Sequences Of Equal Length Research Articles

Distribution of the length of the longest common subsequence of two multi-state biological sequences

The length of the longest common subsequence (LCS) among two biological sequences has been used as a measure of similarity, and the application of this statistic is of importance in genomic studies. Even for the simple case of two sequences of equal length and composed of binary elements with equal state probabilities, the exact distribution of the length of the LCS remains an open question. This problem is also known as an NP-hard problem in computer science. Apart from combinatorial analysis, using the finite Markov chain imbedding technique, we derive the exact distribution for the length of the LCS between two multi-state sequences of different lengths. Numerical results are provided to illustrate the theoretical results.

A specialized fast cross-correlation for acoustical measurements using coded sequences

In acoustics applications, binary maximal-length sequences and related sequences are increasingly used for acoustics system identification tasks. A number of coded sequences, such as binary maximal-length related sequences and ternary sequences possess two-valued or pulselike autocorrelation functions. It is this correlation property that is exploited in most of acoustical applications. However, the length of some of these sequences is not directly suitable for FFT-based cross-correlation algorithms. This paper explores using standard FFTs to calculate the cross-correlation between two periodic finite-length sequences of equal length, where the lengths of the sequences are not a power of 2. We apply our specialized correlation algorithm to analyze data collected in a room-acoustic environment to simultaneously obtain impulse responses between multiple sources and multiple receivers.

A More Complex Isoleucine Aptamer with a Cognate Triplet

The simplest RNA that can meet a column affinity selection for isoleucine was previously defined using selection amplification with decreasing numbers of randomized nucleotides. This simplest UAUU motif was a small asymmetric internal loop. Conserved positions of the loop include isoleucine codon and anticodon triplets (Lozupone C., Changayil, S., Majerfeld, I., and Yarus, M. (2003) RNA (N. Y.) 9, 1315-1322). Using new primer sequences, we now select a somewhat more complex isoleucine binding RNA, requiring 4.7 more bits of information to describe. The newly selected structure is a terminal or hairpin loop of 20 nucleotides, 15 being invariant. An information profile shows that the new binding site contains five short functional loop regions joined by less significant single nucleotide positions. Among the important nucleotides is a conserved isoleucine anticodon, supporting the escaped triplet theory, which posits a stereochemical genetic code originating in RNA amino acid binding sites.

Naturally Occurring Transposable Elements Disrupt hsp70 Promoter Function in Drosophila melanogaster

Naturally occurring transposable element (TE) insertions that disrupt Drosophila promoters are correlated with modified promoter function and are posited to play a significant role in regulatory evolution, but their phenotypes have not been established directly. To establish the functional consequences of these TE insertions, we created constructs with either TE-bearing or TE-lacking hsp70 promoters fused to a luciferase reporter gene and assayed luciferase luminescence in transiently transfected Drosophila cells. Each of the four TEs reduces luciferase signal after heat shock and heat inducibility of the hsp70 promoter. To test if the differences in hsp70 promoter activity are TE-sequence dependent, we replaced each of the TEs with multiple intergenic sequences of equal length. These replacement insertions similarly reduced luciferase signal, suggesting that the TEs affect hsp70 promoter function by altering promoter architecture. These results are consistent with differences in Hsp70 expression levels, inducible thermotolerance, and fecundity previously associated with the TEs. That two different varieties of TEs in two different hsp70 genes have common effects suggests that TE insertion represents a general mechanism through which selection manipulates hsp70 gene expression.

Ancestral maximum likelihood of evolutionary trees is hard.

Maximum likelihood (ML) (Neyman, 1971) is an increasingly popular optimality criterion for selecting evolutionary trees. Finding optimal ML trees appears to be a very hard computational task--in particular, algorithms and heuristics for ML take longer to run than algorithms and heuristics for maximum parsimony (MP). However, while MP has been known to be NP-complete for over 20 years, no such hardness result has been obtained so far for ML. In this work we make a first step in this direction by proving that ancestral maximum likelihood (AML) is NP-complete. The input to this problem is a set of aligned sequences of equal length and the goal is to find a tree and an assignment of ancestral sequences for all of that tree's internal vertices such that the likelihood of generating both the ancestral and contemporary sequences is maximized. Our NP-hardness proof follows that for MP given in (Day, Johnson and Sankoff, 1986) in that we use the same reduction from Vertex Cover; however, the proof of correctness for this reduction relative to AML is different and substantially more involved.

Positional information in short-term memory: relative or absolute?

Evidence suggests that short-term memory for serial order includes information about the positions of items in a sequence. This information is necessary to explain why substitution errors between sequences tend to maintain their position within a sequence. Previous demonstrations of such errors, however, have always used sequences of equal length. With sequences of different length, both transpositions between groups (Experiment 1) and intrusions between trials (Experiment 2) are shown to respect position relative to the end as well as to the start of a sequence. These results support models in which position is coded by start and end markers, but not models in which position is coded in temporal or absolute terms. Possible interpretations of an end marker are discussed.

An HMM-based approach for off-line unconstrained handwritten word modeling and recognition

Describes a hidden Markov model-based approach designed to recognize off-line unconstrained handwritten words for large vocabularies. After preprocessing, a word image is segmented into letters or pseudoletters and represented by two feature sequences of equal length, each consisting of an alternating sequence of shape-symbols and segmentation-symbols, which are both explicitly modeled. The word model is made up of the concatenation of appropriate letter models consisting of elementary HMMs and an HMM-based interpolation technique is used to optimally combine the two feature sets. Two rejection mechanisms are considered depending on whether or not the word image is guaranteed to belong to the lexicon. Experiments carried out on real-life data show that the proposed approach can be successfully used for handwritten word recognition.

A Generalization of the Massey-Ding Algorithm

The set of all linear recurrence relations satisfied by given sequences of finite length is described by the annihilator ideal of the sequences. The Massey-Ding algorithm to compute a linear recurrence relation of minimal order for several finite sequences of equal length is generalized to compute a minimal Grobner basis of the annihilator ideal of several finite sequences of generally different lengths.

Mutational analysis of meiotic and mitotic centromere function in Saccharomyces cerevisiae.

A centromere (CEN) in Saccharomyces cerevisiae consists of approximately 150 bp of DNA and contains 3 conserved sequence elements: a high A + T region 78-86 bp in length (element II), flanked on the left by a conserved 8-bp element I sequence (PuTCACPuTG), and on the right by a conserved 25-bp element III sequence. We have carried out a structure-function analysis of the element I and II regions of CEN3 by constructing mutations in these sequences and subsequently determining their effect on mitotic and meiotic chromosome segregation. We have also examined the mitotic and meiotic segregation behavior of ARS plasmids containing the structurally altered CEN3 sequences. Replacing the periodic tracts of A residues within element II with random A + T sequences of equal length increases the frequency of mitotic chromosome nondisjunction only 4-fold; whereas, reducing the A + T content of element II while preserving the length results in a 40-fold increase in the frequence of chromosome nondisjunction. Structural alterations in the element II region that do not decrease the overall length have little effect on the meiotic segregation behavior of the altered chromosomes. Centromeres containing a deletion of element I or a portion of element II retain considerable mitotic activity, yet plasmids carrying these same mutations segregate randomly during meiosis I, indicating these sequences to be essential for maintaining attachment of the replicated sister chromatids during the first meiotic division. The presence of an intact element I sequence properly spaced from the element III region is absolutely essential for proper meiotic function of the centromere.

On the mean number of random digits until a given sequence occurs

Random digits are collected one at a time until a given sequence is obtained. The mean number of digits until this happens is determined. Generalizations are given to a stopping region consisting of several sequences of equal length.

On the mean number of random digits until a given sequence occurs

Random digits are collected one at a time until a given sequence is obtained. The mean number of digits until this happens is determined. Generalizations are given to a stopping region consisting of several sequences of equal length.

Families of sequences with optimal Hamming-correlation properties

The unnormalized Hamming correlation between two sequences of equal length is the number of positions in which these sequences have identical symbols. In this paper, lower bounds on the out-of-phase autocorrelation and on the cross correlation of sequences of given length and alphabet size are derived. A method of constructing families of sequences that uniformly realize these hounds is presented.