Sequences, Explicit and Recursive Form序列,明确和递归形式 34页PPT

Discourse analysis (DA), or discourse studies, is a general term for a number of approaches to analyzing written, spoken, signed language use or any significant semiotic event.The objects of discourse analysis—discourse, writing, talk, conversation, communicative event, etc.—are variously defined in terms of coherent sequences of sentences, propositions, speech acts or turns-at-talk. Contrary to much of traditional linguistics, discourse analysts not only study language use 'beyond the sentence boundary', but also prefer to analyze 'naturally occurring' language use, and not invented examples. This is known as corpus linguistics; text linguistics is related. The essential difference between discourse analysis and text linguistics is that it aims at revealing socio-psychological characteristics of a person/persons rather than text structure[1].Discourse analysis has been taken up in a variety of social science disciplines, including linguistics, sociology, anthropology, social work, cognitive psychology, social psychology, international relations, human geography, communication studies and translation studies, each of which is subject to its own assumptions, dimensions of analysis, and methodologies. Sociologist Harold Garfinkel was another influence on the discipline: see below.HistorySome scholars consider the Austrian emigre Leo Spitzer's Stilstudien [Style Studies] of 1928 the earliest example of discourse analysis (DA); Michel Foucault himself translated it into French. But the term first came into general use following the publication of a series of papers by Zellig Harris beginning in 1952 and reporting on work from which he developed transformational grammar in the late 1930s. Formal equivalence relations among the sentences of a coherent discourse are made explicit by using sentence transformations to put the text in a canonical form. Words and sentences with equivalent information then appear in the same column of an array. This work progressed over the next four decades (see references) into a science of sublanguage analysis (Kittredge & Lehrberger 1982), culminating in a demonstration of the informational structures in texts of a sublanguage of science, that of immunology, (Harris et al. 1989) and a fully articulated theory of linguistic informational content (Harris 1991). During this time, however, most linguists decided a succession of elaborate theories of sentence-level syntax and semantics.Although Harris had mentioned the analysis of whole discourses, he had not worked out a comprehensive model, as of January, 1952. A linguist working for the American Bible Society, James A. Lauriault/Loriot, needed to find answers to some fundamental errors in translating Quechua, in the Cuzco area of Peru. He took Harris's idea, recorded all of the legends and, after going over the meaning and placement of each word with a native speaker of Quechua, was able to form logical, mathematical rules that transcended the simple sentence structure. He then applied the process to another language of Eastern Peru, Shipibo. He taught the theory in Norman, Oklahoma, in the summers of 1956 and 1957 and entered the University of Pennsylvania in the inte rim year. He tried to publish a paper Shipibo Paragraph Structure, but it was delayed until 1970 (Loriot & Hollenbach 1970). In the meantime, Dr. Kenneth Lee Pike, a professor at University of Michigan, Ann Arbor, taught the theory, and one of his students, Robert E. Longacre, was able to disseminate it in a dissertation.Harris's methodology was developed into a system for the computer-aided analysis of natural language by a team led by Naomi Sager at NYU, which has been applied to a number of sublanguage domains, most notably to medical informatics. The software for the Medical Language Processor is publicly available on SourceForge.In the late 1960s and 1970s, and without reference to this prior work, a variety of other approaches to a new cross-discipline of DA began to develop in most of the humanities and social sciences concurrently with, and related to, other disciplines, such as semiotics, psycholinguistics, sociolinguistics, and pragmatics. Many of these approaches, especially those influenced by thesocial sciences, favor a more dynamic study of oral talk-in-interaction.Mention must also be made of the term "Conversational analysis", which was influenced by the Sociologist Harold Garfinkel who is the founder of Ethnomethodology.In Europe, Michel Foucault became one of the key theorists of the subject, especially of discourse, and wrote The Archaeology of Knowledge on the subject.[edit] T opics of interestTopics of discourse analysis include:∙The various levels or dimensions of discourse, such as sounds (intonation, etc.), gestures, syntax, the lexicon, style, rhetoric, meanings, speech acts, moves, strategies, turns and other aspects of interaction∙Genres of discourse (various types of discourse in politics, the media, education, science, business, etc.)∙The relations between discourse and the emergence of syntactic structure∙The relations between text (discourse) and context∙The relations between discourse and power∙The relations between discourse and interaction∙The relations between discourse and cognition and memory[edit] PerspectivesThe following are some of the specific theoretical perspectives and analytical approaches used in linguistic discourse analysis:∙Emergent grammar∙Text grammar (or 'discourse grammar')∙Cohesion and relevance theory∙Functional grammar∙Rhetoric∙Stylistics (linguistics)∙Interactional sociolinguistics∙Ethnography of communication∙Pragmatics, particularly speech act theory∙Conversation analysis∙V ariation analysis∙Applied linguistics∙Cognitive psychology, often under the label discourse processing, studying the production and comprehension of discourse.∙Discursive psychology∙Response based therapy (counselling)∙Critical discourse analysis∙Sublanguage analysisAlthough these approaches emphasize different aspects of language use, they all view language as social interaction, and are concerned with the social contexts in which discourse is embedded. Often a distinction is made between 'local' structures of discourse (such as relations among sentences, propositions, and turns) and 'global' structures, such as overall topics and the schematic organization of discourses and conversations. For instance, many types of discourse begin with some kind of global 'summary', in titles, headlines, leads, abstracts, and so on.A problem for the discourse analyst is to decide when a particular feature is relevant to thespecification is required. Are there general principles which will determine the relevance or nature of the specification.[2][edit] Prominent discourse analystsMarc Angenot, Robert de Beaugrande, Jan Blommaert, Adriana Bolivar, Carmen Rosa Caldas-Coulthard, Robyn Carston, Wallace Chafe, Paul Chilton, Guy Cook, Malcolm Coulthard, James Deese, Paul Drew, Alessandro Duranti, Brenton D. Faber, Norman Fairclough, Michel Foucault, Roger Fowler, James Paul Gee, Talmy Givón, Charles Goodwin, Art Graesser, Michael Halliday, Zellig Harris, John Heritage, Janet Holmes, Paul Hopper, Gail Jefferson, Barbara Johnstone, Walter Kintsch, Richard Kittredge, Adam Jaworski, William Labov, George Lakoff, Stephen H. Levinson, James A. Lauriault/Loriot, Robert E. Longacre, Jim Martin, David Nunan, Elinor Ochs, Jonathan Potter, Edward Robinson, Nikolas Rose, Harvey Sacks, Svenka Savic Naomi Sager, Emanuel Schegloff, Deborah Schiffrin, Michael Schober, Stef Slembrouck, Michael Stubbs, John Swales, Deborah Tannen, Sandra Thompson, Teun A. van Dijk, Theo van Leeuwen, Jef V erschueren, Henry Widdowson, Carla Willig, Deirdre Wilson, Ruth Wodak, Margaret Wetherell, Ernesto Laclau, Chantal Mouffe, Judith M. De Guzman, Cynthia Hardy, Louise J. Phillips[edit] Further reading1.^Y atsko V.A. Integrational discourse analysis conception2.^ Gillian Brown "discourse Analysis"∙Blommaert, J. (2005). Discourse. Cambridge: Cambridge University Press.∙Brown, G., and George Yule (1983). Discourse Analysis. Cambridge: Cambridge University Press.∙Carter, R. (1997). Investigating English Discourse. London: Routledge.∙Gee, J. P. (2005). An Introduction to Discourse Analysis: Theory and Method. London: Routledge.∙Deese, James. Thought into Speech: The Psychology og a Language.Century Psychology Series. Englewood Cliffs, New Jersey: Prentice Hall, 1984.∙Harris, Zellig S. (1952a). "Culture and Style in Extended Discourse". Selected Papers from the 29th International Congress of Americanists (New Y ork, 1949), vol.III: Indian Tribes of Aboriginal America ed. by Sol Tax & Melville J[oyce] Herskovits, 210-215. New Y ork:Cooper Square Publishers. (Repr., New Y ork: Cooper Press, 1967. Paper repr. in 1970a,pp. 373–389.) [Proposes a method for analyzing extended discourse, with example analyses from Hidatsa, a Siouan language spoken in North Dakota.]∙Harris, Zellig S. (1952b.) "Discourse Analysis". Language 28:1.1-30. (Repr. in The Structure of Language: Readings in the philosophy of language ed. by Jerry A[lan] Fodor & JerroldJ[acob] Katz, pp. 355–383. Englewood Cliffs, N.J.: Prentice-Hall, 1964, and also in Harris 1970a, pp. 313–348 as well as in 1981, pp. 107–142.) French translation "Analyse dudiscours". Langages (1969) 13.8-45. German translation by Peter Eisenberg, "Textanalyse".Beschreibungsmethoden des amerikanischen Strakturalismus ed. by Elisabeth Bense, Peter Eisenberg & Hartmut Haberland, 261-298. München: Max Hueber. [Presents a method for the analysis of connected speech or writing.]∙Harris, Zellig S. 1952c. "Discourse Analysis: A sample text". Language 28:4.474-494. (Repr.in 1970a, pp. 349–379.)∙Harris, Zellig S. (1954.) "Distributional Structure". Word 10:2/3.146-162. (Also in Linguistics Today: Published on the occasion of the Columbia University Bicentennial ed.by Andre Martinet & Uriel Weinreich, 26-42. New Y ork: Linguistic Circle of New Y ork,1954. Repr. in The Structure of Language: Readings in the philosophy of language ed. byJerry A[lan] Fodor & Jerrold J[acob] Katz, 33-49. Englewood Cliffs, N.J.: Prentice-Hall,1964, and also in Harris 1970.775-794, and 1981.3-22.) French translation "La structure distributionnelle,". A nalyse distributionnelle et structurale ed. by Jean Dubois & Françoise Dubois-Charlier (=Langages, No.20), 14-34. Paris: Didier / Larousse.∙Harris, Zellig S. (1963.) Discourse Analysis Reprints. (= Papers on Formal Linguistics, 2.) The Hague: Mouton, 73 pp. [Combines Transformations and Discourse Analysis Papers 3a, 3b, and 3c. 1957, Philadelphia: University of Pennsylvania. ]∙Harris, Zellig S. (1968.) Mathematical Structures of Language. (=Interscience Tracts in Pure and Applied Mathematics, 21.) New Y ork: Interscience Publishers John Wiley & Sons).French translation Structures mathématiques du langage. Transl. by Catherine Fuchs.(=Monographies de Linguistique mathématique, 3.) Paris: Dunod, 248 pp.∙Harris, Zellig S. (1970.) Papers in Structural and Transformational Linguistics. Dordrecht/ Holland: D. Reidel., x, 850 pp. [Collection of 37 papers originally published 1940-1969.]∙Harris, Zellig S. (1981.) Papers on Syntax. Ed. by Henry Hiż. (=Synthese Language Library,14.) Dordrecht/Holland: D. Reidel, vii, 479 pp.]∙Harris, Zellig S. (1982.) "Discourse and Sublanguage". Sublanguage: Studies of language in restricted semantic domains ed. by Richard Kittredge & John Lehrberger, 231-236. Berlin: Walter de Gruyter.∙Harris, Zellig S. (1985.) "On Grammars of Science". Linguistics and Philosophy: Essays in honor of Rulon S. Wells ed. by Adam Makkai & Alan K. Melby (=Current Issues inLinguistic Theory, 42), 139-148. Amsterdam & Philadelphia: John Benjamins.∙Harris, Zellig S. (1988a) Language and Information. (=Bampton Lectures in America, 28.) New Y ork: Columbia University Press, ix, 120 pp.∙Harris, Zellig S. 1988b. (Together with Paul Mattick, Jr.) "Scientific Sublanguages and the Prospects for a Global Language of Science". Annals of the American Association ofPhilosophy and Social Sciences No.495.73-83.∙Harris, Zellig S. (1989.) (Together with Michael Gottfried, Thomas Ryckman, Paul Mattick, Jr., Anne Daladier, Tzvee N. Harris & Suzanna Harris.) The Form of Information in Science: Analysis of an immunology sublanguage. Preface by Hilary Putnam. (=Boston Studies in the Philosophy of, Science, 104.) Dordrecht/Holland & Boston: Kluwer Academic Publishers, xvii, 590 pp.∙Harris, Zellig S. (1991.) A Theory of Language and Information: A mathematical approach.Oxford & New Y ork: Clarendon Press, xii, 428 pp.; illustr.∙Jaworski, A. and Coupland, N. (eds). (1999). The Discourse Reader. London: Routledge.∙Johnstone, B. (2002). Discourse analysis. Oxford: Blackwell.∙Kittredge, Richard & John Lehrberger. (1982.) Sublanguage: Studies of language in restricted semantic domains. Berlin: Walter de Gruyter.∙Loriot, James and Barbara E. Hollenbach. 1970. "Shipibo paragraph structure." Foundations of Language 6: 43-66. The seminal work reported as having been admitted by Longacre and Pike. See link below from Longacre's student Daniel L. Everett.∙Longacre, R.E. (1996). The grammar of discourse. New Y ork: Plenum Press.∙Miscoiu, S., Craciun O., Colopelnic, N. (2008). Radicalism, Populism, Interventionism.Three Approaches Based on Discourse Theory. Cluj-Napoca: Efes.∙Renkema, J. (2004). Introduction to discourse studies. Amsterdam: Benjamins.∙Sager, Naomi & Ngô Thanh Nhàn. (2002.) "The computability of strings, transformations, and sublanguage". The Legacy of Zellig Harris: Language and information into the 21st Century, V ol. 2: Computability of language and computer applications, ed. by Bruce Nevin, John Benjamins, pp. 79–120.∙Schiffrin, D., Deborah Tannen, & Hamilton, H. E. (eds.). (2001). Handbook of Discourse Analysis. Oxford: Blackwell.∙Stubbs, M. (1983). Discourse Analysis: The sociolinguistic analysis of natural language.Oxford: Blackwell∙Teun A. van Dijk, (ed). (1997). Discourse Studies. 2 vols. London: Sage.Potter, J, Wetherall, M. (1987). Discourse and Social Psychology: Beyond attitudes and behaviour. London: SAGE.[edit]。

dna序列分析算法流程English Answer:DNA Sequence Analysis Algorithm Workflow.DNA sequence analysis is a complex process that involves multiple steps. The general workflow of DNA sequence analysis algorithms can be summarized as follows:1. Sample preparation: The first step is to prepare the DNA sample for sequencing. This may involve extracting DNA from cells, purifying the DNA, and fragmenting the DNA into smaller pieces.2. Sequencing: The next step is to sequence the DNA fragments. This is done using a variety of techniques, such as Sanger sequencing, Illumina sequencing, and PacBio sequencing.3. Alignment: Once the DNA fragments have beensequenced, they need to be aligned to a reference genome. This process involves identifying the positions in the reference genome where the DNA fragments match.4. Variant calling: Once the DNA fragments have been aligned, variants can be called. Variants are changes in the DNA sequence that can be caused by mutations, insertions, or deletions.5. Annotation: The final step is to annotate the variants. This involves identifying the genes and transcripts that are affected by the variants.Chinese Answer:DNA序列分析算法流程。

The complexity of stochastic sequencesWolfgang MerkleRuprecht-Karls-Universit¨a t HeidelbergInstitut f¨u r InformatikIm Neuenheimer Feld294D-69120Heidelberg,Germanymerkle@math.uni-heidelberg.deAbstractWe observe that known results on the Kolmogorov com-plexity of prefixes of effectively stochastic sequences extend to corresponding random sequences.First,there are re-cursively random random sequences such that for any non-decreasing and unbounded computable function and for almost all,the uniform complexity of the length prefix of the sequence is bounded by.Second,a similar re-sult with bounds of the form holds for partially-recursive random sequences.Furthermore,we show that there is no Mises-Wald-Church stochastic sequence such that the prefixes of the sequence have Kolmogorov complexity O.This re-sult implies a sharp bound for the complexity of the prefixes of Mises-Wald-Church stochastic and of partially-recursive random sequences.As an immediate corollary to our re-sults,we obtain the known separation of the classes of re-cursively random and of Mises-Wald-Church stochastic se-quences.1.IntroductionIt is well-known that there are effectively stochastic se-quences such that all prefixes of the sequence have rather low Kolmogorov complexity[6,8,Exercise2.5.13and comments].We observe that these results extend to cor-responding random sequences.First,there are recursively random sequences such that for any nondecreasing and un-bounded computable function and for almost all,the uniform complexity of the length prefix of the sequence is bounded by.Second,a similar result with bounds of the form holds for partially-recursive random sequences.While it is known that the result for recursively random sequences cannot be extended to a constant in place of,the corresponding question for the result on partial-recursively random sets has been reported as being open in the monograph by Li and Vit´a nyi[8,Exercise2.5.14]forthe closely related case of partially-recursive stochastic se-quences.Theorem6,our main result,gives a negative an-swer to the question in both cases.This result implies asharp bound for the complexity of the prefixes of partially-recursive random and of Mises-Wald-Church stochastic se-quences.There are such sequences such that for any nonde-creasing and unbounded computable function almost all prefixes of the sequence have Kolmogorov complexity of atmost;however,there are no such sequences suchthat the prefixes have Kolmogorov complexity O.Furthermore,as an immediate corollary of our results weobtain the known separation of the classes of recursivelyrandom and of Mises-Wald-Church stochastic sequences.2.NotationOur notation is mostly standard,for unexplained termsand further details we refer to the textbooks and surveyscited in the bibliography[2,3,5,8,10,12].All functions are meant to be total if not explicitly at-tributed as being partial;in particular,a computable func-tion is a partially computable function that is total.Unless explicitly stated otherwise,the term sequence refers to an infinite binary sequence.For a sequence ,we refer to as bit of the sequence.A word is afinite binary sequence.We write for thelength of a word;the empty word is denoted by.Anassignment is a function from a subset of to.Aword of length is identified in the natural way with anassignment on.For an assignment withfinite domain,the WORD ASSOCIATED WITH is.A sequence can be viewed as a function.Hence restricting a sequenceto a set yields an assignment with domain;in particular,restricting to yields a word,the prefix ofof length.3.Stochastic and random sequencesIn this section,we briefly review notation and concepts related to stochastic sequences,random sequences,and Kol-mogorov complexity;for more detailed accounts see the references[2,3,8,10].Stochastic sequences are defined in terms of selection rules.Intuitively speaking,a(monotonic)selection rule de-fines a process that scans the bits of a given sequence in the natural order where in addition the process has to de-termine for each place whether this place is to be selected. The decision whether a place shall be selected has to be determined before the corresponding bit is scanned and depends solely on the previously scanned bits through.Formally,a selection rule is a partial function that receives as input the wordand outputs a bit that indicates whether is to be selected. Definition1.A SELECTION RULE is a not necessarily total functionThe sequence that is SELECTED by a selection rule from a sequence is the subsequence of that contains exactly the bits such that.For given set and selection rule,the SEQUENCE OF SELECTED PLACES is the subsequence of the natural numbers that contains exactly the where is equal to(accordingly,the selected sequence is).Observe that the se-quence of selected places and the sequence selected from will both befinite in case is undefined on some prefix of. Definition2.A sequence is STOCHASTIC with respect to a given set of admissible selection rules if for every admissible selection rule either the sequence of selected places isfinite or the frequencies of’s in the prefixes of the selected sequence converge to,i.e.,(1)A sequence is M ISES-W ALD-C HURCH STOCHASTIC if it is stochastic with respect to the set of all partially computable selection rules.Stochastic sequences may lack certain statistical prop-erties that are associated with the intuitive understanding of randomness,for example,there are such sequences such that every prefix of the sequence contains more zeroes than ones[14].An attempt to overcome these deficiencies is to define concepts of random sequences in terms of betting games where a player bets on individual bits of an initially unknown sequence.Formally,a player can be identified with a BETTING STRATEGY,i.e.,a not necessarily total function that mapsthe information about the already scanned part of the un-known sequence to a bet on the place to be scanned next, where a bet is determined by a guess for the bit at this place, and a rational in the closed interval that is equal to the fraction of the current capital that shall be bet on this guess.For given betting strategy and initial capital,let be the corresponding PAYOFF FUNCTION or MARTINGALE, i.e.,is the initial capital and is the capital that has accumulated after thefirst bets when betting against an unknown sequence that has the word as a prefix.We assume that payoff is fair in the sense that after each indi-vidual bet the stake is either lost or doubled.Formally,for a martingale this amounts to the fairness condition4.The complexity of the prefixes of random se-quencesTheorem3below asserts that there are recursively and partial-recursively random sequences such that the uniform complexity of the prefixes of the sequences grows com-paratively slow.Similar results on stochastic sequences have been known before and are attributed to Loveland by Daley[6];see also Li and Vit´a nyi[8,Exercise2.5.13 and comments].These results on stochastic sequences are immediate consequences of Theorem3because sequences that are random with respect to computable and partially computable betting strategies are in particular stochastic with respect to selection rules that are computable and par-tially computable,respectively[4].The proof of Theo-rem3is stated in terms of betting strategies and is in fact less involved than the proofs for the more specific results on stochastic sequences given by Daley,which rely on an combinatorial algorithm for constructing stochastic sets,the LMS-algorithm[9].It is known that assertion(i)in Theorem3cannot be strengthened to a constant bound in place of;in fact, any sequence that satisfies such a constant bound is an in-finite branch of a recursively enumerable tree of constant width and is thus computable.The question of whether in assertion(ii)about partial-recursively random sets the fac-tor can be replaced by a constant has been reported as being open in the monograph by Li and Vit´a nyi[8,Ex-ercise2.5.14]for the case of partially-recursive stochastic sequences,which form a proper superclass of the partially-recursive random sequences.Theorem6below gives a neg-ative answer to this question.Theorem3.Let F be the class of all computable functions from to that are nondecreasing and unbounded.(i)There is a recursively random sequence such thatfor all F and almost all,C(ii)There is a partial-recursively random sequence such that for all F and almost all,CProof.Let be the standard effective enumer-ation of the partial recursive function from to and let be an appropriate effective enumeration of all partially computable martingales with initial capital. Proof of(i):For,letF is total Furthermore,let and for all letand for all Consider the following non-effective construction of a set,which is done in stages.During stage, the restriction of to the interval is determined by di-agonalizing against an appropriate weighted sum of the martingales in.More precisely,letfor all and any in.(3) For in there is nothing to prove because is just. In the induction step we distinguish two cases.In case is not minimum in an interval,the induction step is imme-diate because on each individual interval the martingaleis nonincreasing by construction of.In case is mini-mum in some interval,we letand obtainlength and that given access to these two sets,the con-struction up to and including stage can be simulated effec-tively;in fact,there is an effective procedure that given computes the restriction of to the union of the intervals trough.This procedure can be adjusted to output the length prefix of on input whenever is in one of the intervals through.In particular,we have forsome constant,for all,and any in,CAssertion(i)follows because by choice of the,for any in F we have for almost all and all in,Proof of(ii):The construction is similar to the one given for assertion(i)and we just indicate the necessary changes. The martingale against which we diagonalize during stage is now a convex sum over all with,except that on input we omit all the where is undefined for some prefix of.In order to be able to effectively simulate the construction up to and including stage,in worst case this requires the information about places at which one or more of the betting strategies are not defined.So, in order to effectively simulate the construction up to the definition of where is in interval,it suffices to supply numbers less than or equal to plus the set. Coding this information requires not more that bits, i.e.,requires at most bits for all F and almost all.Remark4.Up to an additive constant,the Kolmogorov complexity C and the uniform complexity C of a word of length differ at most by.For a sketch of proof,consider the additively optimal ref-erence Turing machines that have been used when defining Kolmogorov complexity and uniform complexity.A code for a word with respect to one of these machines can be transformed into a code for with respect to the other ma-chine by adding somefinite information about how the in-formation given by is to be used,plus,in case one trans-forms a code for the latter to a code for the former reference Turing machine,some information about the length of.Remark4shows that when considering bounds of the form O or for unbounded,usually it will not be necessary to distinguish between Kolmogorov complexity and uniform complexity.Accordingly,in what follows we will only consider Kolmogorov complexity;for a start,we rephrase assertion(ii)in Theorem3in terms of Kolmogorov complexity.Corollary5.Let F be the class of all computable functions from to that are nondecreasing and unbounded.There is a partial-recursively random sequence such that for all F and almost all,C(4) Proof.Let be a sequence according to assertion(ii)in Theorem3.Fix any in F.Then also the functionis in F,hence by choice of we have for almost all, CBy Remark4,the latter inequality implies(4)for all suffi-ciently large.Can the factor in Corollary5be improved to a con-stant,i.e.,are there partial-recursively random sequences where for almost all or,equivalently,for all,the length prefix has complexity O?The next theorem gives a negative answers to this question;sequences of such low complexity cannot even be found in the more compris-ing class of Mises-Wald-Church stochastic sequences. Theorem6.Let be a sequence such that for some natu-ral number and all,C(5) Then is not Mises-Wald-Church stochastic.Proof.Let.Fix an appropriate computable sequence where all the are multiples of and such that and for all,(6) Divide each interval into consecutive,non-overlapping subintervalsof lengthspeaking,tries to select just places where the correspond-ing bit is.For all,let be the assumed enumer-ation of and,for the sake of simplicity,assume that the enumeration is without repetitions.Pick such that is in for all.Both selection rules select only num-bers in intervals of the form where;on entering such an interval,lets and starts scanning the num-bers in the interval.Assuming that the restriction of tois given by,the selection rule selects the number if and only if the corresponding bit of is.This is done until either the end of the interval is reached or one of the scanned bits differs from the corresponding bit of;in the latter case,the index is incremented and the procedure it-erates by scanning the remaining bits.Observe that is always defined because iteration is only reached in case the true word is not among trough.By construction,for all,every number in inter-val is selected by either or.For the scope of this proof,say a number is selected correctly if it is selected by and the corresponding bit is indeed.Then in each interval there are at most numbers that are selected incorrectly.Hence by assumption,for infinitely many,there at least numbers in the interval that are selected correctly,and thus for some and infinitely many,the selection rule selects among the numbers in at least numbers correctly and at most num-bers incorrectly;moreover,by(6)there are at most numbers that could have been selected before entering the interval.Hence up to and including each such interval, the selection rule selects at least numbers correctly and at most numbers incorrectly,i.e.,witnesses that is not Mises-Wald-Church stochastic.It remains to argue that for some,there is indeed a pro-cedure as assumed above,i.e.,which enumerates sets that satisfy(i)and(ii).For all,let be the word that is associated to the restriction of to the interval and letand CThen is in for almost all.Due to(5)and be-cause follows by choice of the, we haveCi.e.,there is a word of length at most from which the reference Turing machine computes the restric-tion of to the intervals through.By prefixing with the string,which has length of at most,we obtain a code from which some Turing machine that does not depend on computes the restriction of to.This implies that up to an additive constant for all holdsC hence by choice of,the word is in for almost all.In order to obtain sets as required,for all andfor,letand there are at leastwords such that There is a Turing machine that on input enumerates,hence there is a Turing machine that given the indicesand and the word,enumerates the set;i.e.,for any the sets satisfy the condition on enumerability and it suffices to show that(i)and(ii)are true for some.For a start,observe that in case(ii)is not satisfied forsome,then condition(i)is satisfied with replacedby.Indeed,if(ii)is false,then for almost allthere are at least words in,where each of thesewords can be extended by at least words to a word in.Consequently,for each such there are at least words that ex-tend to a word in,i..e.,for almost all,theword is in.Condition(i)is satisfied for,so if(ii)is satis-fied,too,we are done by just letting.Otherwise, by the discussion in the preceding paragraph,condition(i) is satisfied for.Now we can iterate the argument; if(ii)is satisfied for,we are done by letting while,otherwise,condition(i)holds for.This way we proceed inductively and it remains to argue that it cannot be that(ii)is false for.Assuming the latter, for almost all there at least many assignments on that can be extended in ways to a word in,thus for all sufficiently large and some constant,Mises-Wald-Church stochastic but not recursively random can be obtained by a probabilistic argument where the bits of the sequence are chosen by independent tosses of biased coins where the probabilities for converge slowly enough to[7,11,13].5.AcknowledgementsWe are grateful to Klaus Ambos-Spies,Nicolai Vereshchagin,and Paul Vit´a nyi for helpful discussions. References[1]K.Ambos-Spies.Algorithmic randomness revisited.InB.McGuinness(ed.),Language,Logic and Formaliza-tion of Knowledge.Coimbra Lecture and Proceedings ofa Symposium held in Siena in September1997,pages33–52,Bibliotheca,1998.[2]K.Ambos-Spies and A.Kuˇc era.Randomness in Com-putability Theory.In P.Cholak et al.(eds.),Computabil-ity Theory:Current Trends and Open Problems,Con-temporary Mathematics257:1–14,American Mathemat-ical Society,2000.[3]K.Ambos-Spies and E.Mayordomo.Resource-bounded balanced genericity,stochasticity and weak ran-domness.In Complexity,Logic,and Recursion Theory, Marcel Dekker,Inc,1997.[4]K.Ambos-Spies, E.Mayordomo,Y.Wang,andX.Zheng.Resource-bounded measure and random-ness.In C.Puech and R.Reischuk(eds.),13th An-nual Symposium on Theoretical Aspects of Computer Science,STACS’96,Lecture Notes in Computer Science 1046:63–74,Springer,1997.[5]J.L.Balc´a zar,J.D´ıaz and J.Gabarr´o.Structural Com-plexity,Vol.I and II.Springer,1995and1990.[6]R.P.Daley.Minimal-program complexity of pseudo-recursive and pseudo-random sequences.Mathematical Systems Theory,9:83–94,1975.[7]M.van Lambalgen.Random sequences,Doctoral dis-sertation,University of Amsterdam,Amsterdam,1987.[8]M.Li and P.Vit´a nyi An Introduction to Kol-mogorov Complexity and Its Applications,second edi-tion,Springer,1997.[9]D.W.Loveland.A new interpretation of the von Mises’concept of random sequence.Zeitschrift f¨u r mathematis-che Logik und Grundlagen der Mathematik,12:279–294, 1966.[10]J.H.Lutz.The quantitative structure of exponentialtime.In Hemaspaandra,L.A.and A.L.Selman,ed-itors,Complexity theory retrospective II,p.225–260, Springer-Verlag,1997.[11]W.Merkle.The Kolmogorov-Loveland stochastic se-quences are not closed under selecting subsequences.In International Colloquium on Automata,Languages and Programming2002,LNCS2380:390-400,Springer, 2002.[12]P.Odifreddi.Classical Recursion Theory.V ol.I.North-Holland,Amsterdam,1989.[13]A.Kh.Shen’.On relations between different algorith-mic definitions of randomness.Soviet Mathematics Dok-lady,38:316–319,1988.[14]J.Ville,´Etude Critique de la Notion de Collectif.Gauthiers-Villars,Paris,1939.。

llamaforsequenceclassification 的使用LlamaForSequenceClassification is a powerful tool used in natural language processing tasks to classify and analyze sequences of text data. In this article, we will explore the features and functionalities of LlamaForSequenceClassification and learn how to use it effectively in various applications.1. Introduction to LlamaForSequenceClassification: LlamaForSequenceClassification is a library developed by Natural Language Processing (NLP) experts and researchers. It is built on top of the popular Hugging Face's Transformers library and is specifically designed for sequence classification tasks. Sequence classification refers to the process of categorizing a sequence of text into predefined classes or categories.2. Key Features of LlamaForSequenceClassification: LlamaForSequenceClassification offers several key features that make it an ideal choice for sequence classification tasks:a. Pretrained Models: LlamaForSequenceClassification provides access to pre-trained models that have been trained on large-scale datasets. These models have already learned the linguistic patternsand structures of the text, making them highly effective for classification tasks.b. Fine-tuning Capabilities: LlamaForSequenceClassification allows users to fine-tune the pretrained models using their own domain-specific or task-specific datasets. This enables the models to learn and adapt to the specific classification requirements, resulting in improved performance and accuracy.c. Support for Various Models: LlamaForSequenceClassification supports a wide range of models, including popular architectures like BERT (Bidirectional Encoder Representations from Transformers), RoBERTa, GPT (Generative Pre-trained Transformer), and more. This ensures flexibility in choosing the most suitable model for the specific task at hand.d. Efficient Tokenization: LlamaForSequenceClassification provides efficient tokenization of text data, which is a critical step in the preprocessing of NLP tasks. It breaks down the input text into tokens, allowing the models to process and understand the text at a granular level.e. State-of-the-art Performance: By leveraging the power of transformer-based architectures, LlamaForSequenceClassification achieves state-of-the-art performance in various sequence classification tasks. It has been widely adopted and recognized in both academia and industry for its effectiveness and accuracy.3. Getting Started with LlamaForSequenceClassification:Now that we understand the key features and benefits of LlamaForSequenceClassification, let's dive into how to use it step by step:Step 1: Install LlamaForSequenceClassification:Start by installing the LlamaForSequenceClassification library using pip, the Python package manager:pip install llamaforsequenceclassificationStep 2: Import the Required Libraries:Import the necessary libraries, including LlamaForSequenceClassification, torch, and transformers:import llamaforsequenceclassificationfrom llamaforsequenceclassification import LlamaForSequenceClassificationimport torchfrom transformers import RobertaTokenizerStep 3: Load the Pretrained Model:Load a pretrained model of your choice using LlamaForSequenceClassification. For example, let's load the RoBERTa model:model =LlamaForSequenceClassification.from_pretrained('roberta-base')Step 4: Tokenization:Tokenize your text data using the tokenizer provided by LlamaForSequenceClassification. For instance, let's tokenize a sentence:tokenizer = RobertaTokenizer.from_pretrained('roberta-base') text = "This is an example sentence."tokens = tokenizer.tokenize(text)Step 5: Encoding and Classification:Encode the tokenized text and classify it using the pretrained model:input_ids = tokenizer.encode(text, add_special_tokens=True) inputs = torch.tensor([input_ids])outputs = model(inputs)Step 6: Interpret the Output:Interpret the output of the model. Depending on your sequence classification task, you may need to apply additionalpost-processing steps to obtain the final classification results.4. Conclusion:LlamaForSequenceClassification is a powerful library that simplifies and accelerates sequence classification tasks in NLP. Its support for pre-trained models, fine-tuning capabilities, efficient tokenization, and state-of-the-art performance make it a valuable tool for both researchers and practitioners. By following the step-by-step guide provided in this article, you can start using LlamaForSequenceClassification to classify and analyze sequences of text with ease and accuracy.。

第一节语言的本质一、语言的普遍特征（Design Features）1.任意性 Arbitratriness：shu 和Tree都能表示“树”这一概念；同样的声音，各国不同的表达方式2.双层结构Duality：语言由声音结构和意义结构组成（the structure ofsounds and meaning）3.多产性productive: 语言可以理解并创造无限数量的新句子，是由双层结构造成的结果（Understand and create unlimited number withsentences）4.移位性 Displacemennt：可以表达许多不在场的东西，如过去的经历、将来可能发生的事情，或者表达根本不存在的东西等5.文化传播性 Cultural Transmission：语言需要后天在特定文化环境中掌握二、语言的功能（Functions of Language）1.传达信息功能 Informative：最主要功能The main function2.人际功能 Interpersonal：人类在社会中建立并维持各自地位的功能establish and maintain their identity3.行事功能 performative：现实应用——判刑、咒语、为船命名等Judge，naming，and curses4.表情功能 Emotive Function：表达强烈情感的语言，如感叹词/句exclamatory expressions5.寒暄功能 Phatic Communion：应酬话phatic language，比如“吃了没？”“天儿真好啊！”等等6.元语言功能 Metalingual Function：用语言来谈论、改变语言本身，如book可以指现实中的书也可以用“book这个词来表达作为语言单位的“书”三、语言学的分支1. 核心语言学 Core linguistic1)语音学 Phonetics：关注语音的产生、传播和接受过程，着重考察人类语言中的单音。

llamaforsequenceclassification 分类Llama for Sequence Classification: A Step-by-Step GuideIntroduction:In recent years, sequence classification has gained significant attention in various fields such as natural language processing, speech recognition, and bioinformatics. One popular approach that has shown promising results is the Llama algorithm. In this article, we will provide a step-by-step guide on how to effectively use Llama for sequence classification tasks. From understanding the concept to implementing the algorithm, let's dive into the world of Llama.Step 1: Understanding LlamaLlama stands for Long Short-Term Memory (LSTM) and Attention architecture. It combines the power of recurrent neural networks (RNNs) with attention mechanisms to learn dependencies and patterns in sequential data. Llama has proven to be highly effective in capturing long-term dependencies and achievingstate-of-the-art results in various sequence classification tasks.Step 2: Data PreparationTo apply Llama for sequence classification, we need to prepare our data by encoding sequences into numerical representations. This can be done using techniques like one-hot encoding, tokenization, or word embeddings, depending on the nature of the data. It is also essential to split our data into training, validation, and test sets to evaluate the model's performance accurately.Step 3: Building the Llama ModelNow that our data is ready, we can proceed with building the Llama model. The architecture consists of multiple LSTM layers followed by an attention layer and a dense layer for classification. The LSTM layers help capture the sequential information, while the attention layer allows the model to focus on relevant parts of the sequence. The dense layer produces the final classification output.Step 4: Training the Llama ModelWith our model architecture defined, it's time to train the Llama model on our training data. During the training process, the model learns to optimize its parameters based on a given loss function (usually cross-entropy for classification tasks) and minimizes the difference between predicted and actual labels. Training proceeds through multiple epochs, and the model adjusts its weights toimprove performance.Step 5: Model EvaluationOnce the training is complete, it's crucial to evaluate the Llama model's performance on the validation set. Metrics such as accuracy, precision, recall, and F1-score can be used to assess the model's effectiveness. By monitoring these metrics, we can tune hyperparameters and optimize the model accordingly.Step 6: Fine-tuning and OptimizationIf the validation results are not satisfying, we may need to fine-tune our Llama model. This can involve adjusting hyperparameters (e.g., learning rate, number of LSTM layers) or applying techniques like dropout or batch normalization to improve generalization and prevent overfitting.Step 7: Testing the Llama ModelOnce we are confident with the Llama model's performance, we can finally test it on unseen data, or the test set, to assess itsreal-world effectiveness. By evaluating metrics on this set, we can determine the model's ability to generalize to new sequences and compare its performance with other algorithms.Step 8: Deployment and ApplicationAfter successfully training and testing our Llama model, we can deploy it for real-world applications. Whether it's sentiment analysis, speech recognition, or DNA sequence classification, Llama can be deployed in various domains where sequence classification is required. The model can be integrated into existing systems or used to build standalone applications, helping automate decision-making processes.Conclusion:Llama, the Long Short-Term Memory and Attention architecture, is an effective algorithm for sequence classification. By understanding its concept, preparing data, building the model, training, evaluating, and optimizing it, we can harness the power of Llama in solving real-world problems that involve sequences. With its ability to capture long-term dependencies and attention to relevant parts of the sequence, Llama provides a promising and highly accurate approach to sequence classification tasks.。

数学专业英语－Sequences and SeriesSeries are a natural continuation of our study of functions. In the previous cha pter we found howto approximate our elementary functions by polynomials, with a certain error te rm. Conversely, one can define arbitrary functions by giving a series for them. We shall see how in the sections below.In practice, very few tests are used to determine convergence of series. Esse ntially, the comparision test is the most frequent. Furthermore, the most import ant series are those which converge absolutely. Thus we shall put greater emp hasis on these.Convergent SeriesSuppose that we are given a sequcnce of numbersa1,a2,a3…i.e. we are given a number a n, for each integer ｎ＞1.We form the sumsS n=a1+a2+…+a nIt would be meaningless to form an infinite suma1+a2+a3+…because we do not know how to add infinitely many numbers. However, if ou r sums S n approach a limit as n becomes large, then we say that the sum of our sequence converges, and we now define its sum to be that limit.The symbols∑a=1 ∞a nwill be called a series. We shall say that the series converges if the sums app roach a limit as n becomes large. Otherwise, we say that it does not converge, or diverges. If the seriers converges, we say that the value of the series is∑a=1∞=lim a→∞S n=lim a→∞(a1+a2+…+a n)In view of the fact that the limit of a sum is the sum of the limits, and other standard properties of limits, we get:THEOREM 1. Let{ a n}and { b n}(n=1,2,…)be two sequences and assume that the series∑a=1∞a n∑a=1∞b nconverge. Then ∑a=1∞(a n + b n ) also converges, and is equal to the sum of the two series. If c is a number, then∑a=1∞c a n=c∑a=1∞a nFinally, if s n=a1+a2+…+a n and t n=b1+b2+…+b n then∑a=1∞a n ∑a=1∞b n=lim a→∞s n t nIn particular, series can be added term by term. Of course , they cannot be multiplied term by term.We also observe that a similar theorem holds for the difference of two serie s.If a series ∑a n converges, then the numbers a n must approach 0 as n beco mes large. However, there are examples of sequences {an} for which the serie s does not converge, and yet lim a→∞a n=0Series with Positive TermsThroughout this section, we shall assume that our numbers a n are ＞0. Then t he partial sumsS n=a1+a2+…+a nare increasing, i.e.s1＜s2 ＜s3＜…＜s n＜s n+1＜…If they are approach a limit at all, they cannot become arbitrarily large. Thus i n that case there is a number B such thatS n< Bfor all n. The collection of numbers {s n} has therefore a least upper bound ,i.e. there is a smallest number S such thats n<Sfor all n. In that case , the partial sums s n approach S as a limit. In other wo rds, given any positive number ε>0, we haveS –ε< s n < Sfor all n .sufficiently large. This simply expresses the fact that S is the least o f all upper bounds for our collection of numbers s n. We express this as a theo rem.THEOREM 2. Let{a n}(n=1,2,…)be a sequence of numbers>0 and letS n=a1+a2+…+a nIf the sequence of numbers {s n} is bounded, then it approaches a limit S , wh ich is its least upper bound.Theorem 3 gives us a very useful criterion to determine when a series with po sitive terms converges:THEOREM 3. Let∑a=1∞a n and∑a=1∞b n be two series , with a n>0 for all n an d b n>0 for all n. Assume that there is a number c such thata n< cb nfor all n, and that∑a=1∞b n converges. Then ∑a=1∞a n converges, and∑a=1∞a n ≤c∑a=1∞b nPROOF. We havea1+…+a n≤cb1+…+cb n=c(b1+…+b n)≤c∑a=1∞b nThis means that c∑a=1∞b n is a bound for the partial sums a1+…+a n.The least u pper bound of these sums is therefore ≤c∑a=1∞b n, thereby proving our theore m.Differentiation and Intergration of Power Series.If we have a polynomiala0+a1x+…+a n x nwith numbers a0,a1,…,a n as coefficients, then we know how to find its derivati ve. It is a1+2a2x+…+na n x n–1. We would like to say that the derivative of a ser ies can be taken in the same way, and that the derivative converges whenever the series does.THEOREM 4. Let r be a number >0 and let ∑a n x n be a series which conv erges absolutely for ∣x∣<r. Then the series ∑na n x n-1also converges absolutel y for∣x∣<r.A similar result holds for integration, but trivially. Indeed, if we have a series ∑a=1∞a n x n which converges absolutely for ∣x∣<r, then the series∑a=1∞a n/n+1 x n+1=x∑a=1∞a n x n∕n+1has terms whose absolute value is smaller than in the original series.The preceding result can be expressed by saying that an absolutely converge nt series can be integrated and differentiated term by term and and still yields an absolutely convergent power series.It is natural to expect that iff (x)=∑a=1∞a n x n,then f is differentiable and its derivative is given by differentiating the series t erm by term. The next theorem proves this.THEOREM 5. Letf (x)=∑a=1∞a n x nbe a power series, which converges absolutely for∣x∣<r. Then f is differentia ble for ∣x∣<r, andf′(x)=∑a=1∞na n x n-1.THEOREM 6. Let f (x)=∑a=1∞a n x n be a power series, which converges abso lutely for ∣x∣<r. Then the relation∫f (x)d x=∑a=1∞a n x n+1∕n+1is valid in the interval ∣x∣<r.We omit the proofs of theorems 4,5 and 6.Vocabularysequence 序列positive term 正项series 级数alternate term 交错项approximate 逼近,近似 partial sum 部分和elementary functions 初等函数 criterion 判别准则(单数)section 章节 criteria 判别准则(多数)convergence 收敛(名词) power series 幂级数convergent 收敛(形容词) coefficient 系数absolute convergence 绝对收敛 Cauchy sequence 哥西序列diverge 发散radius of convergence 收敛半径term by term 逐项M-test M—判别法Notes1. series一词的单数和复数形式都是同一个字.例如:One can define arbitrary functions by giving a series for them(单数)The most important series are those which converge absolutely(复数)2. In view of the fact that the limit of a sum of the limits, and other standard properties of limits, we get:Theorem 1…这是叙述定理的一种方式: 即先将事实说明在前面,再引出定理. 此句用in view of the fact that 说明事实,再用we get 引出定理.3. We express this as a theorem.这是当需要证明的事实已再前面作了说明或加以证明后,欲吧已证明的事实总结成定理时,常用倒的一个句子,类似的句子还有(参看附录Ⅲ):We summarize this as the following theorem; Thus we come to the following theorem等等.4. The least upper bound of these sums is therefore ≤c∑a=1∞b n, thereby proving our theorem.最一般的定理证明格式是”给出定理…定理证明…定理证毕”,即thereby proving our theorem;或we have thus proves the theorem或This completes the proof等等作结尾(参看附录Ⅲ).5. 本课文使用较多插入语.数学上常见的插入语有:conversely; in practice; essentially; in particular; ind eed; in other words; in short; generally speaking 等等.插入语通常与句中其它成份没有语法上的关系,一般用逗号与句子隔开,用来表示说话者对句子所表达的意思的态度.插入语可以是一个词,一个短语或者一个句子.ExerciseⅠ. Translate the following exercises into Chinese:1. In exercise 1 through 4,a sequence f (n) is defined by the formula given. In each case, (ⅰ)Determine whether the sequence (the formulae are omitted).2. Assume f is a non–negative function defined for all x>1. Use the methodsuggested by the proof of the integral test to show that∑k=1n-1f(k)≤∫1n f(x)d x ≤∑k=2n f(k)Take f(x)=log x and deduce the inequalitiesc•n n•c-n< n！<c•n n+1•c-nⅡ. The proof of theorem 4 is given in English as follows(Read the proof through and try to learn how a theorem is proved, then translate this proof into Chinese ):Proof of theorem 4 Since we are interested in the absolute convergence. We may assume that a n>0 for all n. Let 0<x<r, and let c be a number such that x<c<r. Recall that lim a→∞n1/n=1.We may write n a n x n =a n(n1/n x)n. Then for all n sufficiently large, we conclude that n1/n x<c. This is because n1/n comes arbitrarily close to x and x<c. Hence for all n sufficiently large, we have na n x n<a n c n. We can then compare the series ∑nax n with∑a n c n to conclude that∑na n x n converges. Since∑na n x n-1=1n/x∑na n x n, we have proved theorem 4.Ⅲ. Recall from what you have learned in Calculus about (ⅰ) Cauchy sequence and (ⅱ) the radius of c onvergence of a power series.Now give the definitions of these two terms respectively.Ⅳ. Translate the following sentences into Chinese:1. 一旦我们能证明,幂级数∑a n z n在点z=z1收敛,则容易证明,对每一z1∣z∣<∣z1∣,级数绝对收敛;2. 因为∑a n z n在z=z1收敛,于是,由weierstrass的M—判别法可立即得到∑a n z n在点z,∣z∣<z1的绝对收敛性;3. 我们知道有限项和中各项可以重新安排而不影响和的值,但对于无穷级数,上述结论却不总是真的。