Number Of Input Sequences Research Articles

Accurately clustering biological sequences in linear time by relatedness sorting

Clustering biological sequences into similar groups is an increasingly important task as the number of available sequences continues to grow exponentially. Search-based approaches to clustering scale super-linearly with the number of input sequences, making it impractical to cluster very large sets of sequences. Approaches to clustering sequences in linear time currently lack the accuracy of super-linear approaches. Here, I set out to develop and characterize a strategy for clustering with linear time complexity that retains the accuracy of less scalable approaches. The resulting algorithm, named Clusterize, sorts sequences by relatedness to linearize the clustering problem. Clusterize produces clusters with accuracy rivaling popular programs (CD-HIT, MMseqs2, and UCLUST) but exhibits linear asymptotic scalability. Clusterize generates higher accuracy and oftentimes much larger clusters than Linclust, a fast linear time clustering algorithm. I demonstrate the utility of Clusterize by accurately solving different clustering problems involving millions of nucleotide or protein sequences.

Benefit-aware early prediction of health outcomes on multivariate EEG time series

Given a cardiac-arrest patient being monitored in the ICU (intensive care unit) for brain activity, how can we predict their health outcomes as early as possible? Early decision-making is critical in many applications, e.g. monitoring patients may assist in early intervention and improved care. On the other hand, early prediction on EEG data poses several challenges: (i) earliness-accuracy trade-off; observing more data often increases accuracy but sacrifices earliness, (ii) large-scale (for training) and streaming (online decision-making) data processing, and (iii) multi-variate (due to multiple electrodes) and multi-length (due to varying length of stay of patients) time series. Motivated by this real-world application, we present BeneFitter that infuses the incurred savings from an early prediction as well as the cost from misclassification into a unified domain-specific target called benefit. Unifying these two quantities allows us to directly estimate a single target (i.e. benefit), and importantly, (a) is efficient and fast, with training time linear in the number of input sequences, and can operate in real-time for decision-making, (b) can handle multi-variate and variable-length time-series, suitable for patient data, and (c) is effective, providing up to 2× time-savings with equal or better accuracy as compared to competitors.

Discovering Synchronized Subsets of Sequences: A Large Scale Solution.

Finding the largest subset of sequences (i.e., time series) that are correlated above a certain threshold, within large datasets, is of significant interest for computer vision and pattern recognition problems across domains, including behavior analysis, computational biology, neuroscience, and finance. Maximal clique algorithms can be used to solve this problem, but they are not scalable. We present an approximate, but highly efficient and scalable, method that represents the search space as a union of sets called ϵ-expanded clusters, one of which is theoretically guaranteed to contain the largest subset of synchronized sequences. The method finds synchronized sets by fitting a Euclidean ball on ϵ-expanded clusters, using Jung's theorem. We validate the method on data from the three distinct domains of facial behavior analysis, finance, and neuroscience, where we respectively discover the synchrony among pixels of face videos, stock market item prices, and dynamic brain connectivity data. Experiments show that our method produces results comparable to, but up to 300 times faster than, maximal clique algorithms, with speed gains increasing exponentially with the number of input sequences.

A dominant point-based parallel algorithm that finds all longest common subsequences for a constrained-MLCS problem

The work presented in this paper consists of searching for all the longest common subsequences among r sequences of equal length n which exclude a particular string. This problem is named the constrained-multiple longest common subsequence (constrained-MLCS) and is a general case of the constrained-LCS. Due to its importance, particularly in bioinformatics, the constrained-MLCS is widely studied. Thus, the solution proposed here is a coarse-grained multicomputer-based algorithm that uses an existing serial algorithm for local computation and a master-slave paradigm. This solution requires OD×Σ+ CSSs×MLCSp local computation time on each processor , OMLCS communication rounds and Onr|Σ|p time for preliminary works. |Σ| is the alphabet’s size, p is the number of processors used, |D| is the number of dominants generated during the entire resolution process, CSSs and MLCS are the number of all common subsequences, and the length of the longest common subsequences respectively. The experiments performed indicate that our proposed algorithm is scalable both with the number of processors and the number of input sequences.

A Design of Input-Decimation Technique for Recursive DFT/IDFT Algorithm

In this paper, an input-decimation technique for the recursive discrete Fourier transform (RDFT)/inverse DFT (RIDFT) algorithm is proposed for the high-speed broadband communication systems. It is worth noting that the input-decimation approach is presented to decrease the number of input sequences for the recursive filter so that the computation cycle of RDFT/RIDFT can be shortened to meet the computing time requirement ( $3.6~{\mu }s$ ) for the high-speed broadband communication systems. Therefore, the input-decimation RDFT/RIDFT algorithm is able to carry out at least 55.5% reduction of the total computation cycles compared with the considered algorithms. Furthermore, holding the advantages of input-decimation technique, the computational complexities of the real-multiplication and -addition are reduced to 41.3% and 22.2%, respectively. The area and the power consumption can be minimized by employing the cost-efficient constant multiplier with the refined signed-digit expression of twiddle factors. Finally, the physical implementation results show that the core area is $0.37\times 0.37$ mm2 with $0.18~\mu \text{m}$ CMOS process. The power consumption is 5.16 mW with the supply voltage of 1.8 V and the operating clock of 40 MHz. The proposed design can achieve 258 million of computational efficiency per unit area (CEUA) and really outperform the previous works.

Complex Chaotic Attractor via Fractal Transformation

Based on simplified Lorenz multiwing and Chua multiscroll chaotic systems, a rotation compound chaotic system is presented via transformation. Based on a binary fractal algorithm, a new ternary fractal algorithm is proposed. In the ternary fractal algorithm, the number of input sequences is extended from 2 to 3, which means the chaotic attractor with fractal transformation can be presented in the three-dimensional space. Taking Lorenz system, rotation Lorenz system and compound chaotic system as the seed chaotic systems, the dynamics of the complex chaotic attractors with fractal transformation are analyzed by means of bifurcation diagram, complexity and power spectrum, and the results show that the chaotic sequences with fractal transformation have higher complexity. As the experimental verification, one kind of complex chaotic attractors is implemented by DSP, and the result is consistent with that of the simulation, which verifies the feasibility of digital circuit implement.

Classification of genomic signals using dynamic time warping

BackgroundClassification methods of DNA most commonly use comparison of the differences in DNA symbolic records, which requires the global multiple sequence alignment. This solution is often inappropriate, causing a number of imprecisions and requires additional user intervention for exact alignment of the similar segments. The similar segments in DNA represented as a signal are characterized by a similar shape of the curve. The DNA alignment in genomic signals may adjust whole sections not only individual symbols. The dynamic time warping (DTW) is suitable for this purpose and can replace the multiple alignment of symbolic sequences in applications, such as phylogenetic analysis.MethodsThe proposed method is composed of three main parts. The first part represent conversion of symbolic representation of DNA sequences in the form of a string of A,C,G,T symbols to signal representation in the form of cumulated phase of complex components defined for each symbol. Next part represents signals size adjustment realized by standard signal preprocessing methods: median filtration, detrendization and resampling. The final part necessary for genomic signals comparison is position and length alignment of genomic signals by dynamic time warping (DTW).ResultsThe application of the DTW on set of genomic signals was evaluated in dendrogram construction using cluster analysis. The resulting tree was compared with a classical phylogenetic tree reconstructed using multiple alignment. The classification of genomic signals using the DTW is evolutionary closer to phylogeny of organisms. This method is more resistant to errors in the sequences and less dependent on the number of input sequences.ConclusionsClassification of genomic signals using dynamic time warping is an adequate variant to phylogenetic analysis using the symbolic DNA sequences alignment; in addition, it is robust, quick and more precise technique.

Setting a Complex System to a Known Initial State

Nowadays nondeterministic models are widely used when describing the behavior of complex systems. Nondeterminism occurs due to various reasons such as physical properties, limited controllability, and/or observability of a system under analysis, abstraction level, etc. [1]. Given a complex system, if its behavior can be described using finite sets of states and transitions between them, then homing experiments with nondeterministic Finite State Machines (FSMs) can be applied in order to set the system into a known initial state [2]. If the technical system behavior is described by a deterministic FSM then such experiments are well established. In particular, a complete deterministic FSM with n pairwise distinguishable states always has a homing sequence of length at most n(n – 1)/2. Moreover, the order of length of the homing sequence cannot be reduced when the next input depends on output responses of a system under experiment to the previous inputs, i.e., the complexity of homing experiments cannot be reduced using adaptive experiments instead of preset. For systems with the nondeterministic behavior, investigations of homing experiments are just beginning to develop [3, 4, 5]. In this paper, we briefly present the novel results obtained in this area under the assumption that the behavior of the system under experiment is described by a complete observable nondeterministic FSM. In other words, the behavior of the system in each state is defined for any input, but there can be several output responses to the same input in some states. For the observable FSM, given an input/output pair and a current state, the next state of the system can be uniquely identified. A finite state machine, or simply a machine is a 5-tuple S = (S, I, O, hS, S′), where S is a finite nonempty set of states with a nonempty subset S' of initial states, I and O are finite input and output alphabets, and hS ⊆ S × I × O × S is a transition relation that describes the behavior of the system which moves from state to state when an input of the set I is applied and produces an output response of the set O. Thus, an FSM is a finite representation of a system behavior with respect to the infinite number of input sequences. In this paper, we are interested in nondeterministic complete FSMs, i.e., at each state there is defined transition under each input, while different outputs can be produced at some state under some inputs. We are also interested in observable nondeterministic machines where the next state at each transition can be defined by observing corresponding input/output pair. Given a nondeterministic complete observable FSM S = (S, I, O, hS, S'), an input sequence α ∈ I is a homing sequence for S if for each pair s1, s2 ∈ S ′ of initial states at which the system responses to α with the output sequence β, the input/output pair α/β takes the FSM from states s1, s2 to one and the same single state, i.e., after applying α and observing β, we certainly know which state is reached by the system under experiment. Differently from deterministic FSMs, a homing sequence may not exist for a nondeterministic FSM without equivalent states [3]. Moreover, in [4] it has been shown that the length of a homing sequence for a nondeterministic machine (if such sequence exists) exponentially depends on the FSM size, i.e., on the number of FSM transitions. Different output sequences can be observed when applying the same input sequence to a nondeterministic FSM, and thus adaptive experiments can result in a shorter input sequence that sets the system under experiment into a given initial state, i.e., adaptive experiments can be more efficient than preset. During adaptive experiment, the next input significantly depends on the system outputs produced to the previous inputs. In order to formally define

Longest common subsequence problem for unoriented and cyclic strings

Given a finite set of strings X , the Longest Common Subsequence problem (LCS) consists in finding a subsequence common to all strings in X that is of maximal length. LCS is a central problem in stringology and finds broad applications in text compression, conception of error-detecting codes, or biological sequence comparison. However, in numerous contexts, words represent cyclic or unoriented sequences of symbols and LCS must be generalized to consider both orientations and/or all cyclic shifts of the strings involved. This occurs especially in computational biology when genetic material is sequenced from circular DNA or RNA molecules. In this work, we define three variants of LCS when the input words are unoriented and/or cyclic. We show that these problems are NP -hard, and W [ 1 ] -hard if parameterized in the number of input strings. These results still hold even if the three LCS variants are restricted to input languages over a binary alphabet. We also settle the parameterized complexity of our problems for most relevant parameters. Moreover, we study the approximability of these problems: we discuss the existence of approximation bounds depending on the cardinality of the alphabet, on the length of the shortest sequence, and on the number of input sequences. For this we prove that Maximum Independent Set in r -uniform hypergraphs is W [ 1 ] -hard if parameterized in the cardinality of the sought independent set and at least as hard to approximate as Maximum Independent Set in graphs.

Faster Algorithms for Optimal Multiple Sequence Alignment Based on Pairwise Comparisons

Multiple Sequence Alignment (MSA) is one of the most fundamental problems in computational molecular biology. The running time of the best known scheme for finding an optimal alignment, based on dynamic programming, increases exponentially with the number of input sequences. Hence, many heuristics were suggested for the problem. We consider a version of the MSA problem where the goal is to find an optimal alignment in which matches are restricted to positions in predefined matching segments. We present several techniques for making the dynamic programming algorithm more efficient, while still finding an optimal solution under these restrictions. We prove that it suffices to find an optimal alignment of the predefined sequence segments, rather than single letters, thereby reducing the input size and thus improving the running time. We also identify "shortcuts" that expedite the dynamic programming scheme. Empirical study shows that, taken together, these observations lead to an improved running time over the basic dynamic programming algorithm by 4 to 12 orders of magnitude, while still obtaining an optimal solution. Under the additional assumption that matches between segments are transitive, we further improve the running time for finding the optimal solution by restricting the search space of the dynamic programming algorithm.

Sources of Variation in Ancestral Sequence Reconstruction for HIV-1 Envelope Genes

We characterized the variation in the reconstructed ancestor of 118 HIV-1 envelope gene sequences arising from the methods used for (a) estimating and (b) rooting the phylogenetic tree, and (c) reconstructing the ancestor on that tree, from (d) the sequence format, and from (e) the number of input sequences. The method of rooting the tree was responsible for most of the sequence variation both among the reconstructed ancestral sequences and between the ancestral and observed sequences. Variation in predicted 3-D structural properties of the ancestors mirrored their sequence variation. The observed sequence consensus and ancestral sequences from center-rooted trees were most similar in all predicted attributes. Only for the predicted number of N-glycosylation sites was there a difference between MP and ML methods of reconstruction. Taxon sampling effects were observed only for outgroup-rooted trees, not center-rooted, reflecting the occurrence of several divergent basal sequences. Thus, for sequences exhibiting a radial phylogenetic tree, as does HIV-1, most of the variation in the estimated ancestor arises from the method of rooting the phylogenetic tree. Those investigating the ancestors of genes exhibiting such a radial tree should pay particular attention to alternate rooting methods in order to obtain a representative sample of ancestors.

SledgeHMMER: a web server for batch searching the Pfam database.

The SledgeHMMER web server is intended for genome-scale searching of the Pfam database without having to install this database and the HMMER software locally. The server implements a parallelized version of hmmpfam, the program used for searching the Pfam HMM database. Pfam search results have been calculated for the entire Swiss-Prot and TrEmbl database sequences (approximately 1.2 million) on 256 processors of IA64-based teragrid machines. The Pfam database can be searched in local, glocal or merged mode, using either gathering or E-value thresholds. Query sequences are first matched against the pre-calculated entries to retrieve results, and those without matches are processed through a new search process. Results are emailed in a space-delimited tabular format upon completion of the search. While most other Pfam-searching web servers set a limit of one sequence per query, this server processes batch sequences with no limit on the number of input sequences. The web server and downloadable data are accessible from http://SledgeHmmer.sdsc.edu.

Circular neighbourhood and 1-D DFT features for texture classification and segmentation

The authors introduce a texture descriptor that utilises circular neighbourhoods and 1-D discrete Fourier transforms to obtain rotation-invariant features. Since rotating an image does not change the intensities of its pixels but shifts them circularly, rotation-invariant features can be realised if the relationship between circular motion and spatial shift is established. For each individual circular neighbourhood centred at every pixel, a number of input sequences are formed by the intensities of pixels on concentric rings of various radii measured from the centre of each neighbourhood. Fourier transforming the sequences would generate coefficients whose magnitudes are invariant to rotation. Features extracted from these magnitudes were used in various classification and segmentation experiments. These features outperformed those of the circular simultaneous autoregressive model in classifying rotated images and those of the wavelet transform and the Gaussian Markov random field in classifying unrotated images of 30 classes. They also showed superior performance to those of the CSAR in several rotation-invariant segmentation experiments.

On the Approximation of Shortest Common Supersequences and Longest Common Subsequences

The problems of finding shortest common supersequences (SCS) and longest common subsequences (LCS) are two well-known ${\textbf NP}$-hard problems that have applications in many areas, including computational molecular biology, data compression, robot motion planning, and scheduling, text editing, etc. A lot of fruitless effort has been spent in searching for good approximation algorithms for these problems. In this paper, we show that these problems are inherently hard to approximate in the worst case. In particular, we prove that (i) SCS does not have a polynomial-time linear approximation algorithm unless $\textbf{P} = \textbf{NP}$; (ii) There exists a constant $\delta > 0$ such that, if SCS has a polynomial-time approximation algorithm with ratio $\log^{\delta} n$, where n is the number of input sequences, then ${\textbf NP}$ is contained in $\textbf{DTIME}(2^{\operatorname{polylog} n})$; (iii) There exists a constant $\delta > 0$ such that, if LCS has apolynomial-time approximation algorithm with performance ratio $n^{\delta}$, then $\textbf{P} = \textbf{NP}$. The proofs utilize the recent results of Arora et al. [Proc. 23rd IEEE Symposium on Foundations of Computer Science, 1992, pp. 14–23] on the complexity of approximation problems. In the second part of the paper, we introduce a new method for analyzing the average-case performance of algorithms for sequences, based on Kolmogorov complexity. Despite the above nonapproximability results, we show that near optimal solutions for both SCS and LCS can be found on the average. More precisely, consider a fixed alphabet $\Sigma$ and suppose that the input sequences are generated randomly according to the uniform probability distribution and are of the same length n. Moreover, assume that the number of input sequences is polynomial in n. Then, there are simple greedy algorithms which approximate SCS and LCS with expected additive errors $O(n^{0.707})$ and $O(n^{1/2+\epsilon})$ for any $\epsilon > 0$, respectively. Incidentally, our analyses also provide tight upper and lower bounds on the expected LCS and SCS lengths for a set of random sequences solving a generalization of another well-known open question on the expected LCS length for two random sequences [K. Alexander, The rate of convergence of the mean length of the longest common subsequence,1992, manuscript], [V. Chvatal and D. Sankoff, J. Appl. Probab., 12 (1975), pp. 306–315], [D. Sankoff and J. Kruskall, eds., Time Warps, String Edits, and Macromolecules: The Theory and Practice of Sequence Comparison, Addison-Wesley, Reading, MA, 1983].