Formulas and algorithms for the length of a Farey sequence
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ABSTRACT:
SUBMITTER: Sukhoy V
PROVIDER: S-EPMC8593030 | biostudies-literature |
REPOSITORIES: biostudies-literature
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Project description:BackgroundSequence comparison is a fundamental step in many important tasks in bioinformatics; from phylogenetic reconstruction to the reconstruction of genomes. Traditional algorithms for measuring approximation in sequence comparison are based on the notions of distance or similarity, and are generally computed through sequence alignment techniques. As circular molecular structure is a common phenomenon in nature, a caveat of the adaptation of alignment techniques for circular sequence comparison is that they are computationally expensive, requiring from super-quadratic to cubic time in the length of the sequences.ResultsIn this paper, we introduce a new distance measure based on q-grams, and show how it can be applied effectively and computed efficiently for circular sequence comparison. Experimental results, using real DNA, RNA, and protein sequences as well as synthetic data, demonstrate orders-of-magnitude superiority of our approach in terms of efficiency, while maintaining an accuracy very competitive to the state of the art.
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Project description:IntroductionTo evaluate and compare the effectiveness for reducing the prediction error (PE) of the second eye using formula-specific factors, artificial intelligence (AI) formulas (PEARL-DGS and Kane), and the Cooke-modified axial length (CMAL) methods in bilateral cataract patients with long axial length (AL).MethodsA total of 98 patients with long AL who underwent sequential bilateral cataract surgeries were retrospectively enrolled. The second-eye IOL power was calculated by the formula-specific factors, AI formulas, and CMAL methods when the first eye suffered from refraction surprise. The correction factors of eight formulas were calculated by regression analysis.ResultsThere was a significant correlation between bilateral preoperative biometric parameters (P < 0.05) as well as bilateral PE (P < 0.05). The Kane formula displayed the lowest median absolute error (MedAE) and highest proportion of PE within ± 0.50 and ± 1.00 D compared with other formulas for the first eye. For the second-eye refinement, all three methods could reduce the second-eye MedAE. The formula-specific correction factors were 0.250, 0.331, 0.343, 0.394, 0.409, 0.452, 0.503, and 0.520 for Kane, Barrett Universal II (BUII), PEARL-DGS, Holladay 2, Holladay 1, Haigis, Hoffer Q, and SRK/T, respectively. The new AI-based Kane and PEARL-DGS with or without the CMAL methods could improve the refractive outcomes of the second eye in sequential bilateral cataract patients with long AL. The Kane, BUII, and PEARL-DGS with specific correction factors displayed higher accuracy compared with the other two methods (P < 0.05).ConclusionsThe new AI-based Kane and PEARL-DGS with or without the CMAL methods could improve the refractive outcomes of the second eye in sequential bilateral cataract patients with long AL. Notably, the Kane, PEARL-DGS, and BUII with specific correction factors displayed higher accuracy.
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Project description:An accurate step length estimation can provide valuable information to different applications such as indoor positioning systems or it can be helpful when analyzing the gait of a user, which can then be used to detect various gait impairments that lead to a reduced step length (caused by e.g., Parkinson's disease or multiple sclerosis). In this paper, we focus on the estimation of the step length using machine learning techniques that could be used in an indoor positioning system. Previous step length algorithms tried to model the length of a step based on measurements from the accelerometer and some tuneable (user-specific) parameters. Machine-learning-based step length estimation algorithms eliminate these parameters to be tuned. Instead, to adapt these algorithms to different users, it suffices to provide examples of the length of multiple steps for different persons to the machine learning algorithm, so that in the training phase the algorithm can learn to predict the step length for different users. Until now, these machine learning algorithms were trained with features that were chosen intuitively. In this paper, we consider a systematic feature selection algorithm to be able to determine the features from a large collection of features, resulting in the best performance. This resulted in a step length estimator with a mean absolute error of 3.48 cm for a known test person and 4.19 cm for an unknown test person, while current state-of-the-art machine-learning-based step length estimators resulted in a mean absolute error of 4.94 cm and 6.27 cm for respectively a known and unknown test person.
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Project description:BACKGROUND:In order to find correlated pairs of positions between proteins, which are useful in predicting interactions, it is necessary to concatenate two large multiple sequence alignments such that the sequences that are joined together belong to those that interact in their species of origin. When each protein is unique then the species name is sufficient to guide this match, however, when there are multiple related sequences (paralogs) in each species then the pairing is more difficult. In bacteria a good guide can be gained from genome co-location as interacting proteins tend to be in a common operon but in eukaryotes this simple principle is not sufficient. RESULTS:The methods developed in this paper take sets of paralogs for different proteins found in the same species and make a pairing based on their evolutionary distance relative to a set of other proteins that are unique and so have a known relationship (singletons). The former constitute a set of unlabelled nodes in a graph while the latter are labelled. Two variants were tested, one based on a phylogenetic tree of the sequences (the topology-based method) and a simpler, faster variant based only on the inter-sequence distances (the distance-based method). Over a set of test proteins, both gave good results, with the topology method performing slightly better. CONCLUSIONS:The methods develop here still need refinement and augmentation from constraints other than the sequence data alone, such as known interactions from annotation and databases, or non-trivial relationships in genome location. With the ever growing numbers of eukaryotic genomes, it is hoped that the methods described here will open a route to the use of these data equal to the current success attained with bacterial sequences.
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Project description:BackgroundProgressive alignment is the standard approach used to align large numbers of sequences. As with all heuristics, this involves a tradeoff between alignment accuracy and computation time.ResultsWe examine this tradeoff and find that, because of a loss of information in the early steps of the approach, the alignments generated by the most common multiple sequence alignment programs are inherently unstable, and simply reversing the order of the sequences in the input file will cause a different alignment to be generated. Although this effect is more obvious with larger numbers of sequences, it can also be seen with data sets in the order of one hundred sequences. We also outline the means to determine the number of sequences in a data set beyond which the probability of instability will become more pronounced.ConclusionsThis has major ramifications for both the designers of large-scale multiple sequence alignment algorithms, and for the users of these alignments.
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Project description:The rapid advances of high-throughput sequencing technologies dramatically prompted metagenomic studies of microbial communities that exist at various environments. Fundamental questions in metagenomics include the identities, composition and dynamics of microbial populations and their functions and interactions. However, the massive quantity and the comprehensive complexity of these sequence data pose tremendous challenges in data analysis. These challenges include but are not limited to ever-increasing computational demand, biased sequence sampling, sequence errors, sequence artifacts and novel sequences. Sequence clustering methods can directly answer many of the fundamental questions by grouping similar sequences into families. In addition, clustering analysis also addresses the challenges in metagenomics. Thus, a large redundant data set can be represented with a small non-redundant set, where each cluster can be represented by a single entry or a consensus. Artifacts can be rapidly detected through clustering. Errors can be identified, filtered or corrected by using consensus from sequences within clusters.
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Project description:BackgroundGenome-sequencing projects are currently producing an enormous amount of new sequences and cause the rapid increasing of protein sequence databases. The unsupervised classification of these data into functional groups or families, clustering, has become one of the principal research objectives in structural and functional genomics. Computer programs to automatically and accurately classify sequences into families become a necessity. A significant number of methods have addressed the clustering of protein sequences and most of them can be categorized in three major groups: hierarchical, graph-based and partitioning methods. Among the various sequence clustering methods in literature, hierarchical and graph-based approaches have been widely used. Although partitioning clustering techniques are extremely used in other fields, few applications have been found in the field of protein sequence clustering. It is not fully demonstrated if partitioning methods can be applied to protein sequence data and if these methods can be efficient compared to the published clustering methods.MethodsWe developed four partitioning clustering approaches using Smith-Waterman local-alignment algorithm to determine pair-wise similarities of sequences. Four different sets of protein sequences were used as evaluation data sets for the proposed methods.ResultsWe show that these methods outperform several other published clustering methods in terms of correctly predicting a classifier and especially in terms of the correctness of the provided prediction. The software is available to academic users from the authors upon request.
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