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Symbol level
In knowledge-based systems, agents choose actions based on the principle of rationality to move closer to a desired goal. The agent is able to make decisions based on knowledge it has about the world (see knowledge level). But for the agent to actually change its state, it must use whatever means it has available. This level of description for the agent's behavior is the symbol level. The term was coined by Allen Newell in 1982. For example, in a computer program, the knowledge level consists of the information contained in its data structures that it uses to perform certain actions. The symbol level consists of the program's algorithms, the data structures themselves, and so on.
Hapax legomenon
In corpus linguistics, a hapax legomenon ( also or ; pl. hapax legomena; sometimes abbreviated to hapax, plural hapaxes) is a word or an expression that occurs only once within a context: either in the written record of an entire language, in the works of an author, or in a single text. The term is also sometimes used to describe a word that occurs in just one of an author's works but more than once in that particular work. Hapax legomenon is a transliteration of Greek ἅπαξ λεγόμενον, meaning "said once". The related terms dis legomenon, tris legomenon, and tetrakis legomenon respectively (, , ) refer to double, triple, or quadruple occurrences, but are far less commonly used. Hapax legomena are quite common, as predicted by Zipf's law, which states that the frequency of any word in a corpus is inversely proportional to its rank in the frequency table. For large corpora, about 40% to 60% of the words are hapax legomena, and another 10% to 15% are dis legomena. Thus, in the Brown Corpus of American English, about half of the 50,000 distinct words are hapax legomena within that corpus. Hapax legomenon refers to the appearance of a word or an expression in a body of text, not to either its origin or its prevalence in speech. It thus differs from a nonce word, which may never be recorded, may find currency and may be widely recorded, or may appear several times in the work which coins it, and so on. == Significance == Hapax legomena in ancient texts are usually difficult to decipher, since it is easier to infer meaning from multiple contexts than from just one. For example, many of the remaining undeciphered Mayan glyphs are hapax legomena, and Biblical (particularly Hebrew; see § Hebrew) hapax legomena sometimes pose problems in translation. Hapax legomena also pose challenges in natural language processing. Some scholars consider Hapax legomena useful in determining the authorship of written works. P. N. Harrison, in The Problem of the Pastoral Epistles (1921) made hapax legomena popular among Bible scholars, when he argued that there are considerably more of them in the three Pastoral Epistles than in other Pauline Epistles. He argued that the number of hapax legomena in a putative author's corpus indicates his or her vocabulary and is characteristic of the author as an individual. Harrison's theory has faded in significance due to a number of problems raised by other scholars. For example, in 1896, W. P. Workman found the following numbers of hapax legomena in each Pauline Epistle: At first glance, the last three totals (for the Pastoral Epistles) are not out of line with the others. To take account of the varying length of the epistles, Workman also calculated the average number of hapax legomena per page of the Greek text, which ranged from 3.6 to 13, as summarized in the diagram on the right. Although the Pastoral Epistles have more hapax legomena per page, Workman found the differences to be moderate in comparison to the variation among other Epistles. This was reinforced when Workman looked at several plays by Shakespeare, which showed similar variations (from 3.4 to 10.4 per page of Irving's one-volume edition), as summarized in the second diagram on the right. Apart from author identity, there are several other factors that can explain the number of hapax legomena in a work: text length: this directly affects the expected number and percentage of hapax legomena; the brevity of the Pastoral Epistles also makes any statistical analysis problematic. text topic: if the author writes on different subjects, of course many subject-specific words will occur only in limited contexts. text audience: if the author is writing to a peer rather than a student, or their spouse rather than their employer, again quite different vocabulary will appear. time: over the course of years, both the language and an author's knowledge and use of language will change. In the particular case of the Pastoral Epistles, all of these variables are quite different from those in the rest of the Pauline corpus, and hapax legomena are no longer widely accepted as strong indicators of authorship; those who reject Pauline authorship of the Pastorals rely on other arguments. There are also subjective questions over whether two forms amount to "the same word": dog vs. dogs, clue vs. clueless, sign vs. signature; many other gray cases also arise. The Jewish Encyclopedia points out that, although there are 1,500 hapaxes in the Hebrew Bible, only about 400 are not obviously related to other attested word forms. A final difficulty with the use of hapax legomena for authorship determination is that there is considerable variation among works known to be by a single author, and disparate authors often show similar values. In other words, hapax legomena are not a reliable indicator. Authorship studies now usually use a wide range of measures to look for patterns rather than relying upon single measurements. == Computer science == In the fields of computational linguistics and natural language processing (NLP), esp. corpus linguistics and machine-learned NLP, it is common to disregard hapax legomena (and sometimes other infrequent words), as they are likely to have little value for computational techniques. This disregard has the added benefit of significantly reducing the memory use of an application, since, by Zipf's law, many words are hapax legomena. == Examples == The following are some examples of hapax legomena in languages or corpora. === Arabic === In the Qurʾān: The proper nouns Iram (Q 89:7, Iram of the Pillars), Bābil (Q 2:102, Babylon), Bakka(t) (Q 3:96, Bakkah), Jibt (Q 4:51), Ramaḍān (Q 2:185, Ramadan), ar-Rūm (Q 30:2, Byzantine Empire), Tasnīm (Q 83:27), Qurayš (Q 106:1, Quraysh), Majūs (Q 22:17, Magian/Zoroastrian), Mārūt (Q 2:102, Harut and Marut), Makka(t) (Q 48:24, Mecca), Nasr (Q 71:23), (Ḏū) an-Nūn (Q 21:87) and Hārūt (Q 2:102, Harut and Marut) occur only once. zanjabīl (زَنْجَبِيل – ginger) is a Qurʾānic hapax (Q 76:17). zamharīr (زَمْهَرِيرًۭ) is a Qurʾānic hapax (Q 76:13), usually glossed as referring to extreme cold. The epitheton ornans aṣ-ṣamad (الصَّمَد – the One besought) is a Qurʾānic hapax (Q 112:2). ṭūd (طُودْ - mountain) is a Qurʾānic hapax (Q 26:63). === Chinese and Japanese === Classical Chinese and Japanese literature contains many Chinese characters that feature only once in the corpus, and their meaning and pronunciation has often been lost. Known in Japanese as kogo (孤語), literally "lonely characters", these can be considered a type of hapax legomenon. For example, the Classic of Poetry (c. 1000 BC) uses the character 篪 exactly once in the verse 「伯氏吹塤, 仲氏吹篪」, and it was only through the discovery of a description by Guo Pu (276–324 AD) that the character could be associated with a specific type of ancient flute. === English === It is fairly common for authors to "coin" new words to convey a particular meaning or for the sake of entertainment, without any suggestion that they are "proper" words. For example, P.G. Wodehouse and Lewis Carroll frequently coined novel words. Indexy, below, appears to be an example of this. Flother, as a synonym for snowflake, is a hapax legomenon of written English found in a manuscript entitled The XI Pains of Hell (c. 1275). Honorificabilitudinitatibus is a hapax legomenon of Shakespeare's works, coming from Erasmus' Adagia Indexy, in Bram Stoker's Dracula, used as an adjective to describe a situational state with no other further use in the language: "If that man had been an ordinary lunatic I would have taken my chance of trusting him; but he seems so mixed up with the Count in an indexy kind of way that I am afraid of doing anything wrong by helping his fads." Manticratic, meaning "of the rule by the Prophet's family or clan", was apparently invented by T. E. Lawrence and appears once in Seven Pillars of Wisdom. Nortelrye, a word for "education", occurs only once in Chaucer's The Reeve's Tale. Sassigassity, perhaps with the meaning of "audacity", occurs only once in Dickens's short story "A Christmas Tree". Slæpwerigne, "sleep-weary", occurs exactly once in the Old English corpus, in the Exeter Book. There is debate over whether it means "weary with sleep" or "weary for sleep". === German === The name of the 9th-century poem Muspilli is a back-formation from "muspille", Old High German hapax legomenon of unclear meaning only found in this text (see Muspilli § Etymology for discussion). === Ancient Greek === According to classical scholar Clyde Pharr, "the Iliad has 1,097 hapax legomena, while the Odyssey has 868". Others have defined the term differently, however, and count as few as 303 in the Iliad and 191 in the Odyssey. panaōrios (παναώριος), ancient Greek for "very untimely", is one of many words that occur only once in the Iliad. The Greek New Testament contains 686 local hapax legomena, which are sometimes called "New Testament hapaxes". 62 of these occur in 1 Peter and 54 occur in 2 Peter
Iterative Viterbi decoding
Iterative Viterbi decoding is an algorithm that spots the subsequence S of an observation O = {o1, ..., on} having the highest average probability (i.e., probability scaled by the length of S) of being generated by a given hidden Markov model M with m states. The algorithm uses a modified Viterbi algorithm as an internal step. The scaled probability measure was first proposed by John S. Bridle. An early algorithm to solve this problem, sliding window, was proposed by Jay G. Wilpon et al., 1989, with constant cost T = mn2/2. A faster algorithm consists of an iteration of calls to the Viterbi algorithm, reestimating a filler score until convergence. == The algorithm == A basic (non-optimized) version, finding the sequence s with the smallest normalized distance from some subsequence of t is: // input is placed in observation s[1..n], template t[1..m], // and [[distance matrix]] d[1..n,1..m] // remaining elements in matrices are solely for internal computations (int, int, int) AverageSubmatchDistance(char s[0..(n+1)], char t[0..(m+1)], int d[1..n,0..(m+1)]) { // score, subsequence start, subsequence end declare int e, B, E t'[0] := t'[m+1] := s'[0] := s'[n+1] := 'e' e := random() do e' := e for i := 1 to n do d'[i,0] := d'[i,m+1] := e (e, B, E) := ViterbiDistance(s', t', d') e := e/(E-B+1) until (e == e') return (e, B, E) } The ViterbiDistance() procedure returns the tuple (e, B, E), i.e., the Viterbi score "e" for the match of t and the selected entry (B) and exit (E) points from it. "B" and "E" have to be recorded using a simple modification to Viterbi. A modification that can be applied to CYK tables, proposed by Antoine Rozenknop, consists in subtracting e from all elements of the initial matrix d.
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Irwin Sobel
Irwin Sobel (born September 12, 1940) is a scientist and researcher in digital image processing. == Biography == Irwin Sobel was born in New York City. He graduated from MIT in 1961 and completed his Ph.D. research at the Stanford Artificial Intelligence Project (SAIL) with thesis Camera Models and Machine Perception. His Ph.D. advisor was Jerome A. Feldman. Starting in 1973, he spent nine years doing postdoctoral research at Columbia University. After 1982, he worked as a Senior Researcher at HP Labs. == Sobel operator == In 1968, Sobel gave a talk entitled "An Isotropic 3x3 Image Gradient Operator" at SAIL; this method became known as the Sobel operator. It was developed jointly with a colleague, Gary Feldman, also at SAIL.
Tamara Broderick
Tamara Ann Broderick is an American computer scientist at the Massachusetts Institute of Technology. She works on machine learning and Bayesian inference. == Education and early career == Broderick is from Parma Heights, Ohio. She attended Laurel School and graduated in 2003. Whilst at high school she took part in the inaugural Massachusetts Institute of Technology Women's Technology Program. She studied mathematics at Princeton University, earning a bachelor's degree in 2007. She was a Marshall scholar, allowing her to pursue graduate research at the University of Cambridge. She was a runner-up in the Association for Women in Mathematics Alice T. Shafer Prize for Excellence in Mathematics. She was co-president of the Princeton Math Club and organised a competition for high school maths teams. She won the Phi Beta Kappa Prize for the highest academic average at Princeton University. During her undergraduate degree, Broderick worked on dark matter haloes with Rachel Mandelbaum. Broderick moved to the United Kingdom for her graduate studies, earning a Master of Advanced Studies for completing Part III of the Mathematical Tripos at the University of Cambridge in 2009. Her Master's thesis looked at the Nomon selection method, improving the efficiency of communications. She returned to America in 2009, joining University of California, Berkeley for her Master's and PhD. Her graduate research was supported by the Berkeley Fellowship and a National Science Foundation Fellowship. Her PhD thesis Clusters and features from combinatorial stochastic processes looked at clustering and speeding up the analysis of large, streaming data sets. In 2013 she was selected for the Berkeley EECS Rising Stars conference. == Research and career == Broderick joined Massachusetts Institute of Technology as an assistant professor in 2015. She is interested in Bayesian statistics and graphical models. She was the recipient of a Google Faculty Research Grant and International Society for Bayesian Analysis Lifetime Members Junior Researcher Award. She was awarded an Army Research Office young investigator program award to investigate machine-learning to quantify uncertainty in data analysis. Broderick is also Alfred P. Sloan Foundation scholar. === Academic service === In 2018, Broderick spoke at the Harvard University Institute for Applied Computational Science Women in Data Science conference. She spoke about Bayesian inference at the 2018 International Conference on Machine Learning. She led a three-day Masterclass on machine learning at University College London in June 2018. Broderick is a scientific advisor for AI.Reverie and WiML (Women in Machine Learning). She has developed a high-school level introduction to machine learning with the Women's Technology Program (WTP). Software she has developed is available on her website. === Awards and honors === Broderick was awarded the Evelyn Fix Memorial Medal and Citation and the International Society for Bayesian Analysis Savage Award for her doctoral thesis. She was awarded a National Science Foundation CAREER Award to scale her machine learning techniques. She was a 2021 Leadership Academy winner of the Committee of Presidents of Statistical Societies.