Daniel J. Bernstein, Rahul Dhesi, others in 1996; each originated from a different version of Unix. Mboxcl and mboxcl2 originated from the file format used by Unix System V Release 4 mail tools. Mboxrd was invented by Rahul Dhesi et al. as a rationalisation of mboxo and subsequently adopted by some Unix mail tools including qmail. All these variants have the problem that the content of the message is modified in order to remove the ambiguities, as shown below, so that applications have to know which quoting rule has been used in order to perform the correct reversion, which turned out to be impractical.

Using MIME and choosing a content-transfer-encoding that quotes "From_" lines in a standard-compliant fashion ensures that message content doesn't need to be changed, but only their MIME representation. Therefore checksums remain constant, a necessary precondition for supporting S/MIME and Pretty Good Privacy. Applications which newly create messages and store them in mbox database files will use this approach to detach message content from database storage format. Mboxo and mboxrd locate the message start by scanning for From lines that are found before the email message headers. If a "From " string occurs at the beginning of a line in either the header or the body of a message, the email message must be modified before the message is stored in an mbox mailbox file or the line will be taken as a message boundary. To avoid misinterpreting a "From " string at the beginning of the line in the email body as the beginning of a new email, some systems "From-munge" the message by prepending a greater-than sign: >From my point of view...

In the mboxo format, such lines have irreversible ambiguity. In the mboxo format, this can lead to corruption of the message. If a line contained >From at the beginning, it is unchanged when written. When subsequently read by the mail software, the leading > is erroneously removed. The mboxrd format solves this by converting > From to >> From, etc.. The transformation is always reversible. Example: The mboxcl and mboxcl2 formats use a Content-Length: header to determine the messages’ lengths and thereby the next real From line. Mboxcl still quotes From lines in the messages themselves while mboxcl2 doesn't; some email clients use a modification of the mbox format for their mail folders. Eudora used an mboxo variation where a sender's email address is replaced by the constant string "???@???". Most mbox clients store incoming messages. Eudora separates out attachments embedded in the message, storing the attachments as separate individual files in one folder; the Mozilla family of email clients use an mboxrd variation with more complex From line quoting rules.

Various mutually incompatible mechanisms have been used by different mbox formats to enable message file locking, including fcntl and lockf. This does not work well with network mounted file systems, such as the Network File System, why traditionally Unix used additional "dot lock" files, which could be created atomically over NFS; because more than one message is stored in a single file, some form of file locking is needed to avoid the corruption that can result from two or more processes modifying the mailbox simultaneously. This could happen if a network email delivery program delivers a new message at the same time as a mail reader is deleting an existing message. Mbox files should be locked while they are being read. Otherwise the reader may see corrupted message contents if another process is modifying the mbox at the same time though no actual file corruption occurs. In open source development, it is common to send patches in the diff format to a mailing list for discussion; the diff format allows for irrelevant "headers", such as mbox data.

Version control systems like git have support

Cvet z juga

"Cvet z juga" is a "popera" song by Alenka Gotar, represented Slovenia at the Eurovision Song Contest 2007. The song is about a girl who bids farewell to her boyfriend and gives him a white flower as a reminder. On the night of the semi-final, the song performed twenty-fifth, following Belgium's KMG's with "Love Power" and preceding Turkey's Kenan Doğulu and "Shake It Up Şekerim". At the close of voting, it had received 140 points, placing seventh in a field of twenty eight, bringing Slovenia to the final for the first time since 2003. On the night of the final, the song performed seventh, following Macedonia's Karolina Gočeva with "Mojot svet" and preceding Hungary's Magdi Rúzsa and "Unsubstantial Blues". At the close of voting, it had received 66 points, it was succeeded as Slovene representative at the 2008 contest by Rebeka Dremelj and "Vrag naj vzame". "Cvet z juga" "Cvet z juga" "Cvet z juga" "Cvet z juga" Slovenia in the Eurovision Song Contest 2007

Sarin

Sarin is an toxic synthetic organophosphorus compound. A colourless, odorless liquid, it is used as a chemical weapon due to its extreme potency as a nerve agent. Exposure is lethal at low concentrations, where death can occur within one-to-ten minutes after direct inhalation of a lethal dose, due to suffocation from lung muscle paralysis, unless antidotes are administered. People who absorb a non-lethal dose, but do not receive immediate medical treatment, may suffer permanent neurological damage. Sarin is considered a weapon of mass destruction. Production and stockpiling of sarin was outlawed as of April 1997 by the Chemical Weapons Convention of 1993, it is classified as a Schedule 1 substance. Like some other nerve agents that affect the neurotransmitter acetylcholine, sarin attacks the nervous system by interfering with the degradation of the neurotransmitter acetylcholine at neuromuscular junctions. Death will occur as a result of asphyxia due to the inability to control the muscles involved in breathing.

Initial symptoms following exposure to sarin are a runny nose, tightness in the chest, constriction of the pupils. Soon after, the person will have difficulty breathing and they will experience nausea and drooling; as they continue to lose control of bodily functions, they may vomit and urinate. This phase is followed by jerking; the person becomes comatose and suffocates in a series of convulsive spasms. Moreover, common mnemonics for the symptomatology of organophosphate poisoning, including sarin gas, are the "killer Bs" of bronchorrhea and bronchospasm because they are the leading cause of death, SLUDGE – salivation, urination, gastrointestinal distress, emesis. Death may follow in one to ten minutes after direct inhalation. Sarin has a high volatility relative to similar nerve agents, therefore inhalation is easy and vapor may penetrate the skin. A person's clothing can release sarin for about 30 minutes after it has come in contact with sarin gas, which can lead to exposure of other people.

Treatment measures have been described. Treatment is with the antidotes atropine and pralidoxime. Atropine, an antagonist to muscarinic acetylcholine receptors, is given to treat the physiological symptoms of poisoning. Since muscular response to acetylcholine is mediated through nicotinic acetylcholine receptors, atropine does not counteract the muscular symptoms. Pralidoxime can regenerate cholinesterases if administered within five hours. Biperiden, a synthetic acetylcholine antagonist, has been suggested as an alternative to atropine due to its better blood–brain barrier penetration and higher efficacy. Sarin is a potent inhibitor of acetylcholinesterase, an enzyme that degrades the neurotransmitter acetylcholine after it is released into the synaptic cleft. In vertebrates, acetylcholine is the neurotransmitter used at the neuromuscular junction, where signals are transmitted between neurons from the central nervous system to muscle fibres. Acetylcholine is released from the neuron to stimulate the muscle, after which it is degraded by acetylcholinesterase, allowing the muscle to relax.

A build-up of acetylcholine in the synaptic cleft, due to the inhibition of acetylcholinesterase, means the neurotransmitter continues to act on the muscle fibre, so that any nerve impulses are continually transmitted. Sarin acts on acetylcholinesterase by forming a covalent bond with the particular serine residue at the active site. Fluoride is the leaving group, the resulting phosphoester is robust and biologically inactive, its mechanism of action resembles that of some used insecticides, such as malathion. In terms of biological activity, it resembles carbamate insecticides, such as Sevin, the medicines pyridostigmine and physostigmine. Controlled studies in healthy men have shown that a nontoxic 0.43 mg oral dose administered in several portions over a 3-day interval caused average maximum depressions of 22 and 30% in plasma and erythrocyte acetylcholinesterase levels. A single acute 0.5 mg dose caused mild symptoms of intoxication and an average reduction of 38% in both measures of acetylcholinesterase activity.

Sarin in blood is degraded either in vivo or in vitro. Its primary inactive metabolites have in vivo serum half-lives of 24 hours; the serum level of unbound isopropyl methylphosphonic acid, a sarin hydrolysis product, ranged from 2–135 µg/L in survivors of a terrorist attack during the first four hours post-exposure. Sarin or its metabolites may be determined in blood or urine by gas or liquid chromatography, while acetylcholinesterase activity is measured by enzymatic methods. A newer method called "fluoride regeneration" or "fluoride reactivation" detects the presence of nerve agents for a longer period after exposure than the methods described above. Fluoride reactivation is a technique, explored since at least the early 2000s; this technique obviates some of the deficiencies of older procedures. Sarin not only reacts with the water in the blood plasma through hydrolysis, but reacts with various proteins to form ‘protein adducts’; these protein adducts are not so removed from the body, remain for a longer period of time than the free metabolites.

One clear advantage of this process is that the period, post-exposure, for determination of sarin exposure is much longer five to eight weeks according to at least one study. As a nerve gas, sarin in its purest form is estimated to be 26 times more deadly than cyanide; the LD50

Guided analytics

Guided analytics is a sub-field at the interface of visual analytics and predictive analytics focused on the development of interactive visual interfaces for business intelligence applications. Such interactive applications serve the analyst to take important decisions by extracting information from the data. Guided analytics applications lie in the intersection between business intelligence and predictive analytics. A great number of business analysts rely on business intelligence tools to flexibly extract specific information from data, it is required to automatically run an analysis on the raw data before information can be extracted. However, it is not always possible to automate the entire process from any kind of raw data access to the extraction of useful information. Furthermore, the expertise of data scientists will be necessary each time new data or questions come into the picture; this is true when predictive analytics is applied. To create an application, flexible to different data problems and usable by the domain experts without continuous help by a data scientist, it is required to insert a number of interaction points in the analysis process.

The interactions will determine the sequence of steps in the analysis. In this way, the application guides the user with no need of customization by the data science expert. Guided analytics is about building such interactive applications. By mixing and matching automation and interaction, guided analytics applications empower business analysts to independently extract insights and future outcomes from the data; the term “guided analytics” was coined for the first time in an online magazine by a TIBCO expert in 2004. Back predictive analytics in business intelligence was new. Guided analytics applications were focused on interactive visualization to ease the access to trustworthy KPI metrics through a database; this was seen useful in the pharmaceutical industry. In 2007, a paper published by IEEE Computer Society Press presented guided analytics as one of the future trends in business intelligence. In 2012, one of the main visual analytics experts, Ben Shneiderman, is co-authored in a paper mentioning guided analytics among one of the “interactive dynamics for visual analysis”.

A good quote from J. Heer and B. Schneirderman paper is “visual-analysis systems can incorporate guided analytics to lead analysts through workflows for common tasks”. In 2016, vendors like Qlik and Tableau proposed guided analytics for exploratory data analysis tasks. Around 2018, guided analytics was mentioned by business intelligence vendors when describing applications for advanced analytics use cases, rather than only for interactive dashboards. In fact, guided analytics can be used in each phase of the CRISP-DM data science cycle. In 2018 and 2019, KNIME has released a number of analytical blueprints for guided analytics workflows with a special focus on automated machine learning. KNIME proposed guided analytics as a key mechanism to abstract data science for other users