Family Of Sequences Research Articles

Non-standard limits for a family of autoregressive stochastic sequences

We examine the influence of using a restart mechanism on the stationary distributions of a particular class of Markov chains. Namely, we consider a family of multivariate autoregressive stochastic sequences that restart when hit a neighbourhood of the origin, and study their distributional limits when the autoregressive coefficient tends to one, the noise scaling parameter tends to zero, and the neighbourhood size varies. We show that the restart mechanism may change significantly the limiting distribution. We obtain a limit theorem with a novel type of limiting distribution, a mixture of an atomic distribution and an absolutely continuous distribution whose marginals, in turn, are mixtures of distributions of signed absolute values of normal random variables. In particular, we provide conditions for the limiting distribution to be normal, like in the case without restart mechanism. The main theorem is accompanied by a number of examples and auxiliary results of their own interest.

Studying the Impact of Initialization for Population-Based Algorithms with Low-Discrepancy Sequences

To solve different kinds of optimization challenges, meta-heuristic algorithms have been extensively used. Population initialization plays a prominent role in meta-heuristic algorithms for the problem of optimization. These algorithms can affect convergence to identify a robust optimum solution. To investigate the effectiveness of diversity, many scholars have a focus on the reliability and quality of meta-heuristic algorithms for enhancement. To initialize the population in the search space, this dissertation proposes three new low discrepancy sequences for population initialization instead of uniform distribution called the WELL sequence, Knuth sequence, and Torus sequence. This paper also introduces a detailed survey of the different initialization methods of PSO and DE based on quasi-random sequence families such as the Sobol sequence, Halton sequence, and uniform random distribution. For well-known benchmark test problems and learning of artificial neural network, the proposed methods for PSO (TO-PSO, KN-PSO, and WE-PSO), BA (BA-TO, BA-WE, and BA-KN), and DE (DE-TO, DE-WE, and DE-KN) have been evaluated. The synthesis of our strategies demonstrates promising success over uniform random numbers using low discrepancy sequences. The experimental findings indicate that the initialization based on low discrepancy sequences is exceptionally stronger than the uniform random number. Furthermore, our work outlines the profound effects on convergence and heterogeneity of the proposed methodology. It is expected that a comparative simulation survey of the low discrepancy sequence would be beneficial for the investigator to analyze the meta-heuristic algorithms in detail.

Evolution and enrichment of CYP5035 in Polyporales: functionality of an understudied P450 family

Bioprospecting for innovative basidiomycete cytochrome P450 enzymes (P450s) is highly desirable due to the fungi’s enormous enzymatic repertoire and outstanding ability to degrade lignin and detoxify various xenobiotics. While fungal metagenomics is progressing rapidly, the biocatalytic potential of the majority of these annotated P450 sequences usually remains concealed, although functional profiling identified several P450 families with versatile substrate scopes towards various natural products. Functional knowledge about the CYP5035 family, for example, is largely insufficient. In this study, the families of the putative P450 sequences of the four white-rot fungi Polyporus arcularius, Polyporus brumalis, Polyporus squamosus and Lentinus tigrinus were assigned, and the CYPomes revealed an unusual enrichment of CYP5035, CYP5136 and CYP5150. By computational analysis of the phylogeny of the former two P450 families, the evolution of their enrichment could be traced back to the Ganoderma macrofungus, indicating their evolutionary benefit. In order to address the knowledge gap on CYP5035 functionality, a representative subgroup of this P450 family of P. arcularius was expressed and screened against a test set of substrates. Thereby, the multifunctional enzyme CYP5035S7 converting several plant natural product classes was discovered. Aligning CYP5035S7 to 102,000 putative P450 sequences of 36 fungal species from Joint Genome Institute-provided genomes located hundreds of further CYP5035 family members, which subfamilies were classified if possible. Exemplified by these specific enzyme analyses, this study gives valuable hints for future bioprospecting of such xenobiotic-detoxifying P450s and for the identification of their biocatalytic potential.Graphical abstractKey points• The P450 families CYP5035 and CYP5136 are unusually enriched in P. arcularius.• Functional screening shows CYP5035 assisting in the fungal detoxification mechanism.• Some Polyporales encompass an unusually large repertoire of detoxification P450s.

A new family of polyphase sequences with low correlation

A new family of polyphase sequences with low correlation

Comparative Analysis of Low Discrepancy Sequence-Based Initialization Approaches Using Population-Based Algorithms for Solving the Global Optimization Problems

Metaheuristic algorithms have been widely used to solve diverse kinds of optimization problems. For an optimization problem, population initialization plays a significant role in metaheuristic algorithms. These algorithms can influence the convergence to find an efficient optimal solution. Mainly, for recognizing the importance of diversity, several researchers have worked on the performance for the improvement of metaheuristic algorithms. Population initialization is a vital factor in metaheuristic algorithms such as PSO and DE. Instead of applying the random distribution for the initialization of the population, quasirandom sequences are more useful for the improvement the diversity and convergence factors. This study presents three new low-discrepancy sequences named WELL sequence, Knuth sequence, and Torus sequence to initialize the population in the search space. This paper also gives a comprehensive survey of the various PSO and DE initialization approaches based on the family of quasirandom sequences such as Sobol sequence, Halton sequence, and uniform random distribution. The proposed methods for PSO (TO-PSO, KN-PSO, and WE-PSO) and DE (DE-TO, DE-WE, and DE-KN) have been examined for well-known benchmark test problems and training of the artificial neural network. The finding of our techniques shows promising performance using the family of low-discrepancy sequences over uniform random numbers. For a fair comparison, the approaches using low-discrepancy sequences for PSO and DE are compared with the other family of low-discrepancy sequences and uniform random number and depict the superior results. The experimental results show that the low-discrepancy sequences-based initialization performed exceptionally better than a uniform random number. Moreover, the outcome of our work presents a foresight on how the proposed technique profoundly impacts convergence and diversity. It is anticipated that this low-discrepancy sequence comparative simulation survey would be helpful for studying the metaheuristic algorithm in detail for the researcher.

Comparative genome analysis of Bacillus thuringiensis strain HD521 and HS18-1

Bacillus thuringiensis (Bt) is an important biological insecticide used to management of different agricultural pests by producing toxic parasporal crystals proteins. Strain HD521 has an antagonistic effect against Rhizoctonia solani AG1IA, the causal agent of rice sheath blight. This strain with three cry7 genes can the formation of bipyramidal parasporal crystals (BPCs). BPCs are used for insecticidal activities against Henosepilachna vigintioctomaculata larva (Coleoptera). Strain HS18-1 contains different types of BPCs encoding genes and has effective toxicity for Lepidoptera and Diptera insects. Here we report the whole genome sequencing and assembly of HD521 and HS18-1 strains and analyzed the genome constitution covering virulence factors, types of plasmid, insertion sequences, and prophage sequences. The results showed that the genome of strain HD521 contains a circular chromosome and six circular plasmids, encoding eight types of virulence protein factors [Immune Inhibitor A, Hemolytic Enterotoxin, S-layer protein, Phospholipase C, Zwittermicin A-resistance protein, Metalloprotease, Chitinase, and N-acyl homoserine lactonase (AiiA)], four families of insertion sequence, and comprises six pro-phage sequences. The genome of strain HS18-1 contains one circular chromosome and nine circular plasmids, encoding five types of virulence protein factors [Hemolytic Enterotoxin, S-layer protein, Phospholipase C, Chitinase, and N-acyl homoserine lactonase (AiiA)] and four families of insertion sequence, and comprises of three pro-phage sequences. The obtained results will contribute to deeply understand the B. thuringiensis strain HD521 and HS18-1 at the genomic level.

Genomic Autopsy of Sudden Deaths in Young Individuals

Postmortem genetic testing of young individuals with sudden death has previously identified pathogenic gene variants. However, prior studies primarily considered highly penetrant monogenic variants, often without detailed decedent and family clinical information. To assess genotype and phenotype risk in a diverse cohort of young decedents with sudden death and their families. Pathological and whole-genome sequence analysis was conducted in a cohort referred from a national network of medical examiners. Cases were accrued prospectively from May 2015 to March 2019 across 24 US states. Analysis began September 2016 and ended November 2020. Evaluation of autopsy and clinical data integrated with whole-genome sequence data and family member evaluation. A total of 103 decedents (mean [SD] age at death, 23.7 [11.9] years; age range, 1-44 years), their surviving family members, and 140 sex- and genetic ancestry-matched controls were analyzed. Among 103 decedents, autopsy and clinical data review categorized 36 decedents with postmortem diagnoses, 23 decedents with findings of uncertain significance, and 44 with sudden unexplained death. Pathogenic/likely pathogenic (P/LP) genetic variants in arrhythmia or cardiomyopathy genes were identified in 13 decedents (12.6%). A multivariable analysis including decedent phenotype, ancestry, and sex demonstrated that younger decedents had a higher burden of P/LP variants and select variants of uncertain significance (effect size, -1.64; P = .001). These select, curated variants of uncertain significance in cardiac genes were more common in decedents than controls (83 of 103 decedents [86%] vs 100 of 140 controls [71%]; P = .005), and decedents harbored more rare cardiac variants than controls (2.3 variants per individual vs 1.8 in controls; P = .006). Genetic testing of 31 parent-decedent trios and 14 parent-decedent dyads revealed 8 transmitted P/LP variants and 1 de novo P/LP variant. Incomplete penetrance was present in 6 of 8 parents who transmitted a P/LP variant. Whole-genome sequencing effectively identified P/LP variants in cases of sudden death in young individuals, implicating both arrhythmia and cardiomyopathy genes. Genomic analyses and familial phenotype association suggest potentially additive, oligogenic risk mechanisms for sudden death in this cohort.

Intrinsically disordered electronegative clusters improve stability and binding specificity of RNA-binding proteins

RNA-binding proteins play crucial roles in various cellular functions and contain abundant disordered protein regions. The disordered regions in RNA-binding proteins are rich in repetitive sequences, such as poly-K/R, poly-N/Q, poly-A, and poly-G residues. Our bioinformatic analysis identified a largely neglected repetitive sequence family we define as electronegative clusters (ENCs) that contain acidic residues and/or phosphorylation sites. The abundance and length of ENCs exceed other known repetitive sequences. Despite their abundance, the functions of ENCs in RNA-binding proteins are still elusive. To investigate the impacts of ENCs on protein stability, RNA-binding affinity, and specificity, we selected one RNA-binding protein, the ribosomal biogenesis factor 15 (Nop15), as a model. We found that the Nop15 ENC increases protein stability and inhibits nonspecific RNA binding, but minimally interferes with specific RNA binding. To investigate the effect of ENCs on sequence specificity of RNA binding, we grafted an ENC to another RNA-binding protein, Ser/Arg-rich splicing factor 3. Using RNA Bind-n-Seq, we found that the engineered ENC inhibits disparate RNA motifs differently, instead of weakening all RNA motifs to the same extent. The motif site directly involved in electrostatic interaction is more susceptible to the ENC inhibition. These results suggest that one of functions of ENCs is to regulate RNA binding via electrostatic interaction. This is consistent with our finding that ENCs are also overrepresented in DNA-binding proteins, whereas underrepresented in halophiles, in which nonspecific nucleic acid binding is inhibited by high concentrations of salts.

Half-Graphs, Other Non-stable Degree Sequences, and the Switch Markov Chain

One of the simplest methods of generating a random graph with a given degree sequence is provided by the Monte Carlo Markov Chain method using switches. The switch Markov chain converges to the uniform distribution, but generally the rate of convergence is not known. After a number of results concerning various degree sequences, rapid mixing was established for so-called P-stable degree sequences (including that of directed graphs), which covers every previously known rapidly mixing region of degree sequences.
 In this paper we give a non-trivial family of degree sequences that are not P-stable and the switch Markov chain is still rapidly mixing on them. This family has an intimate connection to Tyshkevich-decompositions and strong stability as well.

A unified construction of all the hypergeometric and basic hypergeometric families of orthogonal polynomial sequences

We construct a set H of orthogonal polynomial sequences that contains all the families in the Askey scheme and the q-Askey scheme. The polynomial sequences in H are solutions of a generalized first-order difference equation which is determined by three linearly recurrent sequences of numbers. Two of these sequences are solutions of the difference equation sk+3=z(sk+2−sk+1)+sk, where z is a complex parameter, and the other sequence satisfies a related difference equation of order five.We obtain explicit expressions for the coefficients of the orthogonal polynomials and for the generalized moments with respect to a basis of Newton type of the space of polynomials. We also obtain explicit formulas for the coefficients of the three-term recurrence relation satisfied by the polynomial sequences in H.The set H contains all the 15 families in the Askey scheme of hypergeometric orthogonal polynomials [8, p. 183] and all the 29 families of basic hypergeometric orthogonal polynomial sequences in the q-Askey scheme [8, p. 413]. Each of these families is obtained by direct substitution of appropriate values for the parameters in our general formulas. The only cases that require some limits are the Hermite and continuous q-Hermite polynomials. We present the values of the parameters for some of the families.

P18 (SRS35/TgSAG4) Plays a Role in the Invasion and Virulence of Toxoplasma gondii

Toxoplasmosis is a prevalent parasitic disease caused by Toxoplasma gondii (T. gondii). Under the control of the host immune system, T. gondii persists as latent bradyzoite cysts. Immunosuppression leads to their reactivation, a potentially life-threatening condition. Interferon-gamma (IFN-γ) controls the different stages of toxoplasmosis. Here, we addressed the role of the parasite surface antigen P18, belonging to the Surface-Antigen 1 (SAG-1) Related Sequence (SRS) family, in a cyst-forming strain. Deletion of P18 gene (KO P18) impaired the invasion of parasites in macrophages and IFN-γ-mediated activation of macrophages further reduced the invasion capacity of this KO, as compared to WT strain. Mice infected by KO P18, showed a marked decrease in virulence during acute toxoplasmosis. This was consequent to less parasitemia, accompanied by a substantial recruitment of dendritic cells, macrophages and natural killer cells (NK). Furthermore, KO P18 resulted in a higher number of bradyzoite cysts, and a stronger inflammatory response. A prolonged survival of mice was observed upon immunosuppression of KO P18 infected BALB/c mice or upon oral infection of Severe Combined Immunodeficiency (SCID) mice, with intact macrophages and natural killer (NK) cells. In stark contrast, oral infection of NSG (NOD/Shi-scid/IL-2Rγnull) mice, defective in macrophages and NK cells, with KO P18, was as lethal as that of the control strain showing that the conversion from bradyzoites to tachyzoites is intact and, suggesting a role of P18 in the response to host IFN-γ. Collectively, these data demonstrate a role for P18 surface antigen in the invasion of macrophages and in the virulence of the parasite, during acute and chronic toxoplasmosis.

Generalized symmetries, first integrals, and exact solutions of chains of differential equations

New integrability properties of a family of sequences of ordinary differential equations, which contains the Riccati and Abel chains as the most simple sequences, are studied. The determination of n generalized symmetries of the nth-order equation in each chain provides, without any kind of integration, n-1 functionally independent first integrals of the equation. A remaining first integral arises by a quadrature by using a Jacobi last multiplier that is expressed in terms of the preceding equation in the corresponding sequence. The complete set of n first integrals is used to obtain the exact general solution of the nth-order equation of each sequence. The results are applied to derive directly the exact general solution of any equation in the Riccati and Abel chains.

Single-Round DNA Aptamer Selection by Combined Use of Capillary Electrophoresis and Next Generation Sequencing: An Aptaomics Approach for Identifying Unique Functional Protein-Binding DNA Aptamers.

In DNA aptamer selection, existing methods do not discriminate aptamer sequences based on their binding affinity and function and the reproducibility of the selection is often poor, even for the selection of well-known aptamers like those that bind the commonly used model protein thrombin. In the present study, a novel single-round selection method (SR-CE selection) was developed by combining capillary electrophoresis (CE) with next generation sequencing. Using SR-CE selection, a successful semi-quantitative and semi-comprehensive aptamer selection for thrombin was demonstrated with high reproducibility for the first time. Selection rules based on dissociation equilibria and kinetics were devised to obtain families of analogous sequences. Selected sequences of the same family were shown to bind thrombin with high affinity. Furthermore, data acquired from SR-CE selection was mined by creating sub-libraries that were categorized by the functionality of the aptamers (e. g., pre-organized aptamers versus structure-induced aptamers). Using this approach, a novel fluorescent molecular recognition sensor for thrombin with nanomolar detection limits was discovered. Thus, in this proof-of-concept report, we have demonstrated the potential of a "DNA Aptaomics" approach to systematically design functional aptamers as well as to obtain high affinity aptamers.

An extension of Lucas identity via Pascal's triangle

The Fibonacci sequence can be obtained by drawing diagonals in a Pascal’s triangle, and from this, we can obtain the Lucas identity. An investigation on the behavior of certain kinds of other diagonals inside a Pascal’s triangle identifies a new family of recursive sequences: the $k$-Padovan sequences. This family both contains the Fibonacci and the Padovan sequences. A general binomial identity for $k$-Padovan sequences which extends both the well-known Lucas identity and the less known Padovan identity is derived.

Characterization of regularity sets for families of sequences of matrices

We show that the regularity set of any family of sequences of matrices is an $F_{\sigma\delta}$-set. Moreover, for any $F_{\sigma\delta}$-set containing zero, we construct a family of sequences of matrices having this regularity set.

Single-Domain Antibodies for the Detection of SARS-CoV-2 Nucleocapsid Protein.

The goal of this work was to develop recombinantly expressed variable domains derived from camelid heavy-chain antibodies known as single-domain antibodies (sdAbs) directed against the SARS-CoV-2 nucleocapsid protein for incorporation into detection assays. To achieve this, a llama was immunized using a recombinant SARS-CoV-2 nucleocapsid protein and an immune phage-display library of variable domains was developed. The sdAbs selected from this library segregated into five distinct sequence families. Three of these families bind to unique epitopes with high affinity, low nM to sub-nM KD, as determined by surface plasmon resonance. To further enhance the utility of these sdAbs for the detection of nucleocapsid protein, homobivalent and heterobivalent genetic fusion constructs of the three high-affinity sdAbs were prepared. The effectiveness of the sdAbs for the detection of nucleocapsid protein was evaluated using MagPlex fluid array assays, a multiplexed immunoassay on color-coded magnetic microspheres. Using the optimal bivalent pair, one immobilized on the microsphere and the other serving as the biotinylated recognition reagent, a detection limit as low as 50 pg/mL of recombinant nucleocapsid and of killed virus down to 1.28 × 103 pfu/mL was achieved. The sdAbs described here represent immune reagents that can be tailored to be optimized for a number of detection platforms and may one day aid in the detection of SARS-CoV-2 to assist in controlling the current pandemic.

Simultaneous Approximation by Modification of Classical Szãsz Operators with Parameter s

This paper is approving the simultaneous approximation order by a modification family of the classical sequence of Szãsz operators. This modification depends on a real parameter s > −1/2. First, we show that this family (or its derivatives) converges to the function (or the corresponding derivatives) being approximated. Next, a Voronovski-type asymptotic formula for this family is given. The order of this approximation is improved from the order O(n −1) (the order of the classical sequence) to the order O(n −(2s+1)) whenever s > 0. Finally, the study supports by some numerical examples and discusses the results obtained.

TSFM 1.0: tRNA Structure-Function Mapper.

Structure-conditioned information statistics have proven useful to predict and visualize tRNA Class-Informative Features (CIFs) and their evolutionary divergences. Although permutation P-values can quantify the significance of CIF divergences between two taxa, their naive Monte Carlo approximation is slow and inaccurate. The Peaks-over-Threshold approach of Knijnenburg et al. (2009) promises improvements to both speed and accuracy of permutation P-values, but has no publicly available API. We present tRNA Structure-Function Mapper (tSFM) v1.0, an open-source, multi-threaded application that efficiently computes, visualizes and assesses significance of single- and paired-site CIFs and their evolutionary divergences for any RNA, protein, gene or genomic element sequence family. Multiple estimators of permutation P-values for CIF evolutionary divergences are provided along with confidence intervals. tSFM is implemented in Python 3 with compiled C extensions and is freely available through GitHub (https://github.com/tlawrence3/tSFM) and PyPI. The data underlying this article are available on GitHub at https://github.com/tlawrence3/tSFM. Supplementary data are available at Bioinformatics online.

Log-concavity of the excedance enumerators in positive elements of Type A and Type B Coxeter Groups

The classical Eulerian Numbers An,k are known to be log-concave. Let Pn,k and Qn,k be the number of even and odd permutations with k excedances. In this paper, we show that Pn,k and Qn,k are log-concave. For this, we introduce the notion of strong synchronisation and ratio-alternating which are motivated by the notion of synchronisation and ratio-dominance, introduced by Gross, Mansour, Tucker and Wang in 2014.We show similar results for Type B Coxeter Groups. We finish with some conjectures to emphasise the following: though strong synchronisation is stronger than log-concavity, many pairs of interesting combinatorial families of sequences seem to satisfy this property.

Zero-TE MRI: Potential Applications in the Oral Cavity and Oropharynx.

Zero-echo time (ZTE) magnetic resonance imaging (MRI) is the newest in a family of MRI pulse sequences that involve ultrafast sequence readouts, permitting visualization of short-T2 tissues such as cortical bone. Inherent sequence properties enable rapid, high-resolution, quiet, and artifact-resistant imaging. ZTE can be performed as part of a "one-stop-shop" MRI examination for comprehensive evaluation of head and neck pathology. As a potential alternative to computed tomography for bone imaging, this approach could help reduce patient exposure to ionizing radiation and improve radiology resource utilization. Because ZTE is not yet widely used clinically, it is important to understand the technical limitations and pitfalls for diagnosis. Imaging cases are presented to demonstrate potential applications of ZTE for imaging of oral cavity, oropharynx, and jaw anatomy and pathology in adult and pediatric patients. Emerging studies indicate promise for future clinical implementation based on synthetic computed tomography image generation, 3D printing, and interventional applications.