WAITING TIMES FOR CLUMPS OF PATTERNS AND FOR STRUCTURED MOTIFS IN

Notice shape of difference curve – position/shape/intensity errors
5
Errors & parameters?
position – lattice parameters, zero point (not common)
- other systematic effects – sample shift/offset shape – profile coefficients (GU, GV, GW, LX, LY, etc. in GSAS) intensity – crystal structure (atom positions & thermal parameters)
9
So how does Rietveld refinement work?
Rietveld Minimize
MR w(Io Ic )2
Io
Exact overlaps - symmetry
Incomplete overlaps
SIc
Residuals:
Rwp
w(I o Ic )2
wI
c2
Least-squares cycles
False minimum
True minimum – “global” minimum
parameter c2 surface shape depends on parameter suite
3
Fluoroapatite start – add model (1st choose lattice/sp. grp.)
c
5i
ig
i
i1
18

生物信息学主要英文术语及释义生物信息学主要英文术语及释义Abstract Abstract Syntax Syntax Syntax Notation Notation Notation (ASN.l)(ASN.l)（NCBI 发展的许多程序，如显示蛋白质三维结构的Cn3D等所使用的内部格式）等所使用的内部格式） A A language language language that that that is is is used used used to to to describe describe describe structured structured structured data data data types types types formally, formally, formally, Within Within Within bioinformatits,it bioinformatits,it bioinformatits,it has has been been used used used by by by the the the National National National Center Center Center for for for Biotechnology Biotechnology Biotechnology Information Information Information to to to encode encode encode sequences, sequences, sequences, maps, maps, taxonomic information, molecular structures, and biographical information in such a way that it can be easily accessed and exchanged by computer software. Accession number （记录号）（记录号）A unique identifier that is assigned to a single database entry for a DNA or protein sequence. Affine gap penalty （一种设置空位罚分策略）（一种设置空位罚分策略）（一种设置空位罚分策略） A gap penalty score that is a linear function of gap length, consisting of a gap opening penalty and a a gap gap gap extension extension extension penalty penalty penalty multiplied multiplied multiplied by by by the the the length length length of of of the the the gap. gap. gap. Using Using Using this this this penalty penalty penalty scheme scheme scheme greatly greatly enhances enhances the the the performance performance performance of of of dynamic dynamic dynamic programming programming programming methods methods methods for for for sequence sequence sequence alignment. alignment. alignment. See See See also also Gap penalty. Algorithm （算法）（算法）A A systematic systematic systematic procedure procedure procedure for solving for solving a a problem problem problem in in in a a a finite finite finite number number number of of of steps, steps, steps, typically typically typically involving involving involving a a repetition of operations. Once specified, an algorithm can be written in a computer language and run as a program. Alignment （联配/比对/联配）联配）Refers to the procedure of comparing two or more sequences by looking for a series of individual characters or character patterns that are in the same order in the sequences. Of the two types of alignment, alignment, local local local and and and global, global, global, a a a local local local alignment alignment alignment is is is generally generally generally the the the most most most useful. useful. useful. See See See also also also Local Local Local and and Global alignments. Alignment score （联配/比对/联配值）联配值）An algorithmically computed score based on the number of matches, substitutions, insertions, and deletions deletions (gaps) (gaps) (gaps) within within within an an an alignment. alignment. alignment. Scores Scores Scores for for for matches matches matches and and and substitutions substitutions substitutions Are Are Are derived derived derived from from from a a scoring scoring matrix matrix matrix such such such as as as the the the BLOSUM BLOSUM BLOSUM and and and P AM P AM matrices matrices matrices for for for proteins, proteins, proteins, and and and aftine aftine aftine gap gap gap penalties penalties suitable for the matrix are chosen. Alignment scores are in log odds units, often bit units (log to the the base base base 2). 2). 2). Higher Higher Higher scores scores scores denote denote denote better better better alignments. alignments. alignments. See See See also also also Similarity Similarity Similarity score, score, score, Distance Distance Distance in in sequence analysis. Alphabet （字母表）（字母表）The total number of symbols in a sequence-4 for DNA sequences and 20 for protein sequences. Annotation （注释）（注释）The The prediction prediction prediction of of of genes genes genes in in in a a a genome, genome, genome, including including including the the the location location location of of of protein-encoding protein-encoding protein-encoding genes, genes, genes, the the sequence of the encoded proteins, anysignificantmatches to other Proteins of known function, and the location of RNA-encoding genes. Predictions are based on gene models; e.g., hidden Markov models models of of of introns introns introns and and and exons exons exons in in in proteins proteins proteins encoding encoding encoding genes, genes, genes, and and and models models models of of of secondary secondary secondary structure structure structure in in RNA. Anonymous FTP （匿名FTP ）When a FTP service allows anyone to log in, it is said to provide anonymous FTP ser-vice. A user can can log log log in in in to to to an an an anonymous anonymous anonymous FTP FTP FTP server server server by by by typing typing typing anonymous anonymous anonymous as as the the user name user name and and his E-mail his E-mail address as a password. Most Web browsers now negotiate anonymous FTP logon without asking the user for a user name and password. See also FTP. ASCII The American Standard Code for Information Interchange (ASCII) encodes unaccented letters a-z, A-Z, A-Z, the the the numbers numbers numbers O-9, O-9, O-9, most most most punctuation punctuation punctuation marks, marks, marks, space, space, space, and and and a a a set set set of of of control control control characters characters characters such such such as as carriage carriage return return return and and and tab. tab. tab. ASCII ASCII ASCII specifies specifies specifies 128 128 128 characters characters characters that that that are are are mapped mapped mapped to to to the the the values values values O-127. O-127. ASCII ASCII tiles tiles tiles are are are commonly commonly commonly called called called plain plain plain text, text, text, meaning meaning meaning that that that they they they only only only encode encode encode text text text without without without extra extra markup. BAC clone （细菌人工染色体克隆）（细菌人工染色体克隆）Bacterial Bacterial artificial artificial artificial chromosome chromosome chromosome vector vector vector carrying carrying carrying a a a genomic genomic genomic DNA DNA DNA insert, insert, insert, typically typically typically 100100100––200 200 kb. kb. Most of the large-insert clones sequenced in the project were BAC clones. Back-propagation （反向传输）（反向传输）When training feed-forward neural networks, a back-propagation algorithm can be used to modify the network weights. After each training input pattern is fed through the network, the network’s output output is is is compared compared compared with with with the the the desired desired desired output output output and and and the the the amount amount amount of of of error error error is is is calculated. calculated. calculated. This This This error error error is is back-propagated through the network by using an error function to correct the network weights. See also Feed-forward neural network. Baum-Welch algorithm （Baum-Welch 算法）算法）An expectation maximization algorithm that is used to train hidden Markov models. Baye ’s rule （贝叶斯法则）（贝叶斯法则）Forms Forms the the the basis basis basis of of of conditional conditional conditional probability probability probability by by by calculating calculating calculating the the the likelihood likelihood likelihood of of of an an an event event event occurring occurring based on the history of the event and relevant background information. In terms of two parameters A and B, the theorem is stated in an equation: The condition-al probability of A, given B, P(AIB), is is equal equal equal to to to the the the probability probability probability of of of A, P(A), A, P(A), times times the the the conditional conditional conditional probability probability probability of of of B, B, B, given given given A, P(BIA), A, P(BIA), divided by the probability of B, P(B). P(A) is the historical or prior distribution value of A, P(BIA) is a new prediction for B for a particular value of A, and P(B) is the sum of the newly predicted values for B. P(AIB) is a posterior probability, representing a new prediction for A given the prior knowledge of A and the newly discovered relationships between A and B. Bayesian analysis （贝叶斯分析）（贝叶斯分析）A A statistical statistical statistical procedure procedure procedure used used used to to to estimate estimate estimate parameters parameters parameters of of of an an an underlyingdistribution underlyingdistribution underlyingdistribution based based based on on on an an observed distribution. See a lso Baye’s rule.Biochips （生物芯片）（生物芯片）Miniaturized arrays of large numbers of molecular substrates, often oligonucleotides, in a defined pattern. They are also called DNA microarrays and microchips. Bioinformatics （生物信息学）（生物信息学）The merger of biotechnology and information technology with the goal of revealing new insights and and principles principles principles in in in biology. biology. biology. /The /The /The discipline discipline discipline of of of obtaining obtaining obtaining information information information about about about genomic genomic genomic or or or protein protein sequence sequence data. data. data. This This This may may may involve involve involve similarity similarity similarity searches searches searches of of of databases, databases, databases, comparing comparing comparing your your your unidentified unidentified sequence sequence to to to the the the sequences sequences sequences in in in a a a database, database, database, or or or making making making predictions predictions predictions about about about the the the sequence sequence sequence based based based on on current current knowledge knowledge knowledge of of of similar similar similar sequences. sequences. sequences. Databases Databases Databases are are are frequently frequently frequently made made made publically publically publically available available through the Internet, or locally at your institution. Bit score （二进制值/ Bit 值）值）The value S' is derived from the raw alignment score S in which the statistical properties of the scoring system used have been taken into account. Because bit scores have been normalized with respect respect to to to the the the scoring scoring scoring system, system, system, they they they can can can be be be used used used to to to compare compare compare alignment alignment alignment scores scores scores from from from different different searches. Bit units From information theory, a bit denotes the amount of information required to distinguish between two two equally equally equally likely likely likely possibilities. possibilities. possibilities. The The The number number number of of of bits bits bits of of of information, information, information, AJ, AJ, AJ, required required required to to to convey convey convey a a message that has A4 possibilities is log2 M = N bits. BLAST （基本局部联配搜索工具，一种主要数据库搜索程序）（基本局部联配搜索工具，一种主要数据库搜索程序）Basic Local Alignment Search Tool. A set of programs, used to perform fast similarity searches. Nucleotide sequences can be compared with nucleotide sequences in a database using BLASTN, for for example. example. example. Complex Complex Complex statistics statistics statistics are are are applied applied applied to to to judge judge judge the the the significance significance significance of of of each each each match. match. match. Reported Reported sequences may be homologous to, or related to the query sequence. The BLASTP program is used to search a protein database for a match against a query protein sequence. There are several other flavours of BLAST. BLAST2 is a newer release of BLAST. Allows for insertions or deletions in the sequences being aligned. Gapped alignments may be more biologically significant. Block （蛋白质家族中保守区域的组块）（蛋白质家族中保守区域的组块）Conserved Conserved ungapped ungapped ungapped patterns patterns patterns approximately approximately approximately 3-60 3-60 3-60 amino amino amino acids acids acids in in in length length length in in in a a a set set set of of of related related proteins. BLOSUM matrices （模块替换矩阵，一种主要替换矩阵）（模块替换矩阵，一种主要替换矩阵）An alternative to PAM tables, BLOSUM tables were derived using local multiple alignments of more distantly related sequences than were used for the PAM matrix. These are used to assess the similarity of sequences when performing alignments. Boltzmann distribution （Boltzmann 分布）分布）Describes Describes the the the number number number of of of molecules molecules molecules that that that have have have energies energies energies above above above a a a certain certain certain level, level, level, based based based on on on the the Boltzmann gas constant and the absolute temperature.Boltzmann probability function(Boltzmann 概率函数) See Boltzmann distribution. Bootstrap analysis A method for testing how well a particular data set fits a model. For example, the validity of the branch branch arrangement arrangement arrangement in in in a a a predicted predicted predicted phylogenetic phylogenetic phylogenetic tree tree tree can can can be be be tested tested tested by by by resampling resampling resampling columns columns columns in in in a a multiple multiple sequence sequence sequence alignment alignment alignment to to to create create create many many many new new new alignments. alignments. alignments. The The The appearance appearance appearance of of of a a a particular particular branch in trees generated from these resampled sequences can then be measured. Alternatively, a sequence sequence may may may be be be left left left out out out of of of an an an analysis analysis analysis to to to deter-mine deter-mine deter-mine how how how much much much the the the sequence sequence sequence influences influences influences the the results of an analysis. Branch length （分支长度）（分支长度）In sequence analysis, the number of sequence changes along a particular branch of a phylogenetic tree. CDS or cds （编码序列）（编码序列）（编码序列） Coding sequence. Chebyshe, d inequality The probability that a random variable exceeds its mean is less than or equal to the square of 1 over the number of standard deviations from the mean. Clone （克隆）（克隆）Population of identical cells or molecules (e.g. DNA), derived from a single ancestor. Cloning V ector （克隆载体）（克隆载体）A molecule that carries a foreign gene into a host, and allows/facilitates the multiplication of that gene in a host. When sequencing a gene that has been cloned using a cloning vector (rather than by by PCR), PCR), PCR), care care care should should should be be be taken taken taken not not not to to to include include include the the the cloning cloning cloning vector vector vector sequence sequence sequence when when when performing performing similarity searches. Plasmids, cosmids, phagemids, Y ACs and PACs are example types of cloning vectors. Cluster analysis （聚类分析）（聚类分析） A method for grouping together a set of objects that are most similar from a larger group of related objects. The relationships are based on some criterion of similarity or difference. For sequences, a similarity or distance score or a statistical evaluation of those scores is used. Cobbler A single sequence that represents the most conserved regions in a multiple sequence alignment. The BLOCKS server uses the cobbler sequence to perform a database similarity search as a way to reach sequences that are more divergent than would be found using the single sequences in the alignment for searches. Coding system (neural networks) Regarding Regarding neural neural neural networks, networks, networks, a a a coding coding coding system system system needs needs needs to to to be be be designed designed designed for for for representing representing representing input input input and and output. output. The The The level level level of of of success success success found found found when when when training training training the the the model model model will will will be be be partially partially partially dependent dependent dependent on on on the the quality of the coding system chosen. Codon usageAnalysis of the codons used in a particular gene or organism. COG （直系同源簇）（直系同源簇）Clusters of orthologous groups in a set of groups of related sequences in microorganism and yeast (S. cerevisiae). These groups are found by whole proteome comparisons and include orthologs and paralogs. See also Orthologs and Paralogs. Comparative genomics （比较基因组学）（比较基因组学）A comparison of gene numbers, gene locations, and biological functions of genes in the genomes of diverse organisms, one objective being to identify groups of genes that play a unique biological role in a particular organism. Complexity (of an algorithm)（算法的复杂性）（算法的复杂性）Describes the number of steps required by the algorithm to solve a problem as a function of the amount of data; for example, the length of sequences to be aligned. Conditional probability （条件概率）（条件概率）The The probability probability probability of of of a a a particular particular particular result result result (or (or (or of of of a a a particular particular particular value value value of of of a a a variable) variable) variable) given given given one one one or or or more more events or conditions (or values of other variables). Conservation （保守）（保守）Changes at a specific position of an amino acid or (less commonly, DNA) sequence that preserve the physico-chemical properties of the original residue. Consensus （一致序列）（一致序列）A A single single single sequence sequence sequence that that that represents, represents, represents, at at at each each each subsequent subsequent subsequent position, position, position, the the the variation variation variation found found found within within corresponding columns of a multiple sequence alignment. Context-free grammars A A recursive recursive recursive set set set of of of production production production rules rules rules for for for generating generating generating patterns patterns patterns of of of strings. strings. strings. These These These consist consist consist of of of a a a set set set of of terminal characters that are used to create strings, a set of nonterminal symbols that correspond to rules and act as placeholders for patterns that can be generated using terminal characters, a set of rules for replacing nonterminal symbols with terminal characters, and a start symbol. Contig （序列重叠群/拼接序列）拼接序列）A A set set set of of of clones clones clones that that that can can can be be be assembled assembled assembled into into into a a a linear linear linear order. order. order. A A A DNA DNA DNA sequence sequence sequence that that that overlaps overlaps overlaps with with another contig. The full set of overlapping sequences (contigs) can be put together to obtain the sequence for a long region of DNA that cannot be sequenced in one run in a sequencing assay. Important in genetic mapping at the molecular level. CORBA （国际对象管理协作组制定的使OOP 对象与网络接口统一起来的一套跨计算机、操作系统、程序语言和网络的共同标准）作系统、程序语言和网络的共同标准）The The Common Common Common Object Object Object Request Request Request Broker Broker Broker Architecture Architecture Architecture (CORBA) (CORBA) (CORBA) is is is an an an open open open industry industry industry standard standard standard for for working working with with with distributed distributed distributed objects, objects, objects, developed developed developed by by by the the the Object Object Object Management Management Management Group. CORBA allows Group. CORBA allows the interconnection of objects and applications regardless of computer language, machine architecture, or geographic location of the computers. Correlation coefficient （相关系数）（相关系数）A numerical measure, falling between - 1 and 1, of the degree of the linear relationship between two variables. A positive value indicates a direct relationship, a negative negative value value value indicates indicates indicates an an an inverse inverse inverse relationship, relationship, relationship, and and and the the the distance distance distance of of of the the the value value value away away away from from from zero zero indicates the strength of the relationship. A value near zero indicates no relationship between the variables. Covariation (in sequences)（共变）（共变）Coincident change at two or more sequence positions in related sequences that may influence the secondary structures of RNA or protein molecules. Coverage (or depth) （覆盖率（覆盖率/厚度）厚度）The average number of times a nucleotide is represented by a high-quality base in a collection of random raw sequence. Operationally, a 'high-quality base' is defined as one with an accuracy of at least 99% (corresponding to a PHRED score of at least 20). Database （数据库）（数据库）A A computerized computerized computerized storehouse storehouse storehouse of of of data data data that that that provides provides provides a a a standardized standardized standardized way way way for for for locating, locating, locating, adding, adding, removing, and changing data. See also Object-oriented database, Relational database. Dendogram A form of a tree that lists the compared objects (e.g., sequences or genes in a microarray analysis) in a vertical order and joins related ones by levels of branches extending to one side of the list. Depth （厚度）（厚度）See coverage Dirichlet mixtures Defined Defined as as as the the the conjugational conjugational conjugational prior prior prior of of of a a a multinomial multinomial multinomial distribution. distribution. distribution. One One One use use use is is is for for for predicting predicting predicting the the expected expected pattern pattern pattern of of of amino amino amino acid acid acid variation variation variation found found found in in in the the the match match match state state state of of of a a a hid-den hid-den hid-den Markov Markov Markov model model (representing one column of a multiple sequence alignment of proteins), based on prior distributions found in conserved protein domains (blocks). Distance in sequence analysis （序列距离）（序列距离）The number of observed changes in an optimal alignment of two sequences, usually not counting gaps. DNA Sequencing （DNA 测序）测序）The The experimental experimental experimental process process process of of of determining determining determining the the the nucleotide nucleotide nucleotide sequence sequence sequence of of of a a a region region region of of of DNA. DNA. DNA. This This This is is done by labelling each nucleotide (A, C, G or T) with either a radioactive or fluorescent marker which which identifies identifies identifies it. it. it. There There There are are are several several several methods methods methods of of of applying applying applying this this this technology, technology, each each with with with their their advantages and disadvantages. For more information, refer to a current text book. High throughput laboratories laboratories frequently frequently frequently use use use automated automated automated sequencers, sequencers, sequencers, which which which are are are capable capable capable of of of rapidly rapidly rapidly reading reading reading large large numbers of templates. Sometimes, the sequences may be generated more quickly than they can be characterised. Domain （功能域）（功能域）A A discrete discrete discrete portion portion portion of of of a a a protein protein protein assumed assumed assumed to to to fold fold fold independently independently independently of of of the the the rest rest rest of of of the the the protein protein protein and and possessing its own function.Dot matrix （点标矩阵图）（点标矩阵图）Dot matrix diagrams provide a graphical method for comparing two sequences. One sequence is written horizontally across the top of the graph and the other along the left-hand side. Dots are placed within the graph at the intersection of the same letter appearing in both sequences. A series of diagonal lines in the graph indicate regions of alignment. The matrix may be filtered to reveal the the most-alike most-alike most-alike regions regions regions by by by scoring scoring scoring a a a minimal minimal minimal threshold threshold threshold number number number of of of matches matches matches within within within a a a sequence sequence window. Draft genome sequence （基因组序列草图）（基因组序列草图）（基因组序列草图） The sequence produced by combining the information from the individual sequenced clones (by creating merged sequence contigs and then employing linking information to create scaffolds) and positioning the sequence along the physical map of the chromosomes. DUST （一种低复杂性区段过滤程序）（一种低复杂性区段过滤程序）A program for filtering low complexity regions from nucleic acid sequences. Dynamic programming （动态规划法）（动态规划法）A dynamic programming algorithm solves a problem by combining solutions to sub-problems that are computed once and saved in a table or matrix. Dynamic programming is typically used when a problem has many possible solutions and an optimal one needs to be found. This algorithm is used for producing sequence alignments, given a scoring system for sequence comparisons. EMBL （欧洲分子生物学实验室，EMBL 数据库是主要公共核酸序列数据库之一）数据库是主要公共核酸序列数据库之一）European Molecular Biology Laboratories. Maintain the EMBL database, one of the major public sequence databases. EMBnet （欧洲分子生物学网络）（欧洲分子生物学网络）European European Molecular Molecular Molecular Biology Biology Biology Network: Network: Network: / / was was established established established in in in 1988, 1988, 1988, and and provides provides services services services including including including local local local molecular molecular molecular databases databases databases and and and software software software for for for molecular molecular molecular biologists biologists biologists in in Europe. There are several large outposts of EMBnet, including EXPASY . Entropy （熵）（熵）From information theory, a measure of the unpredictable nature of a set of possible elements. The higher the level of variation within the set, the higher the entropy. Erdos and Renyi law In a toss of a “fair” coin, the number of heads in a row that can be expected is the logarithm of the number of tosses to the base 2. The law may be generalized for more than two possible outcomes by changing the base of the logarithm to the number of out-comes. This law was used to analyze the number of matches and mismatches that can be expected between random sequences as a basis for scoring the statistical significance of a sequence alignment. EST （表达序列标签的缩写）（表达序列标签的缩写）See Expressed Sequence Tag Expect value (E)（E 值）值）E E value. value. value. The The The number number number of of of different different different alignents alignents alignents with with with scores scores scores equivalent equivalent equivalent to to to or or or better better better than than than S S S that that that are are expected to occur in a database search by chance. The lower the E value, the more significant the score. In a database similarity search, the probability that an alignment score as good as the one found between a query sequence and a database sequence would be found in as many comparisons between random sequences as was done to find the matching sequence. In other types of sequence analysis, E has a similar meaning. Expectation maximization (sequence analysis) An algorithm for locating similar sequence patterns in a set of sequences. A guessed alignment of the sequences is first used to generate an expected scoring matrix representing the distribution of sequence characters in each column of the alignment, this pattern is matched to each sequence, and and the the the scoring scoring scoring matrix matrix matrix values values values are are are then then then updated updated updated to to to maximize maximize maximize the the the alignment alignment alignment of of of the the the matrix matrix matrix to to to the the sequences. The procedure is repeated until there is no further improvement. Exon （外显子）（外显子）。

C OGNITIVE S CIENCE,14, 179-211 (1990).Finding Structure in TimeJ EFFREY L. E LMANUniversity of California, San DiegoTime underlies many interesting human behaviors. Thus, the question ofhow to represent time in connectionist models is very important. Oneapproach is to represent time implicitly by its effects on processing ratherthan explicitly (as in a spatial representation). The current report developsa proposal along these lines first described by Jordan (1986) whichinvolves the use of recurrent links in order to provide networks with adynamic memory. In this approach, hidden unit patterns are fed back tothemselves; the internal representations which develop thus reflect taskdemands in the context of prior internal states. A set of simulations isreported which range from relatively simple problems (temporal versionof XOR) to discovering syntactic/semantic features for words. Thenetworks are able to learn interesting internal representations whichincorporate task demands with memory demands; indeed, in this approachthe notion of memory is inextricably bound up with task processing. Theserepresentations reveal a rich structure, which allows them to be highlycontext-dependent while also expressing generalizations across classes ofitems. These representations suggest a method for representing lexicalcategories and the type/token distinction.___________________________I would like to thank Jay McClelland, Mike Jordan, Mary Hare, Dave Rumelhart, Mike Mozer, Steve Poteet, David Zipser, and Mark Dolson for many stimulating discussions. I thank McClelland, Jordan, and two anonymous reviewers for helpful critical comments on an earlier draft of this paper.This work was supported by contract N00014-85-K-0076 from the Office of Naval Research and contract DAAB-07-87-C-H027 from Army Avionics, Ft. Monmouth. Requests for reprints should be sent to the Center for Research in Language, C-008; University of California, San Diego, CA 92093-0108. The author can be reached via electronic mail as elman@.IntroductionTime is clearly important in cognition. It is inextricably bound up with many behaviors (such as language) which express themselves as temporal sequences. Indeed, it is difficult to know how one might deal with such basic problems as goal-directed behavior, planning, or causation without some way of representing time.The question of how to represent time might seem to arise as a special problem unique to parallel processing models, if only because the parallel nature of computation appears to be at odds with the serial nature of temporal events. However, even within traditional (serial) frameworks, the representation of serial order and the interaction of a serial input or output with higher levels of representation presents challenges. For example, in models of motor activity an important issue is whether the action plan is a literal specification of the output sequence, or whether the plan represents serial order in a more abstract manner (e.g., Lashley, 1951; MacNeilage, 1970; Fowler, 1977, 1980; Kelso, Saltzman, & Tuller, 1986; Saltzman & Kelso, 1987; Jordan & Rosenbaum, 1988). Linguistic theoreticians have perhaps tended to be less concerned with the representation and processing of the temporal aspects to utterances (assuming, for instance, that all the information in an utterance is somehow made available simultaneously in a syntactic tree); but the research in natural language parsing suggests that the problem is not trivially solved (e.g., Frazier & Fodor; 1978; Marcus, 1980). Thus, what is one of the most elementary facts about much of human activity -that it has temporal extent -is sometimes ignored and is often problematic.In parallel distributed processing models, the processing of sequential inputs has been accomplished in several ways. The most common solution is to attempt to “parallels time” by giving it a spatial representation. However, there are problems with this approach, and it is ultimately not a good solution. A better approach would be to represent time implicitly rather than explicitly. That is, we represent time by the effect it has on processing and not as an additional dimension of the input.This paper describes the results of pursuing this approach, with particular emphasis on problems that are relevant to natural language processing. The approach taken is rather simple, but the results are sometimes complex and unexpected. Indeed, it seems that the solution to the problem of time may interact with other problems for connectionist architectures, including the problem of symbolic representation and how connectionist representations encode structure. The current approach supports the notion outlined by Van Gelder (1989; see also Smolensky, 1987, 1988; Elman, 1989), that connectionist representations may have a functional compositionality without being syntactically compositional.The first section briefly describes some of the problems that arise when time is represented externally as a spatial dimension. The second section describes the approach used in this work. The major portion of this report presents the results of applying this new architecture to a diverse set of problems. These problems range in complexity from a temporal version of the Exclusive-OR function to the discovery of syntactic/semantic categories in natural language data.The Problem with TimeOne obvious way of dealing with patterns that have a temporal extent is to represent time explicitly by associating the serial order of the pattern with the dimensionality of the patternvector. The first temporal event is represented by the first element in the pattern vector, the second temporal event is represented by the second position in the pattern vector; and so on. The entire pattern vector is processed in parallel by the model. This approach has been used in a variety of models (e.g., Cottrell, Munro, & Zipser, 1987; Elman & Zipser, 1988; Hanson & Kegl, 1987).There are several drawbacks to this approach, which basically uses a spatial metaphor for time. First, it requires that there be some interface with the world which buffers the input so that it can be presented all at once. It is not clear that biological systems make use of such shift registers. There are also logical problems; how should a system know when a buffer’s contents should be examined?Second, the shift-register imposes a rigid limit on the duration of patterns (since the input layer must provide for the longest possible pattern), and further suggests that all input vectors be the same length. These problems are particularly troublesome in domains such as language, where one would like comparable representations for patterns that are of variable length. This is as true of the basic units of speech (phonetic segments) as it is of sentences.Finally, and most seriously, such an approach does not easily distinguish relative temporal position from absolute temporal position. For example, consider the following two vectors.[ 0 1 1 1 0 0 0 0 0 ][ 0 0 0 1 1 1 0 0 0 ]These two vectors appear to be instances of the same basic pattern, but displaced in space (or time, if we give these a temporal interpretation). However, as the geometric interpretation of these vectors makes clear, the two patterns are in fact quite dissimilar and spatially distant.1 PDP models can of course be trained to treat these two patterns as similar. But the similarity is a consequence of an external teacher and not of the similarity structure of the patterns themselves, and the desired similarity does not generalize to novel patterns. This shortcoming is serious if one is interested in patterns in which the relative temporal structure is preserved in the face of absolute temporal displacements.What one would like is a representation of time which is richer and which does not have these problems. In what follows here, a simple architecture is described which has a number of desirable temporal properties and has yielded interesting results.Networks with MemoryThe spatial representation of time described above treats time as an explicit part of the input. There is another, very different possibility, which is to allow time to be represented by the effect it has on processing. This means giving the processing system dynamic properties which are responsive to temporal sequences. In short, the network must be given memory.1.The reader may more easily be convinced of this by comparing the locations of the vectors [100], [010], and [001] in 3-space. Although these patterns might be considered ’temporally displaced’ versions of the same basic pat-tern, the vectors are very different.activate the output units. The hidden units also feed back to activate the context units. This constitutes the forward activation. Depending on the task, there may or may not be a learning phase in this time cycle. If so, the output is compared with a teacher input and backpropagation of error (Rumelhart, Hinton, & Williams, 1986) is used to incrementally adjust connection strengths. Recurrent connections are fixed at 1.0 and are not subject to adjustment.3 At the next time step t+1 the above sequence is repeated. This time the context units contain values which are exactly the hidden unit values at time t. These context units thus provide the network with memory.Internal Representation of Time. In feedforward networks employing hidden units and a learning algorithm, the hidden units develop internal representations for the input patterns which recode those patterns in a way which enables the network to produce the correct output for a given input. In the present architecture, the context units remember the previous internal state. Thus, the hidden units have the task of mapping both an external input and also the previous internal state to some desired output. Because the patterns on the hidden units are what are saved as context, the hidden units must accomplish this mapping and at the same time develop representations which are useful encodings of the temporal properties of the sequential input. Thus, the internal representations that develop are sensitive to temporal context; the effect of time is implicit in these internal states. Note, however, that these representations of temporal context need not be literal. They represent a memory which is highly task and stimulus-dependent.Consider now the results of applying this architecture to a number of problems which involve processing of inputs which are naturally presented in sequence.Exclusive-ORThe Exclusive-OR (XOR) function has been of interest because it cannot be learned by a simple two-layer network. Instead, it requires at least three-layers. The XOR is usually presented as a problem involving 2-bit input vectors (00, 11, 01, 10) yielding 1-bit output vectors (0, 0, 1, 1; respectively).This problem can be translated into a temporal domain in several ways. One version involves constructing a sequence of 1-bit inputs by presenting the 2-bit inputs one bit at a time (i.e., in two time steps), followed by the 1-bit output; then continuing with another input/output pair chosen at random. A sample input might be:1 0 1 0 0 0 0 1 1 1 1 0 1 0 1. . .Here, the first and second bits are XOR-ed to produce the third; the fourth and fifth are XOR-ed to give the sixth; and so on. The inputs are concatenated and presented as an unbroken sequence.In the current version of the XOR problem, the input consisted of a sequence of 3000 bits constructed in this manner. This input stream was presented to the network shown in Figure 2 (with 1 input unit, 2 hidden units, 1 output unit, and 2 context units), one bit at a time. The task of the network was, at each point in time, to predict the next bit in the sequence. That is, given 3. A little more detail is in order about the connections between the context units and hidden units. In the network used here there were one-for-one connections between each hidden unit and each context unit. This implies there are an equal number of context and hidden units. The upward connections between the context units and the hidden units were fully distributed, such that each context unit activates all the hidden units.averaging of error which was done for Figure 3. If one looks at the output activations it is apparent from the nature of the errors that the network predicts successive inputs to be the XOR of the previous two. This is guaranteed to be successful every third bit, and will sometimes—-fortuitously—also result in correct predictions at other times.It is interesting that the solution to the temporal version of XOR is somewhat different than the static version of the same problem. In a network with 2 hidden units, one unit is highly activated when the input sequence is a series of identical elements (all 1s or 0s), whereas the other unit is highly activated when the input elements alternate. Another way of viewing this is that the network developed units which were sensitive to high and low-frequency inputs. This is a different solution than is found with feedforward networks and simultaneously presented inputs. This suggests that problems may change their nature when cast in a temporal form. It is not clear that the solution will be easier or more difficult in this form; but it is an important lesson to realize that the solution may be different.In this simulation the prediction task has been used in a way which is somewhat analogous to autoassociation. Autoassociation is a useful technique for discovering the intrinsic structure possessed by a set of patterns. This occurs because the network must transform the patterns into more compact representations; it generally does so by exploiting redundancies in the patterns. Finding these redundancies can be of interest for what they tell us about the similarity structure of the data set (cf. Cottrell, Munro, & Zipser, 1987; Elman & Zipser, 1988).In this simulation the goal was to find the temporal structure of the XOR sequence. Simple autoassociation would not work, since the task of simply reproducing the input at all points in time is trivially solvable and does not require sensitivity to sequential patterns. The prediction task is useful because its solution requires that the network be sensitive to temporal structure.Structure in Letter SequencesOne question which might be asked is whether the memory capacity of the network architecture employed here is sufficient to detect more complex sequential patterns than the XOR. The XOR pattern is simple in several respects. It involves single-bit inputs, requires a memory which extends only one bit back in time, and there are only four different input patterns. More challenging inputs would require multi-bit inputs of greater temporal extent, and a larger inventory of possible sequences. Variability in the duration of a pattern might also complicate the problem.An input sequence was devised which was intended to provide just these sorts of complications. The sequence was composed of six different 6-bit binary vectors. Although the vectors were not derived from real speech, one might think of them as representing speech sounds, with the six dimensions of the vector corresponding to articulatory features. Table 1 shows the vector for each of the six letters.The sequence was formed in two steps. First, the 3 consonants (b, d, g) were combined in random order to obtain a 1000-letter sequence. Then each consonant was replaced using the rulesb ¥ bad ¥ diig ¥ guuconsists of a 6-bit rather than a 1-bit vector. One might have reasonably thought that the more extended sequential dependencies of these patterns would exceed the temporal processing capacity of the network. But almost the opposite is true. The fact that there are subregularities (at the level of individual bit patterns) enables the network to make partial predictions even in cases where the complete prediction is not possible. All of this is dependent on the fact that the input is structured, of course. The lesson seems to be that more extended sequential dependencies may not necessarily be more difficult to learn. If the dependencies are structured, that structure may make learning easier and not harder.Discovering the notion “word”It is taken for granted that learning a language involves (among many other things) learning the sounds of that language, as well as the morphemes and words. Many theories of acquisition depend crucially on such primitive types as word, or morpheme, or more abstract categories as noun, verb, or phrase (e.g., Berwick & Weinberg, 1984; Pinker, 1984). It is rarely asked how it is that a language learner knows to begin with that these entities exist. These notions are often assumed to be innate.Yet in fact, there is considerable debate among linguists and psycholinguists about what are the representations used in language. Although it is commonplace to speak of basic units such as “phoneme,” “morpheme,” and “word”, these constructs have no clear and uncontroversial definition. Moreover, the commitment to such distinct levels of representation leaves a troubling residue of entities that appear to lie between the levels. For instance, in many languages, there are sound/meaning correspondences which lie between the phoneme and the morpheme (i.e., sound symbolism). Even the concept “word” is not as straightforward as one might think (cf. Greenberg, 1963; Lehman, 1962). Within English, for instance, there is no consistently definable distinction between words (e.g., “apple”), compounds (“apple pie”) and phrases (“Library of Congress” or “man in the street”). Furthermore, languages differ dramatically in what they treat as words. In polysynthetic languages (e.g., Eskimo) what would be called words more nearly resemble what the English speaker would call phrases or entire sentences.Thus, the most fundamental concepts of linguistic analysis have a fluidity which at the very least suggests an important role for learning; and the exact form of the those concepts remains an open and important question.In PDP networks, representational form and representational content often can be learned simultaneously. Moreover, the representations which result have many of the flexible and graded characteristics which were noted above. Thus, one can ask whether the notion “word” (or something which maps on to this concept) could emerge as a consequence of learning the sequential structure of letter sequences which form words and sentences (but in which word boundaries are not marked).Let us thus imagine another version of the previous task, in which the letter sequences form real words, and the words form sentences. The input will consist of the individual letters (we will imagine these as analogous to speech sounds, while recognizing that the orthographic input is vastly simpler than acoustic input would be). The letters will be presented in sequence, one at a time, with no breaks between the letters in a word, and no breaks between the words of different sentences.Such a sequence was created using a sentence generating program and a lexicon of 15 words.4 The program generated 200 sentences of varying length, from 4 to 9 words. Thesentences were concatenated, forming a stream of 1,270 words. Next, the words were broken into their letter parts, yielding 4,963 letters. Finally, each letter in each word was converted into a 5-bit random vector.The result was a stream of 4,963 separate 5-bit vectors, one for each letter. These vectors were the input and were presented one at a time. The task at each point in time was to predict the next letter. A fragment of the input and desired output is shown in Table 2.Table 6:Input Output0110m0000a0000a0111n0111n1100y1100y1100y1100y0010e0010e0000a0000a1001r1001r1001s1001s0000a0000a0011g0011g0111o0111o0000a0000a0001b0001b0111o0111o1100y1100y0000a0000a0111n0111n0010d0010d0011g0011g0100i0100i1001r1001r0110l0110l1100y1100y4.The program used was a simplified version of the program described in greater detail in the next simulation.as a cue as to the boundaries of linguistic units which must be learned, and it demonstrates the ability of simple recurrent networks to extract this information.Discovering lexical classes from word orderConsider now another problem which arises in the context of word sequences. The order of words in sentences reflects a number of constraints. In languages such as English (so-called “fixed word-order” languages), the order is tightly constrained. In many other languages (the “free word-order” languages), there is greater optionality as to word order (but even here the order is not free in the sense of random). Syntactic structure, selectional restrictions, subcategorization, and discourse considerations are among the many factors which join together to fix the order in which words occur. Thus, the sequential order of words in sentences is neither simple nor is it determined by a single cause. In addition, it has been argued that generalizations about word order cannot be accounted for solely in terms of linear order (Chomsky, 1957; Chomsky, 1965). Rather, there is an abstract structure which underlies the surface strings and it is this structure which provides a more insightful basis for understanding the constraints on word order.While it is undoubtedly true that the surface order of words does not provide the most insightful basis for generalizations about word order, it is also true that from the point of view of the listener, the surface order is the only thing visible (or audible). Whatever the abstract underlying structure be, it is cued by the surface forms and therefore that structure is implicit in them.In the previous simulation, we saw that a network was able to learn the temporal structure of letter sequences. The order of letters in that simulation, however, can be given with a small set of relatively simple rules.5 The rules for determining word order in English, on the other hand, will be complex and numerous. Traditional accounts of word order generally invoke symbolic processing systems to express abstract structural relationships. One might therefore easily believe that there is a qualitative difference in the nature of the computation required for the last simulation, and that required to predict the word order of English sentences. Knowledge of word order might require symbolic representations which are beyond the capacity of (apparently) non-symbolic PDP systems. Furthermore, while it is true, as pointed out above, that the surface strings may be cues to abstract structure, considerable innate knowledge may be required in order to reconstruct the abstract structure from the surface strings. It is therefore an interesting question to ask whether a network can learn any aspects of that underlying abstract structure.Simple sentences. As a first step, a somewhat modest experiment was undertaken. A sentence generator program was used to construct a set of short (two and three-word) utterances. 13 classes of nouns and verbs were chosen; these are listed in Table 3. Examples of each category are given; it will be noticed that instances of some categories (e.g, VERB-DESTROY) may be included in others (e.g., VERB-TRAN). There were 29 different lexical items.5.In the worst case, each word constitutes a rule. More hopefully, networks will learn that recurring orthographic regularities provide additional and more general constraints (cf. Sejnowski & Rosenberg, 1987).Table 3: Categories of lexical items used in sentence simulationCategory ExamplesNOUN-HUM man, womanNOUN-ANIM cat, mouseNOUN-INANIM book, rockNOUN-AGRESS dragon, monsterNOUN-FRAG glass, plateNOUN-FOOD cookie, sandwichVERB-INTRAN think, sleepVERB-TRAN see, chaseVERB-AGPA move, breakVERB-PERCEPT smell, seeVERB-DESTROY break, smashVERB-EA eatThe generator program used these categories and the 15 sentence templates given in Table 4Table 4: Templates for sentence generatorWORD 1WORDS WORD 3NOUN-HUM VERB-EA T NOUN-FOODNOUN-HUM VERB-PERCEPT NOUN-INANIMNOUN-HUM VERB-DESTROY NOUN-FRAGNOUN-HUM VERB-INTRANNOUN-HUM VERB-TRAN NOUN-HUMNOUN-HUM VERB-AG PAT NOUN-INANIMNOUN-HUM VERB-AG PATNOUN-ANIM VERB-EA T NOUN-FOODNOUN-ANIM VERB-TRAN NOUN-ANIMNOUN-ANIM VERB-AG PAT NOUN-INANIMNOUN-ANIM VERB-AG PATNOUN-INANIM VERB-AG PATNOUN-AGRESS VERB-DESTORY NOUN-FRAGNOUN-AGRESS VERB-EA T NOUN-HUMNOUN-AGRESS VERB-EA T NOUN-ANIMNOUN-AGRESS VERB-EA T NOUN-FOODto create 10,000 random two- and three-word sentence frames. Each sentence frame was thenfilled in by randomly selecting one of the possible words appropriate to each category. Each word was replaced by a randomly assigned 31-bit vector in which each word was represented by a different bit. Whenever the word was present, that bit was flipped on. Two extra bits were reserved for later simulations. This encoding scheme guaranteed that each vector was orthogonal to every other vector and reflected nothing about the form class or meaning of the words. Finally, the 27,354 word vectors in the 10,000 sentences were concatenated, so that an input stream of 27,354 31-bit vectors was created. Each word vector was distinct, but there were no breaks between successive sentences. A fragment of the input stream is shown in column 1 of Table 5, with the English gloss for each vector in parentheses. The desired output is given in column 2.Table 5: Fragment of training sequences for sentence simulationINPUT OUTPUT 0000000000000000000000000000010(woman)0000000000000000000000000010000(smash) 0000000000000000000000000010000(smash)0000000000000000000001000000000(plate) 0000000000000000000001000000000(plate)0000010000000000000000000000000(cat) 0000010000000000000000000000000(cat)0000000000000000000100000000000(move) 0000000000000000000100000000000(move)0000000000000000100000000000000(man) 0000000000000000100000000000000(man)0001000000000000000000000000000(break) 0001000000000000000000000000000(break)0000100000000000000000000000000(car) 0000100000000000000000000000000(car)0100000000000000000000000000000(boy) 0100000000000000000000000000000(boy)0000000000000000000100000000000(move) 0000000000000000000100000000000(move)0000000000001000000000000000000(girl) 0000000000001000000000000000000(girl)0000000000100000000000000000000(eat) 0000000000100000000000000000000(eat)0010000000000000000000000000000(bread) 0010000000000000000000000000000(bread)0000000010000000000000000000000(dog) 0000000010000000000000000000000(dog)0000000000000000000100000000000(move) 0000000000000000000100000000000(move)0000000000000000001000000000000(mouse) 0000000000000000001000000000000(mouse)0000000000000000001000000000000(mouse) 0000000000000000001000000000000(mouse)0000000000000000000100000000000(move) 0000000000000000000100000000000(move)1000000000000000000000000000000(book) 1000000000000000000000000000000(book)0000000000000001000000000000000(lionFor this simulation a network was used which was similar to that in the first simulation, except that the input layer and output layers contained 31 nodes each, and the hidden and context layers contained 150 nodes each.The task given to the network was to learn to predict the order of successive words. The training strategy was as follows. The sequence of 27,354 31-bit vectors formed an input sequence. Each word in the sequence was input, one at a time, in order. The task on each input cycle was to predict the 31-bit vector corresponding to the next word in the sequence. At the end of the 27,354 word sequence, the process began again without a break starting with the first。

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