Length Of Input Sequence Research Articles

On reducing test length for FSMs with extra states

SUMMARYA long‐standing problem when testing from a deterministic finite state machine is to guarantee full fault coverage even if the faults introduce extra states in the implementations. It is well known that such tests should include the sequences in a traversal set which contains all input sequences of length defined by the number of extra states. This paper suggests the SPY method, which helps reduce the length of tests by distributing sequences of the traversal set and reducing test branching. It is also demonstrated that an additional assumption about the implementation under test relaxes the requirement of the complete traversal set. The results of the experimental comparison of the proposed method with an existing method indicate that the resulting reduction can reach 40%. Experimental results suggest that the additional assumption about the implementation can help in further reducing the test suite length. Copyright © 2011 John Wiley & Sons, Ltd.

Representing Musical Sounds With an Interpolating State Model

A computationally efficient algorithm is proposed for modeling and representing time-varying musical sounds. The aim is to encode individual sounds and not the statistical properties of several sounds representing a certain class. A given sequence of acoustic feature vectors is modeled by finding such a set of ?states? (anchor points in the feature space) that the input data can be efficiently represented by interpolating between them. The proposed interpolating state model is generic and can be used to represent any multidimensional data sequence. In this paper, it is applied to represent musical instrument sounds in a compact and accurate form. Simulation experiments were carried out which show that the proposed method clearly outperforms the conventional vector quantization approach where the acoustic feature data is k-means clustered and the feature vectors are replaced by the corresponding cluster centroids. The computational complexity of the proposed algorithm as a function of the input sequence length T is O(T log T).

CentroidAlign: fast and accurate aligner for structured RNAs by maximizing expected sum-of-pairs score

The importance of accurate and fast predictions of multiple alignments for RNA sequences has increased due to recent findings about functional non-coding RNAs. Recent studies suggest that maximizing the expected accuracy of predictions will be useful for many problems in bioinformatics. We designed a novel estimator for multiple alignments of structured RNAs, based on maximizing the expected accuracy of predictions. First, we define the maximum expected accuracy (MEA) estimator for pairwise alignment of RNA sequences. This maximizes the expected sum-of-pairs score (SPS) of a predicted alignment under a probability distribution of alignments given by marginalizing the Sankoff model. Then, by approximating the MEA estimator, we obtain an estimator whose time complexity is O(L(3)+c(2)dL(2)) where L is the length of input sequences and both c and d are constants independent of L. The proposed estimator can handle uncertainty of secondary structures and alignments that are obstacles in Bioinformatics because it considers all the secondary structures and all the pairwise alignments as input sequences. Moreover, we integrate the probabilistic consistency transformation (PCT) on alignments into the proposed estimator. Computational experiments using six benchmark datasets indicate that the proposed method achieved a favorable SPS and was the fastest of many state-of-the-art tools for multiple alignments of structured RNAs. The software called CentroidAlign, which is an implementation of the algorithm in this article, is freely available on our website: http://www.ncrna.org/software/centroidalign/. hamada-michiaki@aist.go.jp Supplementary data are available at Bioinformatics online.

Sequence length limits for controlling false positives in discovering nucleotide sequence motifs

In the study of motif discovery, especially the transcription factor DNA binding sites discovery, a too long input sequence would return non-informative motifs rather than those biological functional motifs. This paper gave theoretical analyses and computational experiments to suggest the length limits of the input sequence. When the sequence length exceeds a certain critical point, the probability of discovering the motif decreases sharply. The work not only gave an explanation on the unsatisfying results of the existed motif discovery problems that the input sequence length might be too long and exceed the point, but also provided an estimation of input sequence length we should accept to get more meaningful and reliable results in motif discovery.

Adaptive sorting: an information theoretic perspective

We present two algorithms that are near optimal with respect to the number of inversions present in the input. One of the algorithms is a variation of insertion sort, and the other is a variation of merge sort. The number of comparisons performed by our algorithms, on an input sequence of length n that has I inversions, is at most $$n\,{\rm log}_{2} (\frac{I}{n} + 1) + O(n)$$. Moreover, both algorithms have implementations that run in time $$O(n\,{\rm log}_{2} (\frac{I}{n} + 1)\,+\,n)$$. All previously published algorithms require at least $$cn\,{\rm log}_{2} (\frac{I}{n} + 1)$$ comparisons for some c > 1.

In search of lost introns

Many fundamental questions concerning the emergence and subsequent evolution of eukaryotic exon-intron organization are still unsettled. Genome-scale comparative studies, which can shed light on crucial aspects of eukaryotic evolution, require adequate computational tools. We describe novel computational methods for studying spliceosomal intron evolution. Our goal is to give a reliable characterization of the dynamics of intron evolution. Our algorithmic innovations address the identification of orthologous introns, and the likelihood-based analysis of intron data. We discuss a compression method for the evaluation of the likelihood function, which is noteworthy for phylogenetic likelihood problems in general. We prove that after O(n l) preprocessing time, subsequent evaluations take O(n l/log l) time almost surely in the Yule-Harding random model of n-taxon phylogenies, where l is the input sequence length. We illustrate the practicality of our methods by compiling and analyzing a data set involving 18 eukaryotes, which is more than in any other study to date. The study yields the surprising result that ancestral eukaryotes were fairly intron-rich. For example, the bilaterian ancestor is estimated to have had more than 90% as many introns as vertebrates do now. The Java implementations of the algorithms are publicly available from the corresponding author's site http://www.iro.umontreal.ca/~csuros/introns/. Data are available on request.

An Exact Data Mining Method for Finding Center Strings and All Their Instances

Common substring problems allowing errors are known to be NP-hard. The main challenge of the problems lies in the combinatorial explosion of potential candidates. In this paper, we propose and study a generalized center string (GCS) problem, where not only all models (center strings) of any length, but also the positions of all their (degenerative) instances in input sequences are searched for. Inspired by frequent pattern mining techniques in data mining field, we present an exact and efficient method to solve GCS. First, a highly parallelized Trie-like structure, consensus tree, is proposed. Based on this structure, we present three Bpriori algorithms step by step. Bpriori algorithms can solve GCS with reasonable time and/or space complexities. We have proved that GCS is fixed parameter tractable with respect to fixed symbol set size and fixed length of input sequences. Experiment results on both artificial and real data have shown the correctness of the algorithms and the validity of our complexity analysis. A comparison with some current algorithms for solving common approximate substring problems is also given

A linear memory algorithm for Baum-Welch training

Background:Baum-Welch training is an expectation-maximisation algorithm for training the emission and transition probabilities of hidden Markov models in a fully automated way. It can be employed as long as a training set of annotated sequences is known, and provides a rigorous way to derive parameter values which are guaranteed to be at least locally optimal. For complex hidden Markov models such as pair hidden Markov models and very long training sequences, even the most efficient algorithms for Baum-Welch training are currently too memory-consuming. This has so far effectively prevented the automatic parameter training of hidden Markov models that are currently used for biological sequence analyses.Results:We introduce the first linear space algorithm for Baum-Welch training. For a hidden Markov model with M states, T free transition and E free emission parameters, and an input sequence of length L, our new algorithm requires O(M) memory and O(LMTmax (T + E)) time for one Baum-Welch iteration, where Tmax is the maximum number of states that any state is connected to. The most memory efficient algorithm until now was the checkpointing algorithm with O(log(L)M) memory and O(log(L)LMTmax) time requirement. Our novel algorithm thus renders the memory requirement completely independent of the length of the training sequences. More generally, for an n-hidden Markov model and n input sequences of length L, the memory requirement of O(log(L)Ln-1 M) is reduced to O(Ln-1 M) memory while the running time is changed from O(log(L)Ln MTmax + Ln(T + E)) to O(Ln MTmax (T + E)).An added advantage of our new algorithm is that a reduced time requirement can be traded for an increased memory requirement and vice versa, such that for any c ∈ {1, ..., (T + E)}, a time requirement of Ln MTmax c incurs a memory requirement of Ln-1 M(T + E - c).ConclusionFor the large class of hidden Markov models used for example in gene prediction, whose number of states does not scale with the length of the input sequence, our novel algorithm can thus be both faster and more memory-efficient than any of the existing algorithms.

Monotonicity-Based Fast Algorithms for MAP Estimation of Markov Sequences Over Noisy Channels

In this correspondence, we study algorithmic approach to solving the problem of maximum a posteriori (MAP) estimation of Markov sequences transmitted over noisy channels, which is also known as the MAP decoding problem. For the class of memoryless binary channels that produce independent substitution and erasure errors, the MAP sequence estimation problem can be formulated and solved as one of the longest path in a weighted directed acyclic graph. But for algorithm efficiency, we transform the graph problem to one of matrix search. If the underlying matrix is totally monotone, then the complexity of MAP sequence estimation can be greatly reduced. We give a sufficient condition for the matrix induced by MAP sequence estimation to be totally monotone, which is indeed the case if the input sequence is Gaussian Markov. Under this condition, the complexity of MAP decoding can be reduced from O(N/sup 2/M) to O(NM), where N is the size of source alphabet and M is the length of input sequence. Furthermore, for Markov sequences of fixed-length code we propose a block parsing strategy to reduce the complexity of MAP sequence estimation to O(M+N/sup 2/M/logM) or to O(M+NM/logM), depending on if the total monotonicity holds. Another significance of this correspondence lies in the applicability of the presented algorithmic approach, which has been thoroughly studied in computer science literature, to many other discrete optimization problems encountered in both source and channel coding, ranging from optimal multiresolution and multiple-description quantizer design, to context quantization for minimum conditional entropy, and to optimal packetization with uneven error protection.

Random sampling techniques for space efficient online computation of order statistics of large datasets

In a recent paper [MRL98], we had described a general framework for single pass approximate quantile finding algorithms. This framework included several known algorithms as special cases. We had identified a new algorithm, within the framework, which had a significantly smaller requirement for main memory than other known algorithms. In this paper, we address two issues left open in our earlier paper. First, all known and space efficient algorithms for approximate quantile finding require advance knowledge of the length of the input sequence. Many important database applications employing quantiles cannot provide this information. In this paper, we present a novel non-uniform random sampling scheme and an extension of our framework. Together, they form the basis of a new algorithm which computes approximate quantiles without knowing the input sequence length. Second, if the desired quantile is an extreme value (e.g., within the top 1% of the elements), the space requirements of currently known algorithms are overly pessimistic. We provide a simple algorithm which estimates extreme values using less space than required by the earlier more general technique for computing all quantiles. Our principal observation here is that random sampling is quantifiably better when estimating extreme values than is the case with the median.

Monitoring of randomly varying chemical processes by correlation chromatography

Correlation chromatography (CC) is a well known method for reducing detection limits in chromatographic analysis. Its usefulness for the monitoring of varying substance flows is however more ambiguous. Although generally believed as a useful tool for this purpose, very little work has been done to prove it. In this paper CC and common, single injection chromatography (SIC) were compared with respect to their restoration capabilities of a stochastic first order process, which is assumed to be the varying concentration input function of a chromatograph. It is demonstrated that CC can restore the input function with a smaller error than SIC when the process rate and input sequence length are related by a certain condition. The effect was found to be more profound when measurement noise is present due to the multiplex advantage of the CC method.

Enhancing Mersenne transforms by RNS with application to discrete convolution

The paper develops an enhanced algorithm for the exact computation of discrete convolution based on Mersenne transforms and multi-moduli residue number systems (RNSs). The proposed algorithm combines the advantages of Mersenne transforms and the advantages of the RNS system. The computation of Mersenne transforms involves only simple operations: addition and circular shift operations. The RNS system is used to increase the length of input sequences, to extend the unsatisfactory limited numerical range of Mersenne transforms, and to split convolution computations onto several smaller channels. A comparison of this algorithm with the traditional algorithm verifies the ability of this algorithm to solve many convolution problems. Numerical examples and tables are given to illustrate the new algorithm. In addition, practical considerations are discussed.

Lay people's evaluations of health: are there variations between different subgroups?

To elicit lay concepts of health and to see whether these are related to various sociodemographic factors, as has been suggested by previous smaller studies. A total of 196 people aged 18 and over were selected, as a representative sample of the general population, from the electoral registers of Walsall and Dudley in the West Midlands. Respondents were interviewed in their own homes in the autumn of 1989. Open ended and structured questions were used to elicit concepts of health. The three main stages consisted of an unprompted section in which respondents were asked to describe the features of good or poor health in themselves or others; a prompted section in which they were asked to rate 37 health statements using a series of categories from "very important" to "not at all important"; and a section in which they were asked to indicate which of six groups of statements, each representing a particular concept of health, best represented their own notions of health. Health was seen as multidimensional. Irrespective of whether respondents addressed health in self or health in others, or good or poor health, the biomedical dimension remained an important one. The manner by which concepts of health are elicited may provide some explanation as to why so many and varied concepts are alleged to be held by different subgroups of the population (notably different social classes). The differences found in this study between models of health employed by different subgroups of the general population have not been as great as has previously been suggested in the published reports. This is encouraging for those using existing health status measurements.

Parallel Compact FFTs for Real Sequences

Eight algorithms for the in-place, compact, fast Fourier transform (FFT) of real and conjugate-symmetric sequences are presented for single instruction multiple data (SIMD) and multiple instruction multiple data (MIMD) distributed-memory multiprocessors. The “conditional ordering” is introduced for conjugate-symmetric sequences as the natural ordering that leads to minimal communication costs. For a transform of a real, naturally ordered, input sequence of length N distributed evenly across P processors, $2 + \log _2 P$ nearest neighbor communication exchanges of $\tfrac{1}{2}N/P$ contiguous elements (i-cycles) are necessary. For a transform of a conjugate-symmetric, conditionally ordered input sequence, $1 + \log _2 P$i-cycles are necessary. In all cases the computational complexity is $\tfrac{5}{2}N/ P\log _2 N$, and there are no extra memory requirements. The algorithms require about half the communication of a parallel FFT of a real sequence that involves a complex FFT and pre- or postprocessing. Communication complexity is based on the hypercube topology; the algorithms, however, can be implemented on general connection topologies. Some of the schemes are implemented on an nCUBE/2 MIMD multiprocessor, and timings are given.

On the gap between the structural controllability of time-varying and time-invariant systems

Structural controllability of time-invariant and time-varying systems when the input control sequences have a restricted length k is compared. The dimensions of controllable space coincide in the following three special cases: the input sequences have length k=2; the input sequences have k=n, where n is the size of the system (i.e., the ultimate controllability is the same in both cases); and for every length of input sequences provided that the system has a single input only. It is proved that there may appear a gap for every input length k such that 2 >

Motif recognition and alignment for many sequences by comparison of dot-matrices

Calculation of dot-matrices is a widespread tool in the search for sequence similarities. When sequences are distant, even this approach may fail to point out common regions. If several plots calculated for all members of a sequence set consistently displayed a similarity between them, this would increase its credibility. We present an algorithm to delineate dot-plot agreement. A novel procedure based on matrix multiplication is developed to identify common patterns and reliably aligned regions in a set of distantly related sequences. The algorithm finds motifs independent of input sequence lengths and reduces the dependence on gap penalties. When sequences share greater similarity, the same approach converts to a multiple sequence alignment procedure.

Interpolation by the FFT revisited-an experimental investigation

A numerical investigation into the accuracy of interpolation by, fast Fourier transform (FFT), using a sinusoidal test signal, is described. The method is precisely defined, including a previously unnoticed detail which makes a significant difference to the accuracy of the result. The experiments show that, with no input windowing, the accuracy of interpolation is almost independent of sinusoidal wavelength very close to the Nyquist limit. The resulting RMS error is inversely proportional to input sequence length and is very low for sequence lengths likely to be encountered in practice. As wavelength passes through the Nyquist limit, there is a sudden increase in error, as is expected from sampling theory. If the sequence ends are windowed by short, cosine half-bells, accuracy is further improved at longer wavelengths. In comparison, small-kernal convolution methods, such as linear interpolation and cubic convolution, perform badly at wavelengths anywhere near the Nyquist limit. >

Binarization effects in a correlator with noisy input data

Correlations of binarized data and gray-scale data in the presence of additive noise are compared using two performance criteria (mean ratio and peak-to-sidelobe ratio). General expressions are provided to evaluate these performance measures as a function of input data length, bandwidth, and signal-to-noise ratio. We find that binarized correlators outperform gray-scale correlators when the input SNR(i) exceeds a threshold level that depends on input bandwidth and sequence length.

Convolution Computer

A special purpose computer is described to evaluate the discrete convolution of two sequences of numbers. This computer abandons the traditional model of convolution as a series of inner products which, for input sequences of length n, requires n multipliers and (n - 1) adders to complete a convolution calculation in (2n - 1) time steps. Instead, it is shown that by reorganizing the algorithm, n interconnected processing units are able to evaluate a convolution in n time steps. Each processing unit consists of a multiplier, an adder, and the necessary buffers. In addition to providing increased throughput, the proposed organization results in a highly modular structure with a well defined interconnection pattern.

Control of switching nets.

Switching nets have long been used as models of biological phenomena. In this paper, control properties of switching nets are discussed. Bounds on control parameters for general nets, linear nets and nets with linear inputs are obtained. In particular, bounds are obtained on the maximum distance between two states and on the length of input sequences needed to synchronize two copies of the same net. Bounds on the number of input lines that must be added to an autonomous net to make it controllable are obtained in terms of the number of cycles and transient chains of the net.