An upper bound on the convergence rate of a second functional in optimal sequence alignment

We study Banach envelopes for commutative symmetric sequence or function spaces, and noncommutative symmetric spaces of measurable operators. We characterize the class (HC) of quasi-normed symmetric sequence or function spaces E for which their Banach envelopes \(\widehat{E}\) are also symmetric spaces. The class of symmetric spaces satisfying (HC) contains but is not limited to order continuous spaces. Let \(\mathcal {M}\) be a non-atomic, semifinite von Neumann algebra with a faithful, normal, \(\sigma \)-finite trace \(\tau \) and E be as symmetric function space on \([0,\tau (\mathbf 1 ))\) or symmetric sequence space. We compute Banach envelope norms on \(E(\mathcal {M},\tau )\) and \(C_E\) for any quasi-normed symmetric space E. Then we show under assumption that \(E\in (HC)\) that the Banach envelope \(\widehat{E(\mathcal {M},\tau )}\) of \(E(\mathcal {M},\tau )\) is equal to \(\widehat{E}\left( \mathcal {M},\tau \right) \) isometrically. We also prove the analogous result for unitary matrix spaces \(C_E\).

Efficient biological sequence (proteins or DNA) alignment is an important and challenging task in bioinformatics. It is similar to string matching in the context of biological data and is used to infer the evolutionary relationship between a set of protein or DNA sequences. An accurate alignment can provide valuable information for experimentation on the newly found sequences. It is indispensable in basic research as well as in practical applications such as pharmaceutical development, drug discovery, disease prevention and criminal forensics. Many algorithms and methods, such as, dot plot (Gibbs & McIntyre, 1970),Needleman-Wunsch (N-W) (Needleman & Wunsch, 1970), Smith-Waterman (S-W) (Smith & Waterman, 1981), FASTA (Pearson & Lipman, 1985), BLAST (Altschul et al., 1990), HMMER (Eddy, 1998) and ClustalW (Thompson et al., 1994) have been proposed to perform and accelerate sequence alignment activities. An overview of these methods is given in (Hasan et al., 2007). Out of these, S-W algorithm is an optimal sequence alignment method, but its computational cost makes it inappropriate for practical purposes. To develop efficient and optimal sequence alignment solutions, the S-W algorithm has recently been implemented on emerging accelerator platforms such as Field Programmable Gate Arrays (FPGAs), Cell Broadband Engine (Cell/B.E.) and Graphics Processing Units (GPUs) (Buyukkur & Najjar, 2008; Hasan et al., 2010; Liu et al., 2009; 2010; Lu et al., 2008). This chapter aims at providing a broad overview of sequence alignment in general with particular emphasis on the classification and discussion of available methods and their comparison. Further, it reviews in detail the acceleration approaches based on implementations on different platforms and provides a comparison considering different parameters. This chapter is organized as follows: The remainder of this section gives a classification, discussion and comparison of the available methods and their hardware acceleration. Section 2 introduces the S-W algorithm which is the focus of discussion in the succeeding sections. Section 3 reviews CPU-based acceleration. Section 4 provides a review of FPGA-based acceleration. Section 5 overviews GPU-based acceleration. Section 6 presents a comparison of accelerations on different platforms, whereas Section 7 concludes the chapter.

BackgroundSequence alignment has become an indispensable tool in modern molecular biology research, and probabilistic sequence alignment models have been shown to provide an effective framework for building accurate sequence alignment tools. One such example is the pair hidden Markov model (pair-HMM), which has been especially popular in comparative sequence analysis for several reasons, including their effectiveness in modeling and detecting sequence homology, model simplicity, and the existence of efficient algorithms for applying the model to sequence alignment problems. However, despite these advantages, pair-HMMs also have a number of practical limitations that may degrade their alignment performance or render them unsuitable for certain alignment tasks.ResultsIn this work, we propose a novel scheme for comparing and aligning biological sequences that can effectively address the shortcomings of the traditional pair-HMMs. The proposed scheme is based on a simple message-passing approach, where messages are exchanged between neighboring symbol pairs that may be potentially aligned in the optimal sequence alignment. The message-passing process yields probabilistic symbol alignment confidence scores, which may be used for predicting the optimal alignment that maximizes the expected number of correctly aligned symbol pairs.ConclusionsExtensive performance evaluation on protein alignment benchmark datasets shows that the proposed message-passing scheme clearly outperforms the traditional pair-HMM-based approach, in terms of both alignment accuracy and computational efficiency. Furthermore, the proposed scheme is numerically robust and amenable to massive parallelization.

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.

Let V be a finite dimensional complex vector space, and for each positive integer n let denote the vector space whose elements are the complex valued symmetric n-linear functions on (n-copies). If , that is, f is a linear functional on V, then we define the symmetric n-linear function by for all . It is well known that the elements , known as polar elements, span . A basis for consisting entirely of polar elements is a polar basis. We present a surprisingly simple recursive algorithm for the generation of polar bases. Explicit stand alone formulas for polar bases are also presented. One such explicit basis is so natural that it should probably be called the canonical polar basis for . We introduce the notion of subspace filter and show that each subspace filter of order n provides polar bases for all of the spaces simultaneously, and we extend this result to the entire symmetric algebra .

Resource elasticity and server consolidation have long been among two of cloud computing’s most relevant management tools. Yet, exemplified with a scientific application use case, this paper highlights how judicious scheduling of tasks can help maximize resource utilization and improve performance and costs for both users and cloud providers. Developing an efficient cloud service for DNA sequence comparisons is adopted as a motivating use case. Using the bioinformatics tool MASA that finds an optimal pair-wise sequence alignment, we propose a model for co-scheduling multiple alignments on a single cloud instance. The resulting, practically optimal, non-preemptive schedule can effectively double the throughput of MASA-based sequence alignment workflows.

Multi-objective two-level swarm intelligence approach for multiple RNA sequence-structure alignment

Background: Platelets play a vital role in acute humoral xenograft rejection (AHXR) in pig-to-primate xenotransplantation, presenting as microvascular thrombosis in the graft and/or consumptive coagulopathy in the recipient. Adhesion and aggregation of primate platelets to the activated vascular endothelial cells through sequential binding of ligands on endothelial cells and subendothelial matrix ultimately trigger a complex biological process of prothrombotic signaling cascades. Increasing evidence suggests that the molecular incompatibilities in effector molecules across species may partially contribute to dysregulated microvascular thrombosis in xenografts. Method: We selected candidate genes from the NCBI database with keywords: platelet-endothelium interaction，platelet adhension, platelet aggregation, and subendothelial matrix ligands. Pair-wise amino acid alignments were made using the Emboss Needle method. Emboss needle created optimal global alignment of the amino acid sequences of human genes and pig genes using ClustalW2.Results: Most of the proteins involved in platelet-EC interaction in Homo sapiens share high sequence similarity with their homologues in Sus scrofa. Cytokines that potentially induce endothelial damage (such as CD40L, TNF-α) were highly conserved between Homo sapiens and Sus scrofa. Some endothelium-derived cytokines (such as IL-8, CCL2, CCL5) that can induce platelet activation or enhance aggregation share high sequence similarity between Homo sapiens and sus scrofa. Some regulators that potentially transduce inhibitory signaling to control platelet activation or complement activation have relatively poor sequence identity between Homo sapiens and Sus scrofa, and some even lack their homologues in Sus scrofa.Conclusion: The characteristic of sequence similarity of proteins involved in platelet-EC interaction indicated the molecular incompatibilities between humans (Homo sapiens) and pigs (Sus scrofa). This study provides a clue for explanation of excessive platelet activity in pig-to-primate xenotransplantation.

We introduce a unital associative algebra A associated with degenerate CP1. We show that A is a commutative algebra and whose Poincaré series is given by the number of partitions. Thereby, we can regard A as a smooth degeneration limit of the elliptic algebra introduced by Feigin and Odesskii [Int. Math. Res. Notices 11, 531 (1997)]. Then we study the commutative family of the Macdonald difference operators acting on the space of symmetric functions. A canonical basis is proposed for this family by using A and the Heisenberg representation of the commutative family studied by Shiraishi [ Commun. Math. Phys. 263, 439 (2006)]. It is found that the Ding–Iohara algebra [Lett. Math. Phys. 41, 183 (1997)] provides us with an algebraic framework for the free field construction. An elliptic deformation of our construction is discussed, showing connections with the Drinfeld quasi-Hopf twisting [Leningrad Math. J. 1, 1419 (1990)] in the sence of Babelon-Bernard–Billey [Phys. Lett. B. 375, 89 (1996)], the Ruijsenaars difference operator [Commun. Math. Phys. 110, 191 (1987)], and the operator M(q,t1,t2) of Okounkov–Pandharipande [e-print arXiv:math-ph/0411210].

This paper introduces a heuristic for multiple sequence alignment aimed at improving real-time object recognition in short video streams with uncertainties. It builds upon the idea of the progressive alignment but is cognitively economical to the extent that the underlying edit distance approach is adapted to account for human working memory limitations. Thus, the proposed heuristic procedure has a reduced computational complexity compared to optimal multiple sequence alignment. On the other hand, its relevance was experimentally confirmed. An extrinsic evaluation conducted in real-life settings demonstrated a significant improvement in number recognition accuracy in short video streams under uncertainties caused by noise and incompleteness. The second line of evaluation demonstrated that the proposed heuristic outperforms humans in the post-processing of recognition hypotheses. This indicates that it may be combined with state-of-the-art machine learning approaches, which are typically not tailored to the task of object sequence recognition from a limited number of frames of incomplete data recorded in a dynamic scene situation.

We present a new method for the calculation of multiple sequence alignments (MSAs). The input to our problem are n protein sequences. We assume that the sequences are related with each other and that there exists some unknown evolutionary tree that corresponds to the MSA. One advantage of our method is that the scoring can be done with reference to this phylogenetic tree, even though the tree structure itself may remain unknown. Instead of computing an evolutionary tree, we only need to compute a circular tour of the tree which is determined via a traveling salesman problem (TSP) algorithm. Our algorithm can calculate a near optimal MSA and has a performance guarantee of n-1/n.opt (where opt is the optimal score of the MSA). The algorithm runs in O(k/sup 2/n/sup 2/) time, where k is the length of the longest input sequence. From there, we improve the alignment further. Experimental results are shown at the end.

Space and time optimal parallel sequence alignments

BackgroundVSEARCH is an open source and free of charge multithreaded 64-bit tool for processing and preparing metagenomics, genomics and population genomics nucleotide sequence data. It is designed as an alternative to the widely used USEARCH tool (Edgar, 2010) for which the source code is not publicly available, algorithm details are only rudimentarily described, and only a memory-confined 32-bit version is freely available for academic use.MethodsWhen searching nucleotide sequences, VSEARCH uses a fast heuristic based on words shared by the query and target sequences in order to quickly identify similar sequences, a similar strategy is probably used in USEARCH. VSEARCH then performs optimal global sequence alignment of the query against potential target sequences, using full dynamic programming instead of the seed-and-extend heuristic used by USEARCH. Pairwise alignments are computed in parallel using vectorisation and multiple threads.ResultsVSEARCH includes most commands for analysing nucleotide sequences available in USEARCH version 7 and several of those available in USEARCH version 8, including searching (exact or based on global alignment), clustering by similarity (using length pre-sorting, abundance pre-sorting or a user-defined order), chimera detection (reference-based or de novo), dereplication (full length or prefix), pairwise alignment, reverse complementation, sorting, and subsampling. VSEARCH also includes commands for FASTQ file processing, i.e., format detection, filtering, read quality statistics, and merging of paired reads. Furthermore, VSEARCH extends functionality with several new commands and improvements, including shuffling, rereplication, masking of low-complexity sequences with the well-known DUST algorithm, a choice among different similarity definitions, and FASTQ file format conversion. VSEARCH is here shown to be more accurate than USEARCH when performing searching, clustering, chimera detection and subsampling, while on a par with USEARCH for paired-ends read merging. VSEARCH is slower than USEARCH when performing clustering and chimera detection, but significantly faster when performing paired-end reads merging and dereplication. VSEARCH is available at https://github.com/torognes/vsearch under either the BSD 2-clause license or the GNU General Public License version 3.0.DiscussionVSEARCH has been shown to be a fast, accurate and full-fledged alternative to USEARCH. A free and open-source versatile tool for sequence analysis is now available to the metagenomics community.

Aligning multiple DNA or protein sequences is a fundamental step in the analyses of phylogeny, homology and molecular structure. Heuristic algorithms are applied because optimal multiple sequence alignment is prohibitively expensive. Heuristic alignment algorithms represent a practical trade-off between speed and accuracy, but they can be improved. We present EVALYN (EVolved ALYNments), a novel approach to multiple sequence alignment in which sequences are progressively aligned based on a guide tree optimized by a genetic algorithm. We hypothesize that a genetic algorithm can find better guide trees than traditional, deterministic clustering algorithms. We compare our novel evolutionary approach to CLUSTAL W and find that EVALYN performs consistently and significantly better as measured by a common alignment scoring technique. Additionally, we hypothesize that evolutionary guide tree optimization is inherently efficient and has less time complexity than the commonly-used neighbor-joining algorithm. We present a compelling analysis in support of this scalability hypothesis.

Multiple Sequence Alignment (MSA) is an important operation in Bioinformatics, used to simultaneously compare 3 or more sequences. The MSA problem was proven NP-Hard, so strategies have been proposed to reduce the search space and solve it in parallel. Recently, asymmetric multicore processors (AMPs) have become popular, with performance and energy-efficient cores, like the P-Cores and E-cores from Intel. However, parallel MSA applications have complex access patterns and adapting them for AMPs can be challenging. In this paper, we propose PA-Star2<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup>, an asymmetric-aware strategy based on A-Star, which computes optimal MSAs taking asymmetry into account when distributing the search space among threads. Our experimental results show that the proposed optimizations can reduce considerably the average execution time of PA-Star2 achieving a speedup of up to 7.70×. We also show that the asymmetric-aware strategy can reduce the average execution time for one of the hardest sequences set from the BAliBASE benchmark, when compared to the symmetric counterpart. Finally, we show that our approach is energy-efficient.<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup>1PA-Star2 is open source and the code is publicly available at1PA-Star2 is open source and the code is publicly available at https://github.com/danielsundfeld/astar_msa